Brian beckers msc thesis vanderlande

Eindhoven, May 2018

Moving towards proactive services How can Vanderlande exploit usage-based maintenance in its maintenance and spare parts department?

B.R.W. (Brian) Beckers

BSc Industrial Engineering and Management Sciences – TU/e 2015 Student identity number 0803649

In partial fulfilment of the requirements for the degree of Master of Science in Operation Management and Logistics

Supervisors: dr. ir. R.J.I. Basten, TU/e, OPAC dr. A.S. Eruguz – Çolak, TU/e, OPAC dr. ir. S.D.P. Flapper, TU/e, OPAC ir. J. van Montfort, Vanderlande Industries B.V.

TUE. School of Industrial Engineering.

Series Master Thesis Operations Management and Logistics

Subject headings: Advance demand information, Data availability, Single component usage based maintenance, Single-location multi-item spare parts inventory control, Two demand streams

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ABSTRACT After-sales services represent an important source of profit that evolves into the desire to better manage services like maintenance and spare parts supply. This is also the case at Vanderlande. This research investigates how usage-based maintenance (UBM) can be applied at Vanderlande and how it can be beneficial for their service as well as for their spare parts department. The connection between UBM and spare parts supply is made via advance demand information (ADI), which is defined as customer orders that are available prior to their materialization. We first investigate the availability of failure and usage data from different data sets. After selecting the best data sets, we define a single-item UBM policy and conclude that the value of UBM is not only dependent on the component, but also on the customer site. Next, we define a multi-item, single-location inventory model with emergency shipments.

We show that the number of parts on stock decreases with on average 50% for considered components while reaching the required service level when we apply this inventory model. Last, we develop an ADI policy, which serves the two demand streams, one for corrective maintenance (CM) and one for preventive maintenance (PM). The PM stock is controlled by ordering the part in a just-in-time strategy and the CM stock by the developed inventory control model.This ADI policy prioritizes the CM demand stream as it check if PM stock is needed for CM demand before allocating the PM stock to a PM action.

Numerical experiments show that the ADI policy outperforms the non-ADI policy. Furthermore, it turns out that, compared to an ADI policy that uses UBM, a failure based policy might be beneficial when we loosen the assumption of always having a spare part on stock if maintenance is needed. Finally, we find that having a lower variation in the lifetime distribution of the components results into more savings of the non-ADI policy compared to the non-UBM policy and the ADI-policies over the non-ADI policy.

III

EXECUTIVE SUMMARY This research is conducted at Vanderlande Industries B.V. (Vanderlande) in Veghel. Vanderlande is the global market leader for value-added process automation at airports and in the parcel market.

Problem definition The objective of the global services department of Vanderlande is to become an integrated solution provider. The solution means that the system and the service are provided together, i.e. the service is not optional. To become an integrated solution provider, Vanderlande needs to change the business model of certain departments and improve their services by becoming more proactive. Previous work indicate that condition based maintenance is not the best policy for all components of Vanderlande (Alcorta, 2017). Therefore, we investigate the feasibility and the value of usage based maintenance (UBM). Furthermore, the spare parts department requires an adapted business model to shift from selling spare parts to being part of the integrated solution. The spare parts department is at the very start of this change and is looking for the best business model to support the new strategy. Spare parts and maintenance are closely related to each other as maintenance actions often generate spare parts demand. With a preventive maintenance (PM) policy, like a UBM policy, more information about when to do maintenance, and thus when spare parts are needed, becomes available. The information from UBM could be used as advance demand information (ADI) to optimise spare parts inventory decisions.

Combining these goals leads to the following main research question: How can UBM be applied as preventive maintenance strategy and how can the information resulting from the UBM policy be used in the spare parts inventory control?

Research To answer this research question, we focus on the POSISORTER (SPO), which is a piece of equipment in a Vanderlande system in the parcel and postal market, and deal with four challenges.

The combination of failure data of components and usage data of sites is very hard to gather The first challenge concerns the data availability. To be able to apply UBM, we need information on failures and the usage of components. We first investigate the availability of the data at Vanderlande and then we access the quality of this data. We investigate several possible datasets but find that there is no failure data available on component level. The main problem is that it is hard to match the data to a specific component failure. Therefore, we use spare part sales data to approximate the failure rates of the components, based on some requirements and assumptions. Furthermore, usage data is very hard to get at Vanderlande, especially data covering the complete lifetime of a system. Eventually, we got data for some systems over a few months and extrapolated this to its complete lifetime. The main conclusion is that the combination of failure data for components and usage data for sites is very hard to gather. A list of components is made for which enough data was available and for these components we determine whether UBM is a suitable policy using the maintenance policy selection (MPS) model of Alcorta (2017). We conclude that the timing belt in the entry of the SPO is the only component for which enough data is available and UBM is a suitable strategy. Because we only have usage data about throughput and running hours and based on an interview with a SPO expert, we conclude that, at this moment, running hours of the system is the best usage measurement to indicate a failure of the timing belt.

IV

UBM can save up to at least 16% in costs compared to a failure-based policy. However, the value of UBM is not only dependent on the component but also on the customer site.

Secondly, we investigate how UBM can be implemented at Vanderlande. We define a single-item UBM policy that finds the optimal moment to replace a component based on the costs for preventive maintenance (PM) and corrective maintenance (CM) and the lifetime distribution of the component.

This policy is applied to the selected component and we compare the UBM policy to the current maintenance policy to show the possible benefits of UBM for Vanderlande. We perform a scenario analyses that takes a small, medium, and large SPO site into account. We find that, compared to a failurebased policy, the UBM policy for the timing belt can save 16%, 13% and 0% in expected cost for the small, medium and large SPO site scenario, respectively. We thus show that the value of UBM is not only dependent on the component but also on the customer site.

A basic spare parts inventory control model without ADI already saves in parts at stock Thirdly, we develop a multi-item, single-location inventory model with emergency shipments that can be used for the most downstream warehouse: a quick response stock (QRS). Currently, Vanderlande does not have a spare parts inventory control model in place, since these parts are stored and managed by the customers. When Vanderlande moves to selling spare parts as a service, it needs to take responsibility for the spare part inventory control and to setup a control model. The developed model aims to find the optimal number of items to put on stock at a QRS to minimise expected costs and meet the aggregate mean waiting time objective. Using this model for three different items and for 152 SPO sites in Europe, we see that the number of the parts on stock decreases with 50%.

The ADI policies outperform the non-ADI policy in all tested Lastly, we investigate how information from the UBM policy can be used as ADI in the spare parts inventory control model. We develop an ADI-policy for the QRS and compare this policy with a non-ADI policy, where the service and spare parts department do not work together by ADI, to show the possible benefits of ADI. The ADI policy serves the demand for CM from an inventory pool controlled by a base stock policy and demand for PM is served by an inventory pool controlled by ordering the amount of parts that have passed a set advanced order threshold. This ADI policy prioritizes the CM demand stream as it serves this demand before allocating the PM stock to a PM action. Numerical experiments indicate that the ADI policy outperforms to the non-ADI policy in all scenarios. We conclude that the cost savings are increasing in the demand rate and lead time and decreasing in price. Furthermore, we compare the ADI policy with the non-UBM policy. We conclude that a failure based policy might be beneficial when we loosen the assumption of always having a spare part on stock if maintenance is needed. Third, we find that having a lower variation in the lifetime distribution of the components results into 25% more savings of the non-ADI policy compared to the non-UBM policy and up to 3% savings of the ADI-policies over the non-ADI policy. Last, we find that having the incorrect data reduces the savings of the ADI policies over the non-ADI. Furthermore, lower costs can be achieved when we have a higher PM threshold and stock levels than the individual policies indicate as optimal.

Recommendations Collect data on the lifetime of components and the usage of the systems We recommend that the service engineers keep track of their maintenance actions in more detail. When all maintenance engineers record exactly which components have been replaced, the MTTFs can be easily subtracted. As a service engineer already receives a work order with the parts he needs to inspect, V

it is not much extra effort to also store when he replaces a part and match this to a specific component.

Second, it is recommended that Vanderlande stores usage data regularly. This can be done by using for example the Flow System Controller (FSC). A program should be developed which makes sure that the FSC writes this information to an overall database like VIDI. This program can be developed by R&D on initiative from the service department who should be the problem owner. As basic solution, the maintenance engineers can report the running hours of the system, which are recorded via a time counter, during an inspection.

Implement UBM maintenance for the right components It is advised that Vanderlande optimizes the maintenance strategy per component. When using a MPS model, more components are identified for which UBM is a suitable strategy. It is recommended that Vandelande uses the developed UBM policy for these components. This extra PM service is a good addition to the current service proposition of Vanderlande as it improves the uptime of the systems and decreases maintenance costs. It is recommended optimising the PM threshold further, as more information on the lifetime of components and insights in downtime costs becomes available.

When providing spare parts as a service, use the basic spare parts inventory control model for the QRS which does not include ADI When providing spare parts as a service, it is advised to move to a multi-echelon inventory model and we recommend using (a version of) the developed spare parts inventory control for the QRS’s as this results into less spare parts downstream the supply chain due to a pooling effect. Before moving to spare parts as a service, it is advised to investigate what time a customer wants to wait for a component and consider the work of van den Bosch (2017) to decide where to stock which spare parts.

When a spare parts inventory control model and predictive maintenance policies are in place, investigate the possible savings of an ADI policy at Vanderlande We recommend that Vanderlande considers ADI policies when a spare parts inventory control model and PM policies are in place. This is because we found that ADI policies outperform a way of working where the UBM policy and spare parts inventory control model are used without departments exchange information, i.e. a non-ADI policy. At this moment there is a lack of data on the lifetime of a component at Vandelande. Therefore we recommend a more specific case study, as we see that UBM combined with spare parts inventory control may not be suitable when the variation of the lifetime distribution is high. Next to that, we recommend that the business case about the use of ADI takes the shared information between the cooperating departments into account. Because different departments are incorporated, information exchange and responsibilities need to be defined. To use ADI, Vanderlande needs to monitor the usage of a system, their systems should facilitate this data exchange Academic relevance Our first scientific contribution is that we use a broad view where we define a UBM policy and a spare parts inventory model in a way for them to be combined into an ADI policy. Secondly, UBM policies, spare parts inventory models, and ADI models are topics that are considered in literature but are, to the author his best knowledge, never developed together in the same research. Next to that, we developed a new ADI policy for controlling inventory at a QRS. This policy is based on Coumans (2017) and Basten and Ryan (2015), but our policy prioritizes CM demand and considers stochastic aging of the components. Thirdly, the developed models are tested in the company environment of Vanderlande which closes the gap between theory and practice.

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PREFACE This report is the result of a research project that I conducted in partial fulfilment of the requirements of the degree of Master of Science in Operations Management and Logistics at Eindhoven University of Technology. This research is conducted at global services department of Vanderlande Industries B.V in Veghel, The Netherlands.

I would not have been able to conduct this research without the support and guidance of a couple of people. First, I would like to thank my first supervisor of the university, Rob Basten. Rob and I had regular meeting about once every two weeks where we discussed the progress and the encountered problems.

Rob, I always enjoyed our meetings and discussions and I really appreciated your support, guidance and valuable insights. Thank you for the time you put into supervising me, by always keeping me sharp with a critical look. Without your guidance, this project have the same quality as it has now. Second, I would like to thank Sena Eruguz – Çolak for being my second supervisor. Although, we did not meet that many times, I would like the thank you for the time you put into reading my report and providing me with feedback.

Next, there are a lot of people who helped me at Vanderlande in conducting this thesis. First, I would like to thank my company supervisor Joost van Montfort. I want to thank you for the way you supervised me. You always made time to answer my question and were always interested in the progress and encountered problems. Second, I want to thank Frank van Schijndel for being my supervisor for the spare parts related part of this project. I was always able to walk into your office whenever I had a question and you always made time to answer them. Next, I would like Marco Vijfvinkel for providing the opportunity to conduct this project at Vanderlande. Last, I would like to thank all the people from the department who were located in the office for the pleasant and enjoyable working environment. I enjoyed our talks and lunch breaks and I always felt like going to the office.

Last, I would like to thank the friend I made during my study and from my home town for providing enough opportunities to relax between working on this project. Special thanks goes to Zoë, who always listened to my stories about my work and my project. Your we always the listening ear I needed. Next to that, thank you for reading my thesis and checking my English. Finally, I would like my parents for making it possible for me to go to a university and always supporting me a 100%.

Brian Beckers May 2018, Veghel

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Table of Content LIST OF ABBRIVIATIONS ...................................................................................................... XI LIST OF VARIABLES ............................................................................................................ XII INTRODUCTION .......................................................................................................... 1 1.1.

Brief literature review ........................................................................................................... 1

1.2.

Thesis environment ............................................................................................................... 2

1.3.

Service proposition and policies ............................................................................................. 4

1.4.

Available tools....................................................................................................................... 5

1.5.

Thesis outline ........................................................................................................................ 5

RESEARCH DESIGN ...................................................................................................... 6 2.1.

Previous research at Vanderlande .......................................................................................... 6

2.2.

Problem statement................................................................................................................ 6

2.3.

Research questions................................................................................................................ 7

2.4.

Scope .................................................................................................................................... 9

2.5.

Deliverables .......................................................................................................................... 9

DATA COLLECTION .................................................................................................... 10 3.1.

Equipment selection ............................................................................................................ 10

3.2.

Failure data ......................................................................................................................... 11

3.3.

Is UBM a good strategy for the remaining components? ....................................................... 14

3.4.

Usage data .......................................................................................................................... 15

3.5.

Conclusions ......................................................................................................................... 18

USAGE BASED MAINTENANCE ................................................................................... 19 4.1.

UBM policy: single-component age based maintenance policy.............................................. 19

4.2.

Using the data and determining cost equations .................................................................... 20

4.3.

Case study: optimal UBM policy ........................................................................................... 23

4.4.

Conclusions ......................................................................................................................... 25

INVENTORY CONTROL MODEL .................................................................................. 26 5.1.

Multi-item, single-location inventory model with emergency shipments ............................... 26

5.2.

Greedy algorithm ................................................................................................................ 29

5.3.

Results ................................................................................................................................ 30

5.4.

Conclusion .......................................................................................................................... 32 VIII

INVENTORY CONTROL MODEL WITH ADI FROM THE UBM POLICY ............................. 33 6.1.

PMAO and PMAO-extension policy ...................................................................................... 33

6.2.

PMAO-CM-priority policy ..................................................................................................... 34

6.3.

Comparison to other literature ............................................................................................ 39

6.4.

Conclusion .......................................................................................................................... 39

NUMERICAL EXPERIMENTS ....................................................................................... 40 7.1.

Policies without ADI ............................................................................................................ 40

7.2.

Input values for the numerical experiments ......................................................................... 40

7.3.

Results of the numerical experiments .................................................................................. 42

7.4.

Conclusion .......................................................................................................................... 46

CONCLUSIONS, RECOMMENDATIONS AND FUTURE RESEARCH.................................. 47 8.1.

Conclusions ......................................................................................................................... 47

8.2.

Recommendations............................................................................................................... 48

8.3.

Critical assumptions, limitations and future research............................................................ 50

REFERENCES ...................................................................................................................... 51 APPENDIX A – OTHER CONSIDERED DATA SETS FOR FAILURE DATA .................................... 54 APPENDIX B– PRODUCT SPECIFICATIONS FOR COMBINED DATA POINTS ............................ 56 APPENDIX C – NUMBER OF DATA POINTS PER ITEM NUMBER PER CONSIDERED GROUP .... 62 APPENDIX D – MPS-MODEL BY ALCORTA (2017)................................................................. 63 APPENDIX E – COMPONENT CRITICALITY BY VAN DEN BOSCH (2017) ................................. 65 APPENDIX F – AVAILABLE DATA POINTS ............................................................................. 67 APPENDIX G – WAYS TO DESIGN AN FUTURE MAINTENANCE PROGRAM ............................ 69 APPENDIX H – SHORT OVERVIEW OF RENEWAL REWARD THEORY ..................................... 71 APPENDIX I – THE WEIBULL DISTRIBUTION......................................................................... 73 APPENDIX J – CONVEXITY OF THE AVERAGE COST PER TIME UNIT ...................................... 74 APPENDIX K – EXPLANATION INPUT VALUES FOR THE UBM POLICY.................................... 77 APPENDIX L - CUSTOMERS CONSIDERED FOR INVENTORY CONTROL .................................. 78 IX

APPENDIX M – SEQUENCE OF EVENTS PMAO POLICY AND PMAO-EXTENSION POLICY ........ 82 APPENDIX N – DIFFERENT SPARE PARTS IN THE NUMERICAL EXPERIMENTS........................ 83 APPENDIX O – DIFFERENT NUMERICAL EXPERIMENTS ........................................................ 84 APPENDIX P – DETERMINATION OF INPUT VALUES FOR ADI POLICIES................................. 86 APPENDIX Q – OUTCOME STATISTICS OF THE NUMERICAL EXPERIMENTS ........................... 87

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LIST OF ABBRIVIATIONS ADI AIC BPI CBM CFR CM CV DFR ECC ECL HDS IB IFR KM mm MPS MTTF MTTR PLC PM PMAO ProSeLoNext QRS R&D RMR RQ Scada SKU SLA SPO TICO TU/e UBM Vanderlande VIDI V-sale X-sale Y-sale

Advance demand information Akaike Information Criterion Business process information Condition based maintenance Constant failure rate Corrective maintenance Coefficient of variance Decreasing failure rate Expected cycle cost Expected cycle length High dynamic storage Installed base Increasing failure rate Kilometre Millimetre Maintenance policy selection Mean time to failure Mean time to repair Programmable logic controller Preventive maintenance Preventive maintenance advance order Proactive service logistics for capital goods: the next steps Quick response stock Research and development Revisions, modifications and retrofits Research question Supervisory control and data acquisition Stock keeping unit Service level agreement POSISORTER Toyota industries corporation Eindhoven University of Technology Usage based maintenance Vanderlande Industries B.V. Vanderlande Industries data intelligence Spare parts sale, sold in a spare parts package Spare parts sale, sold as replenishment Spare parts sale, sold for corrective maintenance

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LIST OF VARIABLES Fitting a distribution Îą Scale parameter β Shape parameter MTTFUsage Mean time to failure in terms of usage MTTFDays Mean time to failure in terms of days Dweek Number of days the site is operational per week U Best usage measurement to indicate a failure of the component in usage per day UBM policy Cip Ciu Ď„ đ??šđ?‘‡ (đ?œ?)

Preventive maintenance cost for component i Corrective maintenance cost for component i Preventive replacement threshold The distribution function of a random variable T, đ??šđ?‘‡ (đ?œ?) = P(T≤ đ?œ?)

đ?‘“đ?‘‡ (đ?œ?) The density function of a random variable T, đ?‘‘đ??š (đ?‘Ą)

g(Ď„) Cisparepart WMaintenance tireplacement ttravel CiDT CiOT CiET Bi Ri

Cap q WOperational Shi ExtraTruck c Av Th nSPO WIParcel WIMaxTruck nKM WKM

� we assume �� (�)= �� Average cost per time unit, which depend on τ Cost for the spare part i Hourly wages of a maintenance engineer Time needed to replace component i Time needed to travel to the customer for maintenance The down time cost for SKU i The cost made due to extra hours of work to finish all orders when SKU i fails The cost for the extra truck that must be arrange unexpectedly when SKU i fails The average number of handling units that arrive to late due to failure of component type i Number of parts that should be to late when component i fails but the system can make up for due to redundancy The maximum capacity of the system Number of employees The hourly wages of the operational employees The duration of a shift The fixed price paid for an extra truck per too late handling unit The availability of the system Throughput of the system Number of SPOs running in parallel The average weight of a parcel Maximum weight allowed in a truck Number of KM the truck needs to drive Amount of ₏ that needs to be paid per KM

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Inventory control policy I J mij mi nij M Si S Li ttravel tem

Cih Cjem Ci(Si) C(S) Cie βi(Si) Wi(Si) W(S) Wobj

Set of SKU’s Set of customers Demand for SKU i at customer j Demand for SKU i at the QRS Number of times SKU i is in the system of customer j Total demand rate for all SKU’s at the QRS Base stock level for SKU i the vector consisting of all base stock levels, S = (S1, ‌ , SI) Time needed to replenish SKU i at the QRS Time needed to send a SKU from the QRS to the customer Time needed to send an SKU from the central warehouse to the customer via and emergency shipment Cost for holding one SKU of type i at the QRS Cost for sending an emergency shipment to customer j Total cost for SKU i at the QRS Total cost for the QRS for all SKU’s Weighted average cost the QRS faces for an emergency shipment for SKU i Fill rate for SKU i Mean waiting time for SKU i Aggregated mean waiting time Target aggregated mean waiting time

PMAO-CM-priority policy All variable from Inventory control policy See above T Set of time periods CM đ??ˇđ?‘–đ?‘— (đ?‘Ą) Corrective demand for number n of SKU i of customer j at time t PM đ??ˇđ?‘–đ?‘— (đ?‘Ą) Preventive demand for number n of SKU i of customer j at time t đ?‘&#x;đ?‘–đ?‘—đ?‘› (đ?‘Ą) Realized aging rate at period t for number n of SKU i of customer j đ?œ‡đ?‘–đ?‘—đ?‘› Mean aging for number n of SKU i of customer j (normal distribution) đ?œŽđ?‘–đ?‘—đ?‘› Standard deviation for number n of SKU i of customer j (normal distribution) đ??´đ?‘–đ?‘—đ?‘› (đ?‘Ą) Age of number n of SKU i of customer j at time t đ?‘‡đ?‘–đ?‘—đ?‘› Advance order threshold for number n of SKU i of customer j Ď„ij Preventive replacement threshold for SKU i for customer j βPM Preventive maintenance fill rate đ?‘Žđ?‘– (đ?‘Ą) Number of advance order alarms for SKU i at time t XIII

đ?‘‚đ??ťđ?‘–CM (đ?‘Ą) Number of parts for CM demand of SKU i physically on hand at the end of period t CM đ??źđ?‘‡đ?‘– (đ?‘Ą) Number of parts for CM demand SKU i that are intransit, ordered but not yet received, to the QRS at the moment of ordering in period t PM đ?‘‚đ??ťđ?‘– (đ?‘Ą) Number of parts for PM demand of SKU i physically on hand at the end of period t PM đ??źđ?‘ đ?‘– (đ?‘Ą) Net inventory for PM demand of SKU đ?‘– at the end of period đ?‘Ą đ?‘ƒđ?‘€ Ě‚ đ?‘‚đ??ťđ?‘– (đ?‘Ą) PM parts of SKU i actually available for PM demand in period t PM Number of parts for PM demand SKU i that are (đ?‘Ą) đ??źđ?‘‡đ?‘– in-transit, ordered but not yet received, to the QRS at the moment of ordering in period t em (đ?‘Ą) đ?‘ đ?‘– Number of emergency shipment for SKU i in period t PM Number of backorders of SKU i at the end of (đ?‘Ą) đ??ľđ?‘‚đ?‘– period t đ?‘ƒđ?‘€đ??ˇđ?‘’đ?‘™đ?‘Žđ?‘Śđ?‘– (đ?‘Ą) Number of PM delays for SKU i in period t đ?‘ƒđ?‘€đ?‘– (đ?‘Ą) Number of PM replacements for SKU i in period t đ??ś PMDelay Cost for a PM delay đ??śđ?‘–P Cost for a PM action of SKU i đ??śđ?‘–U Cost for a CM action of SKU i đ??śđ?‘– (đ?‘Ą) Total cost for SKU i in the period t TCQRS Total cost for the QRS

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INTRODUCTION This master thesis is the result of a graduation project conducted at Vanderlande Industries B.V. (Vanderlande) to obtain a master’s degree in Operations Management & Logistics at Eindhoven University of Technology (TU/e). Vanderlande is the global market leader for value-added logistic process automation at airports, warehouses, and the postal and parcel market (Vanderlande, 2017).

“During last decades, firms have recognized that after sales services represent an important source of profit” (Frazzon, Israel, Albrecht, Pereira, & Hellingrath, 2014, p. 148). For Vanderlande, this evolves into the desire to better manage the after sales services as maintenance and spare parts. Vanderlande’s customers are very dependent on the uptime of its systems and therefore, Vanderlande delivers services to guarantee this uptime. It is important for Vanderlande to know the optimal moments to do maintenance and make sure that the right people and equipment is available at the right time. This research elaborates on how usage-based maintenance (UBM) can be applied and how this can be beneficial for the service department and the spare parts department.

This chapter is structured as follows. In Section 1.1, a brief literature review about maintenance strategies and advance demand information (ADI) is given. In Section 1.2, we discuss the thesis environment. In Section 1.3, we discuss Vanderlande’s current way of working and in Section 1.4, we elaborate on the available tools. In Section 1.5, We outline the remainder of the report.

1.1.

Brief literature review

In this section, we give a brief literature review about maintenance strategies and advance demand information (ADI) to give the reader a basic idea about these topics. For more information about these two topics we refer to the literature review of Beckers (2018).

1.1.1.

Maintenance strategies

A commonly used classification of maintenance strategies is proposed by Arts (2017), which classifies the maintenance strategies in modificative, preventive, and breakdown corrective maintenance. An overview of his classification is shown in Figure 1. Arts (2017) defines a maintenance strategy as a strategy to determine when the maintenance or the replacement of a component needs to take place.

He mentions, “which types of maintenance are prevalent for a given component depends very much on the technical nature of the equipment involved” (Arts, 2017, p.9), so not all strategies fit all components.

First, there is modificative maintenance. Modificative maintenance is replacing a component with a technically more advanced component to make the product perform better. At Vanderlande, these actions are part of the RMR-projects (revisions, modifications and retrofits). Next to modificative maintenance, there is breakdown corrective maintenance (CM) and preventive maintenance (PM).

When a component follows a CM strategy, the component is not being maintained or replaced before it has failed. This can be a good strategy for components that do not wear. For PM, Arts mentions, it is the aim to replace the components before the failure occurs, which is not always the case. PM can be split into usage based maintenance (UBM) and condition based maintenance (CBM). When a UBM strategy is applied, the total usage of a component is measured and maintenance is performed when a certain threshold is reached. UBM can be performed per component (component replacement and/or 1

overhaul). However, when the set-up cost associated to maintenance are very high, it can be beneficial to replace multiple components at the same time (block replacement and/or overhaul). The other form of preventive maintenance is CBM. In CBM, the condition of a component is monitored or checked and the maintenance plan is based on that condition. The condition of a component can be measured periodically or continuously, for example by a sensor. When applying UBM or CBM, notice that the usage or conditions that need to be measured are different depending on the considered component.

Maintenance strategies

Modificative maintenance

Preventive maintenance

Usage based maintenance

Component replacement and/or overhaul

Breakdown corrective maintenance

Condition based maintenance

Block replacement and/or overhaul

Condition monitoring

Periodic inspections

Figure 1: Maintenance strategies (Arts, 2017)

1.1.2.

Advance demand information

Due to developments in information technology, it has become easier and cheaper to collect information on the quantity and timing of demand, for example for spare parts, before this demand occurs. This information is called advance demand information (ADI). There exist various definitions of ADI, but we use the following definition: “Customer orders that are available prior to their materialization” (Tan, Güllü, & Erkip, 2007). Nowadays, every company wants to make sure that their systems are up and running and try to predict the failures of critical components. Topan et al. (2016) mention that since these (predicted) failures result in demands for spare parts, we can use these predictions as ADI to optimise the spare parts inventory control.

One of the first papers on the use of ADI in inventory control is the paper of Hariharan and Zipkin (1995).

They conclude that “demand lead times improve performance, in precisely the same way that replenishment lead times degrade it” (Hariharan & Zipkin, 1995). In this statement, demand lead time refers to the time between a customer order and the due date of that order (i.e. the ADI). Note that ADI can be perfect as well as imperfect. In perfect ADI, the exact information about the future orders is known, while in imperfect ADI there is only an estimate about the future demand (Benjaafar, Cooper, & Mardan, 2011). The more perfect the ADI, the higher the cost savings can be (Topan et al., 2016). The ADI at Vanderlande is imperfect since the information about UBM gives us an estimate of failure instead of a certainty, since the demand could occur earlier than indicated, i.e. a failure occurs.

1.2.

Thesis environment

Vanderlande was founded by Eddie van der Lande in Veghel (the Netherlands) in 1949. The company initially refurbished and later produced machines for the textile industry. Later they moved into the manufacturing of hoisting apparatus, cranes and conveyor belts for bulky materials and barrels of oil. In 1963, it began to develop and build customised transport systems and in 2017, Vanderlande was 2

acquired by Toyota Industries Corporation (TICO). TICO’s financial strength helps Vanderlande to continue its sustainable profitable growth (Vanderlande, 2017b). The research is conducted at the global services department, which is primarily responsible for life-cycle services. More specific, this research is conducted within the data science and service innovation team. Currently, this team is responsible for all activities involved in the acquisition and processing of large amounts of data to be used for further professionalising the products and services of Vanderlande.

The research is part of a project on proactive service logistics for capital goods, called ProSeLoNext, worked on by a consortium comprising four universities and nine companies, including both the TU/e and Vanderlande. ProSeLoNext comprises three work packages: predictive maintenance and service logistics, service business models and service control towers. The proposed research is part of the first work package, which focuses on applying previously developed models for timely maintenance and efficient service logistics, and using the results to improve the models (NWO, 2017).

1.2.1.

Company background

Vanderlande focusses on “the optimisation of its customers’ business processes and competitive positions” (Vanderlande, 2017, p.3). Vanderlande had a revenue of 1.1 billion euros in 2016 and has more than 5000 employees worldwide (Vanderlande, 2017). It has established a global reputation as a highly reliable partner for value-added logistic process automation, by working closely together with its customers to improve operations and logistics performance throughout the entire life cycle. The headquarter is still located in Veghel and Vanderlande is carrying out 260 projects in 105 countries.

Vanderlande operates in four main market segments: airports, warehousing, parcel, and life-cycle services. For these market segments, Vanderlande has an extensive portfolio of logistics process automation solutions, which are innovative systems, intelligent software (both for the airports, warehousing and parcel segment), and life-cycle services (for the life-cycle services segment). This research focuses on the life-cycle services and the parcel segment. These two market segments are briefly discussed below based on information from the annual report of 2016 (Vanderlande, 2017). First, this research is expected to contribute to the life-cycle services activities of Vanderlande. Life-cycle services has grown significantly in recent years and now accounts for about 20% of Vanderlande’s total turnover (Peijnenburg, 2016). The life-cycle services segment is concerned with the delivery of services to the customer’s installed base (IB). Examples of services are inspections, maintenance actions, spare parts supply, and life-cycle planning. Vanderlande has more than 100 service teams based at customer’s sites spread over the entire world. Second, we take into account equipment pieces that are used in the parcel segment. The parcel segment refers to the business unit involved in delivering solutions to parcel and postal companies all over the world. The world’s leading parcel companies, like UPS, TNT, DHL, and FedEx work with Vanderlande systems, which sort more than 20 million parcels on a daily basis.

1.2.2.

Vanderlande’s systems

The solutions that Vanderlande delivers to its customers can be viewed from different levels of detail.

The complete solution for the customer is called the system. A system consists of different sub-systems, which are referred to as an area. An area is a group of products of Vanderlande together, for example a sorter with some conveyer belts. These products are called equipment. The equipment itself consists of components, such as motors and bearings. An example of the hierarchical structure is given in Figure 2.

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Vanderlande follows an engineering-to-order approach. This means that all Vanderlande systems are custom made and thus no two systems are the same. However, the pieces of equipment are build up in the same way and consist out of the same components (not considering updates or special requirements). Because of this, we focus on the component level in this research. The products of Vanderlande are highly expensive capital goods. Therefore, the industry is characterised by high expectations from customers on, for example, availability. Customers want the cost associated with the service of the solutions to be as low as possible, since great investment is made for the acquisition.

Equipment

Area

System

Area

Component

Component

Equipment

Component

Equipment

Component

Figure 2: Hierarchical structure of Vanderlande’s systems (Alcorta, 2017)

1.3.

Service proposition and policies

Vanderlande uses a service proposition to sell its services and has three levels of partnerships: asset services, logistics services, and business services. The service scope and responsibilities towards the customers increase from asset services to business services. Based on the customer’s requirements a partnership is offered and hopefully the customer accepts it. This research focuses on the prevent and spare parts services that are part of the asset services partnership.

1.3.1.

Current maintenance strategy

Vanderlande mostly performs CM. This means that when a component breaks down, it is replaced during a scheduled down, in case the component is not critical, or during an unscheduled down, in case the component is critical. Next to that, Vanderlande performs inspections. During inspections, a maintenance engineer inspects if the component can last until the next inspection. However, no formal rejection criteria are defined. Thus, the decision to replace a component during an inspection is mostly based on the experiences of the maintenance engineer who performs the inspection. In few cases, UBM is used as maintenance strategy but this is mostly on the own initiative of the site based teams. They use their own expertise, which means that there is no standard and documented way of working. Note that not all customers are obligated to use Vanderlande’s maintenance service. Some customers prefer to do the maintenance themselves or hire other companies. However, Vanderlande always provides a maintenance manual per equipment. In this maintenance manual, Vanderlande advices on how to maintain a component. These manuals are made by research & development (R&D) and are mostly based on endurance testing and information from third party suppliers. Although these manuals propose inspection periods and what to inspect, they do mostly not mention clear rejection criteria.

1.3.2.

Current spare parts strategy

Vanderlande sells spare parts to keep the customer’s systems up and running. Currently, when a system is delivered to the customer, Vanderlande recommends certain spare parts in the form of a spare parts package. The content of the package is determined by looking at the number of times a spare part occurs 4

in a system and multiply it by a, by R&D set, percentage. This number is then compared with a predetermined minimum and maximum and the final content of the spare parts package is determined.

In most cases, the customer follows this recommendation and this spare parts package is then stocked and owned by the customer. However, sometimes the spare parts packages are adjusted based on the wishes of the customer. If the customer wants to spend initially less money on spare parts, some of the parts are cut from the package. This is not done based on a specific rule, but is based upon experience of what parts are most important. After delivering the spare parts, the customer takes ownership of the parts and Vanderlande is not involved until the customer needs new or other spare parts. When additional parts are needed, the customer can choose to order at Vanderlande or, when it is a standard part, at another supplier.

1.4.

Available tools

In this section, we discuss the different available tools that can be used to gather data from. The first tool is Maximo, which is used for enterprise asset management. Inhere, work orders are prepared for CM and for PM. The work orders include the required spare parts and human resources. Second, JDEdwards is the enterprise resource planning tool of Vanderlande. This tool “manages all transactions with financial consequences and is used for the administration of Vanderlande” (van der Heijden, 2017).

JDEdwards is used by the spare parts department as it enters the replenishment or acquisition orders of spare parts in this tool. Third, Vanderlande has SmarTeam, which is a product lifecycle management system. It is Vanderlande’s system for technical drawings, functional product and system data and document management. In SmarTeam, the complete IB of a customer can be found. These three discussed tools are corporate IT systems while the following tools are customer onsite IT systems.

Fourth, Vanderlande uses Scada (Supervisory Control and Data Acquisition), which is a “computer software that visualizes the status of a, and controls the, (part of a) system” (van Asseldonk, 2017). Scada uses real-time data about the availability of the system and the operator makes use of this information to control the system. Scada also reports all of the operational errors. Another onsite IT system is the performance management tool called BPI (Business Process Information). “BPI is software for gathering, storing and analysing data and providing information to help users make better decisions” (Schwering, 2017). It is also used to provide performance reports to the customers based on different data sources.

The successor of BPI is called VIDI (Vanderlande Industries Data Intelligence). This is the big data platform of Vanderlande. It uses data from different sources and dashboards, which can be used for continuous optimisation and improvements of the customers’ business. With VIDI, Vanderlande moves reporting and analysis from a local BPI solution to a central solution that is accessible from the customer’s site and from the headquarters in Veghel.

1.5.

Thesis outline

The remainder of this thesis is structured as follows: in Chapter 2, the research design with the problem statement and research questions is discussed. In Chapter 3, we discuss the data collection and decide which data set and components to use in this research. Chapter 4 focusses on the development of a UBM strategy and Chapter 5 discusses the inventory control model for Vanderlande without the use of ADI. In Chapter 6, we present policies that takes the ADI from the UBM strategy into account in an inventory control model and in Chapter 7 we compare the ADI policies with a policy without ADI and a policy without UBM. In Chapter 8, we end with the conclusions and recommendations.

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RESEARCH DESIGN In this chapter, we first discuss some previous research conducted at Vanderlande in Section 2.1 and state the problem in Section 2.2. After that, we formulate the research questions in Section 2.3, the scope of this research in Section 2.4 and we end with the deliverables in Section 2.5.

2.1.

Previous research at Vanderlande

Already research is done about how Vanderlande can move to a more proactive way of providing service.

First, van Schijndel (2016) investigates how the services of Vanderlande’s spare parts department needs to be in 2020. For this, he focusses on the current way of working at Vanderlande and then compares it with how other mayor companies are taking care of their spare parts services. He finds that all these companies use a service-level-agreement (SLA), have multi-echelon warehousing systems and understand the importance of easy and real-time access to data. He concludes that these aspects are not currently in place at Vanderlande and that this is possible and desirable in the future. If Vanderlande want to move to an SLA for its spare parts service, it needs to know the expected cost of spare parts for a system, so they can set a fixed price per year to bill to the customer. Hanegraaf (2017) makes a predictive model for the total cost of spare parts per year for sites in the parcel and postal segment. This regression model predicts the yearly cost of spare parts but it cannot forecast which spare parts are to be used at what moment in time. When Vanderlande wants to use a multi-echelon warehousing system, they need to pool spare parts from the customer to local warehouses. Van den Bosch(2017) investigates where these warehouse should be placed and which parts needs to be stocked at these warehouses.

The first (and only) research done at Vanderlande for the ProSeLoNext project is done by Alcorta (2017).

She first investigates what data is available and what data should be available for predictive maintenance. Next, she makes a maintenance policy selection (MPS) model with which Vanderlande can determine which maintenance policy is best for which component. After that, she considers error data and designs a CBM policy in the form of a control chart for one specific component. One of her recommendations is to investigate how Vanderlande can incorporate UBM into Vanderlande’s operations. A reason for this is that she claims that because UBM is cheaper to implement than CBM because less product changes are needed.

2.2.

Problem statement

The objective of the global services department of Vanderlande is to become an integrated solution provider. The solution means that the system and the service are provided together, i.e. the service is not optional. To become an integrated solution provider, Vanderlande needs to change their business model of certain departments and improve the added value of their services by becoming more proactive.

To increase the added value, Vanderlande wants to become more proactive in the services. Previous work indicates that condition based maintenance is not the best policy for all components of Vanderlande (Alcorta, 2017). One of the possible maintenance policies suggested by of the MPS-model of Alcorta (2017) is UBM but at this moment no strategy is in place for this. Therefore, this research focusses on the feasibility and the value of UBM. 6

Furthermore, the spare parts department requires an adapted business model to shift from selling spare parts to being part of the integrated solution. The spare parts department is at the very start of this change and is looking for the best way to do this. To build a business case, they want to know the value of moving to a multi-echelon inventory system.

To move to service oriented models, better knowledge is required about when spare parts are needed.

Spare parts and maintenance are closely related to each other as maintenance actions often generate for spare parts demand. With a UBM policy, more information about when to do maintenance, and thus when spare parts are needed, becomes available. The information from UBM could be used as advance demand information (ADI) to optimise spare parts inventory decisions. Combining these goals leads to the following problem statement: Vanderlande wants to apply UBM and explore its benefits for service as well as spare parts department but does not know how to do this.

2.3.

Research questions

In this section, the research questions are defined to address the problem and we discuss how we plan to answer these research questions. The main research question we want to answer is: How can UBM be applied as preventive maintenance strategy and how can the information resulting from the UBM strategy be used in the spare parts inventory control?

To answer this main research question, several research questions (RQ) are formulated. An overview of the questions is given in Figure 3. Note that we only consider one piece of equipment, the POSISORTER. Before being able to apply UBM, we need to elaborate on the availability and quality of failure and usage data. First, we focus on failure data of components. This data is not trivial at Vanderlande because this is not documented or logged directly. It became clear that the best usable failure data comes from the spare parts sales. We need to assume here that a sale of a spare part corresponds to a failure of a component. Next to that, we need to find which usage data is available for components. To find out which usage data is available, meetings with data analysists are held. This answers RQ1: 1. What is the available failure and usage data at Vanderlande and what is its quality?

Based on the available data, there are components for which Vanderlande is currently unable to determine a UBM strategy as not enough data is available. These components are excluded. Next, we need to check if UBM is a good strategy for these components. This is done with the MPS-model from Alcorta (2017). Furthermore, we need to find the best usage indicator to predict a failure of the components. This can be based on data or on the knowledge of experts. Note that without available or useful usage data, it is still possible to do UBM as we can use time as usage measurement (time based maintenance). Now we can answer RQ2: 2. Given the availability of data, what are the possible components to apply UBM on? a.

Is UBM a good strategy for these components?

b. What is the best usage measurement to indicate a failure of these components?

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At this point, we can select one component for which we are going to determine a UBM strategy in this research. We use the failure data and the usage data of this component to fit a failure distribution. With this distribution, we can find the optimal UBM policy based on the corresponding cost, i.e. what is the optimal replacement moment for the component to achieve the minimal expected cost per time unit.

When we have found the optimal replacement moment, we can compare it to the current policy for the component and see what the benefits of the UBM policy are. This is done in RQ3: 3. What is a good UBM policy for Vanderlande? a. What are the optimal maintenance moments under this UBM policy? b. What are the benefits of the UBM policy compared to the current maintenance policy?

The fact that more information is known about when to do maintenance results into ADI for spare parts.

We want to investigate how this can be helpful in the inventory management model. Before determining the possible benefits of an ADI policy, we need to come up with a basic inventory model as Vanderlande does currently not have a multi-echelon spare parts inventory model. We define a model that determines the optimal stock levels for components to minimize costs while a certain objective is met.

Because of time constraints, we focus on the most downstream echelon, which is the echelon between the customer and the local warehouse. We assume that the central warehouse has always sufficient stock on hand, therefore the problem becomes a single location problem. By doing this, we keep it less complex and thus less time consuming. After that, we investigate how ADI from the UBM policy can be incorporated in an inventory control model to reduce the inventory levels but still reach the set objectives. This results into RQ4 and RQ5: 4. What should the basic inventory control model of Vanderlande look like for the component(s) in this research and how large is the benefit compared to the current model?

5. How can ADI from the UBM policy be used in the spare parts inventory control model?

After determining an ADI policy in RQ5, we want to compare it with a non-ADI policy to determine how large the benefits of ADI can be. This is done via numerical experiments between a non-UBM policy, a non-ADI policy and the possible ADI policies. This results into RQ6: 6. How large are the benefits of using the ADI policies of Research Question 5 compared to policies without ADI? Best component

UBM-policy for

Basic and ADI

Quantitative

Description of

to do UBM on in

the selected

Benefits of the

spare parts

benefit of ADI vs

available data for UBM

this study

component

UBM-policy

inventory models

non-ADI

Available data (RQ1)

Shortlist of possible UBM components (RQ2a) best usage measurement for components resulting form RQ2a (RQ2b)

Optimal replacement moment under the UBM policy (RQ3a)

Basic spare parts inventory model (RQ4) Compare UBM with current policy (RQ3b)

Spare parts inventory model with ADI (RQ5)

Figure 3: Overview of research questions and deliverables

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Numerical experiments: no-ADI vs ADI models (RQ6)

2.4.

Scope

We first scope to one piece of equipment, the POSISORTER (SPO). Why we focus on the SPO is explained in Section 3.1. Next, we scope down to the timing belt as this is the only component in the SPO for which there is enough data and UBM is useful. This is further explained in Chapter 3.

Considering the service proposition of Vanderlande, we focus on the prevent service for the UBM strategy and the spare part service for a spare parts inventory model without ADI. Then, we connect these services via ADI. According to the classification from Arts (2017), we focus on the component replacement and/or overhaul strategy of UBM because we consider one single component.

For the spare parts inventory model, we only take the most downstream echelon into account and assume that the central warehouse in the multi-echelon model always has sufficient stock. Because of this, the spare parts inventory model becomes a single-location model.

The interface between the service and the spare parts department is out of scope. We do not focus at how the data can best be communicated between the departments and who is responsible for what data, but only focus on the models that can be used.

2.5.

2.5.1.

Deliverables Academic deliverables

The first academic deliverable is that we use a broad view where we define a UBM policy and a spare parts inventory model in a way for them to be combined into an ADI policy. UBM policies, spare parts inventory models and ADI models are topics that are considered in literature but are, to the author his best knowledge, this holistic approach is never done before. By considering real data, we not only look at the technical and theoretical problems for these models but also to the problems regarding applying a policy in practice. By doing this, we close the gap between literature and practice and explain the pitfalls of using data from spare parts sales in the capital goods industry as failure data for UBM. 2.5.2.

Deliverables for Vanderlande

The following deliverables are defined: • • • • • • •

A research report in which an answer is given to the research questions and a solution to the problem.

A list of available data sets that are useful for doing UBM with in the future and how Vanderlande needs to change the current data collection for these sets for them to be useful for UBM. A specific case that proves the concept of UBM and its profitability compared to the current policy.

A basic inventory control model for the most downstream echelon, which Vanderlande can easily switch to before it moves to a multi-echelon model.

A spare parts inventory model that uses the information from UBM as ADI. The (financial) benefits between a model without ADI and a model with ADI. Recommendations for the next steps on implementing an UBM policy in combination with ADI.

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DATA COLLECTION In this chapter, we discuss the data collection and, thus answering RQ1 and RQ2. First, in Section 3.1, we discuss which piece of equipment we consider in this research. After this, we focus on the availability of the two data types we need for UBM: failure data and usage data. In Section 3.2, we discuss which failure data is available and which components are possible to consider based on this. In Section 3.3, we investigate if UBM is a good maintenance strategy for these components and in Section 3.4 we discuss the availability of the other required data, the usage data. In Section 3.5, we provide the conclusions.

3.1.

Equipment selection

As mentioned in Section 2.4, we have scoped this research to the POSISORTER (SPO) as piece of equipment to investigate. In this section, we explain why we came to this decision.

From interviews with stakeholders, we conclude that there are two pieces of equipment worth considering in this research. These two pieces of equipment were the SPO and the high dynamic storage (HDS). A picture of both is shown in Figure 4. The SPO is a piece of equipment used to sort parcels.

“Divert shoes slide across the full-width carriers, pushing the products gently into the output spurs in a diagonal movement” (Vanderlande POSISORTER, n.d.). Vanderlande installed about 450 SPO systems worldwide. The HDS is a shuttle system that is used for storage. “The shuttle system is a cost-effective solution for short-term storage of order totes. The HDS has been implemented in a wide range of industries, such as parts and components, food retail and e-commerce” (Vanderlande HDS, n.d.). Both pieces of equipment are almost always critical to the customers process and they are installed in multiple sites.

Figure 4: Left a picture of a SPO and right a picture of a HDS

The SPO and HDS are evaluated based on availability of failure and usage data about them. Because we eventually use the spare parts sales data as failure data, we discuss the availability of this data with the spare parts manager. It turned out that the HDS is originally from BEEWEN and Vanderlande bought this company. Because this happened quite recently (2 years ago), a lot of sales are not recorded in terms of Vanderlande item numbers, which makes is hard to find spare parts sales data of the components. This is not a problem for the SPO. Another problem with the HDS is that there is almost always more than one HDS system per site, this means that it is hard to find unique components in the system (one of the requirements). This is less a problem for the SPO as there are multiple sites that have only one SPO. Furthermore, the HDS systems are used in different markets (e.g. airports, food retail and e-commerce).

Different markets come with different requirements which makes these systems also differ from each other. SPO systems are only used in the parcel and postal market, which all have about the same 10

requirements. A disadvantage for the SPO is that, according to the data science team, there is less usage data available for it compared to the HDS as they have more BPI systems active at HDS sites.

Taking these advantages and disadvantages of the HDS and the SPO into account, we eventually chose to consider the SPO in this research. This was because it had a higher chance in finding useful failure data. The fact that there is less usage data available can be compensated since that with failure data alone we can already do time-based maintenance. Next to that, information about the usage can in some extent also be extracted from experts instead of data.

3.2.

Failure data

Failure data is one of the two types of data needed to apply UBM. Failure contains information on which moments the components failed. With this data, we can fit a failure distribution, thus also determining the mean time to failure (MTTF). Unfortunately, failure data is not easy to obtain at Vanderlande. There is no company-wide information available about failure times and associated customers. Because of this, we need to find another way to come up with this information.

3.2.1.

Failure data set: spare parts sales data

In this section, we discuss the data set that we chose to use for the failure data together with the needed requirements and assumptions. This data is the spare parts sales data. We also considered other data sets from tool like Scada and DOS Maximo. We discuss these data sets in Appendix A. Because maintenance actions cause a demand for spare parts, we can use this data as failure data when we assume that when a customer orders a spare part at Vanderlande, this component has recently failed in its system. However, in the case of Vanderlande, there are a few concerns related to this assumption.

First, the customers of Vanderlande are not obliged to buy their spare parts at Vanderlande. If a customer buys spare parts at other suppliers, we are missing data points for these customers, which means that the time between failures may be shorter than what the data indicates. To overcome this, we require that the customers considered in this research buy all their spare parts at Vanderlande.

Together with the spare parts manager, we determine which customers only buy their spare parts at Vanderlande. This decision is based on his expertise. Second, if a component exists more than once in the system we do not know which one has failed when the customer orders a new component. Because of this, we require components to exist only once in the system. With these two extra requirements, we started collecting the data. The spare parts list per customer is found in SmarTeam. In the spare parts list, we find if and how often a part is in the system of the customer and in which piece of equipment the part is used. Using the spare parts list, we can filter on components that exist only once in the SPO. The spare parts sales data is extracted from JD Edwards. We checked if there were sales for the components that exist once in the system and if there were, these sales are considered as possible data points.

During this data collection, we encounter some issues that need to be taken into account before considering a data point as valid. First, there are different types of spare part sales. As explained in Section 1.3.2, Vanderlande sells spare part packages to their customers. These sales are marked with a ‘V’ (V-sale). These sales are not useful data points for the failure data, because these spare parts packages are mostly bought when the system is sold and not when a failure has occurred. The 11

replenishment orders are marked with an ‘X’ (X-sale), these data points are useful as failure data. If a component was sold in a spare parts package and there is a replenishment sale later in time, it is assumed that the customer follows the advice of Vanderlande and immediately replenishes the stock to keep it on the right level, i.e. follow a base stock policy. If there is no spare parts package sale for a component, it is assumed that the customer does not have this part on stock and thus orders immediately when a failure occurs. Furthermore, there are ‘Y’ sales (Y-sale), which are considered as valid data points as they stand specifically for corrective maintenance sales. A second issue is that a customer orders multiple of the same component at the same time. Because we only focus on components that exist once in a system, the customer cannot use more than one of the ordered parts.

Possible reasons for these orders are that the customer decides to put this component on stock or the price at Vanderlande is low enough that the customer decides to buy items and sell possible them on a local market. Because this is a rather strange and unexpected action and the customer does not follow the instructions of Vanderlande, we conclude that the data points that occur after this moment are not valid anymore. However, the replenishment orders up to this point are still considered as valid. Last, it is assumed that all the spare part sales are used for corrective maintenance. This means that the component has failed and thus used up all his lifetime. However, it was found that some customers order a lot of different components on the same date. The chance that all these different components are used for corrective maintenance, and thus have failed, is not high. If a customer orders a lot of different spare parts on the same date, it indicates a preventive maintenance action. Because the lifetime of a component is not completely used when preventive maintenance is performed, these data points are not considered as possible data points for failure data. An overview of all the assumptions and requirements needed to extract useful data points from this data source can be found in Table 1.

Table 1: Assumptions and requirements needed to use spare parts sales data

Assumptions or requirement needed to use spare parts sales data Requirement The considered customers need to buy all their spare parts at Vanderlande Requirement Only components that exist only once in the system are considered Assumption If there was no V-sale: there is no stock on site for that item and the customer orders a component immediately when the part fails Assumption If there was a V-sale: customer replenishes stock immediately after the part is used Assumption If there are multiple of the same parts ordered at the same date, the customer decided to put them on stock. Data points before this moment are still valid, data points from this moment onwards are not Assumption The parts ordered are always used for corrective maintenance unless the data clearly indicated that preventive maintenance actions make more sense (e.g. when a lot of items are ordered on the same date) 3.2.2.

Collecting the failure data from the spare part sales data

In this section, we discuss which components can be used in this research based on the spare parts sales data taking into account the assumptions and requirements mentioned in Table 1. We obtain data on the installed base for all 456 sites where Vanderlande has placed a SPO. Through a discussion with the spare parts manager, we determine that there are 280 customers (61% of the total) who buy all their spare parts at Vanderlande. These customers are thus considered to be loyal and can be used in this research. We collect the spare part lists and the spare parts sales data for these customers and use these to investigate if there are data points that meet all the assumptions and requirements (Table 1). This 12

results in a total of 155 data points for 77 different item numbers at 49 customers (17.5% of the 280 loyal customers).

For some data points, we need to know the date the site of the customer started running. To find this, we look up the start commissioning date for the remaining 49 customer sites. The start commissioning date is a tollgate that Vanderlande uses to make sure they do not start commissioning before the system has reached a certain state of readiness and before all required deliverables are ready for use. This date can be found in Primavera (Vanderlande’s planning software) when the right project number is known.

We intend to find the start commissioning date based on the project number that is mentioned in the IB. Unfortunately, for only 32 of the 49 sites (65%) there is a start commissioning date recorded on this project number. Furthermore, for four sites of these 32 sites, there are already spare part replenishment sales before this date, which resulted into a negative time to failure. Furthermore, it turns out that there can be more project numbers connected to a customer and it is not possible the find out on which project number the SPO is placed. The only way to do this is to go to the customer site and look at the project number on the SPO. Due to time limitations, it is not possible to do this. Instead, we use the creation date recorded by the spare parts departments, which is the moment that this department creates the customer in their system. We compare this creation date with the reliable and available start commissioning dates and find that the start commissioning date is on average 9 months (with a standard deviation of about 4.5 months) later than the creation date. We use the creation date plus nine months as start date for the sites where the start commissioning date was unreliable or unavailable. This is done because this was the only available indication of the start date. Therefore we recommend that Vanderlande documents when their sites start running, since it is hard to do UBM without knowing when the systems are started being used. Lastly, because Vanderlande started recording their spare part sales in JD Edwards from January 2010 onwards, we cannot use data points that are based on the date the customer site started running, for customers for which their system started running before 2010. This is because we do not know if there was already a sale (and thus a failure) before 2010. For customers for which the system started running after 2010, there are no further limitations. After this final restriction, there are 123 data points remaining for 65 different components.

3.2.3.

Combining data points

Unfortunately, we find that only three of the 65 different remaining item numbers have five or more available data points. Having less than five available data points, which is already very low, makes it not reliable to conclude something about the failure distribution. To overcome this problem, we combine item numbers for components that have the same characteristics and have the same function in the SPO. For example, there are two different item numbers (004885-92030 and 004885-12003) for the timing belt at the entry of the SPO. These timing belts at the entry are used in the same place and have the same function in the SPO, however, they differ in length. Since these differences are minor, we assume that the degradation of these components is the same. This method is discusses with a senior trainer at Vanderlande who is an expert on SPO and its components. He agrees with the fact that the combination of data points is possible for components with these similarities. There are more groups of components with the same function but different item numbers. We check if it was possible to combine the data points of those components by discussing it with the expert and looking at the component specifications, which can be found in Appendix B. In this appendix, we conclude that there are only minor differences between the different item numbers that are combined. If combining is possible, we set the 13

requirement that the combined number of useful data points should be five or more to be considered in this research. Although more data points would provide a better and more reliable failure distribution, we choose to include the components already if they would have five or more data points. The reason for this is because we want to show that UBM is also possible with a low data availability. It is recommended that Vanderlande continues with gathering data about the failure of their components and more insight in the failure distribution of their components.

By setting the requirement of at least five useful data points, there are five (combined) components left that are worth considering. The combined components are the timing belt entry, the timing belt end, the assy merge, a cable, and the drive pulley Ø75 cylindrical. The number of useful data points per group of components that are still possible to use are shown in Table 2. The item numbers that are considered per combined group, together with the number of data points per item number is given in Appendix C. Table 2: Useful components based on available failure data

Group description

Combined data points 19 5 10 7 5

Timing Belt entry Timing Belt end Assy merge Cable Drive pulley Ø75 cylindrical 3.3.

Is UBM a good strategy for the remaining components?

In this section, we answer RQ2a by checking if UBM is a good strategy for the remaining components.

We do this by using the MPS-model of Alcorta (2017).

3.3.1.

MPS-model of Alcorta (2017)

In her research at Vanderlande, Alcorta (2017) develops a MPS-model to determine the best maintenance strategy for specific components. This MPS-model is a decision tree that consists out of tree smaller decision trees. The decision tree, a short explanation of the tree and how she did develop this tree is given in Appendix D. The MPS-model of Alcorta is applied on the components in Table 2. The output of the model can be found in Table 3 and a description of the answers can be found below. Note that the answer should indicate ‘yes’ for the component to precede to the next split in the tree.

Table 3: Outcome of the MPS-model of Alcorta (2017)

Component Timing belt Entry Timing belt end Assy merge Cable Drive pulley Ø75 cylindrical

Split 1 No

Split 2 No

Split 3 Yes

Split 4 Yes

Split 5 Yes

Split 6 Yes

No

No

Yes

Yes

Yes

Yes

No No No

No No No

No No No

n.a. n.a. n.a.

n.a. n.a. n.a.

n.a. n.a. n.a.

14

Split 7 No, +/- €15 No, +/- €15 n.a. n.a. n.a.

Split 8 n.a.

Policy UBM

n.a.

UBM

n.a. n.a. n.a.

CM CM CM

Split 1 and 2: safety issue and legislation: For the first two decisions, we assumed that the answer is no.

This was because these splits are very system and customer dependent and it was hard to find a universal answer to these splits. If safety or legislation is compromised, another policy is used for those systems, but this does not affect the decision which policy is best for the component itself.

Split 3: IFR: Information about this question is gathered by interviewing the SPO expert. According to him, only the timing belts wear over time. He mentioned that the assy merge, although it has a moving component, does not wear. It is possible that the part is replaced during a revision or a big maintenance stop, but for most systems it is used for the complete lifetime. Also, the drive pulley Ă˜75 cylindrical does not wear. This is a roller and there are some layers attached to it. These layers do wear and get replaced but the drive pulley itself does not wear. Lastly, the cables are electrical components that generally do not wear. The expert mentions that it is possible that they get less flexible if a lot of oil and dust gets attached to it and break during maintenance when an engineer works around them. This dependents on the environmental conditions and not on the system itself.

Split 4: critical to customer: The timing belt entry and timing belt end are the only components that are still in the decision tree. For this decision point, we assume that the SPO is critical for the system of the customer. The level of criticality can be different per customer but it is a reasonable assumption because the SPO is mostly the main piece of equipment of the customers system.

Split 5: critical to SPO: To check if this is true we use the thesis of van den Bosch (2017). In his report he tries, amongst other things, to find the criticality of spare parts. This criticality is based on the component itself and the location of the component in the system. Eventually he classified the components in eight different categories. More information about this is given in Appendix E. The timing belts are assessed as criticality level 5, which means that the timing belts are highly critical standard parts of low value.

Split 6: failures predictable?: This is discussed with the SPO expert. He mentions that it would be possible to predict when a timing belt is going to fail based on the usage of the system but it would be hard to detect a coming failure by eye.

Split 7: high spare parts cost?: As van den Bosch (2017) already mentioned in his description of criticality level 5, the timing belt has a low value. This is true because the timing belts are sold for about â‚Ź 15.

Alcorta (2017) did not give a definition on when spare parts cost is considered high or low. An indication for when to mark a spare part as high or low value for Vanderlande is given by van den Bosch (2017) (Appendix E).

Concluding, it would be beneficial for the timing belts to have a UBM strategy. For the other three components that had enough data points, it would be better to use a corrective maintenance strategy.

The reason for this is that the other components did not have an IFR. For the rest of the research, we only consider the timing belt entry and the timing belt end.

3.4.

Usage data

The second type of data needed to perform UBM is usage data. Different usage measurements like throughput or running hours can be used as indicator to predict a failure. In this section, we discuss how we collect the usage data and what usage measurement is the best indicator for failures of the timing belt.

15

3.4.1.

Usage data collection

We try to collect usage data via VIDI or BPI as these are the performance management tools that Vanderlande sells to its customers. Focussing on useful failure data points for the timing belt entry and the timing belt end, there are 13 customers remaining for which check if we can collect usage data via BPI or VIDI. A data analyst at Vanderlande checks if BPI/VIDI is available for these sites. As can be seen in Table 4, BPI/VIDI is only available for two of the thirteen sites: OZ export and DHL Goteborg. For OZ export, there is a VIDAR database available. VIDAR is an old version of BPI that runs in Access.

Unfortunately, the data cannot be reached at Vanderlande. The other site equipped with BPI/VIDI is DHL Goteborg. For this site, the data is available until 2013. After this point, they stopped recording the data.

This means that there is no data available for the last five years.

Table 4: BPI/VIDI available or Usage data available according to service contract manager?

Customer

BPI/VIDI available?

Interview service contract manager Amazon FR - Saran No information Nothing available Amazon FR - Montelimar No information Nothing available Amazon Koblenz CGN1 No information Nothing available Amazon Pforzheim STR1 No information Nothing available DPD Best No BPI/VIDI Yes, alibi memory TNT Milmort No BPI/VIDI Yes, alibi memory TNT Antwerpen No BPI/VIDI Yes, alibi memory DHL Goteborg Yes, BPI data until 2013 Yes, BPI data until 2013 DHL Regensdorf No BPI/VIDI Nothing available OZ export Yes, VIDAR but password unknown Yes, alibi memory Fleura Export BV No BPI/VIDI Yes, alibi memory but not found Syncreon Technologies No BPI/VIDI Yes, life cycle sheet Schenker Mechelen BV No BPI/VIDI Nothing available For the other sites, there is either no BPI/VIDI available or there is no information available about whether there is BPI/VIDI. According to the data analyst, there is a slight chance that there is BPI/VIDI available even when there is no information about it. it is then not documented correctly. However, due to the high time effort and the low possibility that there is BPI/VIDI available, we decide that having no information means that there is no BPI/VIDI available. The main reason that these sites have no BPI/VIDI is because they are relatively small sites, so they have less need for a performance monitoring tool like BPI/VIDI. The reason that a lot of small sites are remaining is because of our assumption that the component may only occur once in the system. SPOs are mostly constructed in the same way, which means that the component can occur more than once. Therefore there are not a lot of sites where multiple SPOs running remaining. Some other problems are that BPI/VIDI is sold but not always used by the customer or the data is not stored structurally. Vanderlande should continue selling the BPI/VIDI to customers and may even consider it as standard equipment for a system. If customers do not want to pay for it, Vanderlande can consider sponsoring VIDI in return for using the data. With this data they can increase the added value of Vanderlande to their customers. Collecting this usage data is very valuable and is less expensive than placing sensors for condition data.

Due to the low amount of BPI/VIDI available, we need to find another way to usage information. To get more insight in the usage of these sites, interviews with the service contract managers of these sites are conducted. Table 4 shows the results of these interviews. For six of the remaining thirteen sites, no data 16

was available about the usage and nobody could give even an approximation of the usage of the systems.

The last option for these sites is to contact the customer directly and ask about the usage of the system.

We decide not to do this as it would be time consuming and we do not want to inform the customer about the research yet. For five sites, there should be alibi memory available and for one site a life cycle sheet is available. Alibi memory is data about the usage of the system, which is used to generate management reports about the throughput of the system per day, the number of running hours per day, and the sort rate of the system per day. This data is mostly stored for one to three months. This alibi memory is extracted by a process engineer at Vanderlande for four of the five sites for which it should be available. For the remaining site, Fleura export, he could not find any alibi memory data. In the life cycle sheet, the customer mentions their average throughput per hour, running hours per day and operation days per week. The estimations on the life cycles sheeft are used to get an estimating of the usage of this site.

Based on the BPI data, alibi memory and the life cycle sheet for these sites, we calculated the average throughput per day, the average running hours per day of the systems, and the days per week that the system is operational. These numbers can also be found in Table 5, together with the amount of days of data we received and the time span over which this data was spread. Because we only have usage information for these sites, we need to reduce our available data points as the failure data points for which no usage information is available cannot be used. This brings the number of useful data points for the timing belt entry to 14 (3 for the 004885-12003 and 10 for the 004885-92030) and for the timing belt end to one. Because of this, we do not consider the timing belt end anymore but only focus on the timing belt entry.

Table 5: Usage data per customer

Customer

DPD Best

Number of days data available 59

TNT Milmort

39

TNT Antwerpen

28

DHL Goteborg

339

OZ export

22

Syncreon Technologies

1

3.4.2.

Time span

Average throughput (parcels/day) 30-11-2017 42800 21-2-2018 11-12-2017 7374 26-2-2018 19-1-2018 3382 23-2-2018 12-3-2009 18500 21-2-2013 25-1-2018 16207 15-2-2018 Average 19250

Average running hours per day 16.1

Number of days/week operational 5

10.4

5

11.1

5

15.4

5

11.3

5

11.0

5

Best usage measurement for the timing belt

If we want to use UBM for the timing belt entry, we need to know which usage measurement is the best indicator for its failures. A way to do this is to check the correlations between the MTTF in days (MTTFDays) and the MTTF in usage (MTTFusage). In this case, the highest correlation would indicate the best usage measurement. The usage data we have is an average throughput per day and an average number of running hours per day. As the we observe large differences in average throughput and average running 17

hours per site, we decide not the use the MTTFDays but try to define a MTTFUsage. We use the following equation for the MTTFUsage, assuming that the usage does not change over the years: MTTFusage =

đ?‘€đ?‘‡đ?‘‡đ??š Days 7

∗ (đ?‘ˆđ?‘– ∗ đ??ˇ Week ),

(1)

where Ui is the best usage measurement to indicate a failure for part i (per day) and đ??ˇ Week is the number of days the system is operational per week. Because we use Equation (1) to find the MTTFusage, there is always a strong positive correlation between the MTTFusage and the MTTFDays. If we would have the specific usage data of the system at any moment in time, we can determine the exact MTTFusage and investigate the correlation to base the best usage measurement on data.

The SPO expert concludes that the running hours of the SPO is probably the best usage indicator for the failure of the timing belt. If the SPO is running, it means that the timing belt is moving and thus wears.

The expert mentions that throughput probably has no impact on the failures of the timing belt as the parcels do not though the timing belt. In Appendix F, the final available data points can be found. In this appendix, the MTTF is given in days and in running hours, which we calculated by Equation (1).

3.5.

Conclusions

In this chapter we answer RQ1: What is the available failure and usage data at Vanderlande and what is its quality? We conclude that the availability is very low and the quality is not that good. We investigate several possible datasets but find that there is no failure data available on component level. The main problem is that it is hard to match the data to a specific component failure. Therefore, we use spare part sales data to approximate the failure rates of the components, based on some requirements and assumptions. Also, usage data is very hard to obtain at Vanderlande, especially data covering the complete lifetime of a system. We eventually found some usage data, but it is limited to only a few months and we needed to extrapolate this by assuming that the usage did not change over the years.

The main conclusion is that the combination of failure data for components and usage data for sites is very hard to gather. In our research, we focussed on relatively small customer sites due to our requirements and assumptions for the failure data. At these sites almost no usage data is available, as these sites have no need for VIDI/BPI. If we consider larger sites where BPI or VIDI is installed, we would get usage data, but we cannot deduct failure data for components.

For RQ2: Given the availability of data, what are the possible components to apply UBM on?, we investigate the data found in RQ1. First, we answer RQ2a: Is UBM a good strategy for these components?

For this we focussed on the components for which we have enough data to do UBM and check if UBM is a good policy using the MPS-model of Alcorta (2017). We conclude that UBM is only useful for the timing belts as these components have an IFR. Based on the available data, we reduce the possible components to consider in this research to the timing belt in the entry of the SPO. Based on the expertise of the SPO expert, we answer RQ2b: What is the best usage measurement to indicate a failure of these components? and conclude that the running hours of the system is the best usage indicator for a failure of the timing belt entry.

18

USAGE BASED MAINTENANCE In this chapter we elaborate on UBM. In Section 4.1, we present the UBM policy. In Section 4.2, we discuss what distribution fits the data best and discuss how we determine the relevant costs. In Section 4.3, we find the optimal maintenance moment and compare this policy with the current policy at Vanderlande and in Section 4.4, we answer RQ3a and RQ3b.

4.1.

UBM policy: single-component age based maintenance policy

UBM considers the total usage of a component and maintenance is performed when a certain threshold is reached. UBM can be performed per component or for a group of components when the set-up cost is very high. We choose to focus on a single component UBM policy because Vanderlande is not have high fixed maintenance costs, we consider parts that occur only once in the system and the goal of this research is to create a success case to show that UBM is possible and beneficial for Vanderlande. In the future, Vanderlande wants to create a maintenance program for a complete customer site and thus also adjust the maintenance interval for UBM to that overall program. This is not done in this research as this is outside the scope; however, Appendix G provides some interesting ways to consider this in the future.

We present a single-component age-based maintenance policy. The idea is that “a component is replaced whenever it has been used for a fixed amount of usage Ď„ or if it fails before this timeâ€? (Arts, 2017, p.30). In the case of the timing belt, this usage is measured in terms of running hours. This policy was first introduced by Barlow and Hunter (1960) and is based on renewal theory. A brief introduction of reliability and renewal theory is given in Appendix H. Our policy assumes that a maintenance action can be performed any moment and there is always a part available. The degradation of a timing belt happens continuously but the data is collected in a discrete way as the MTTFusage is calculated with Equation (1). In the future, Vanderlande checks the usage of a system daily and determines if maintenance is needed and if this is the case they perform the maintenance the next day. It is likely that the maintenance is not done on exactly the moment that the policy would indicate as optimal as the usage is observed periodically. We observe a measuring error in the usage data of one day but because the lifetime of the timing belt of more than two years, this one day measuring error should not be a big issue. Furthermore, we assume that we are not dependent on predetermined maintenance stops as most customers do not run 24 hours per day and maintenance actions can performed when the system is not running. Also, we assume that minimal repair is not possible. Minimal repair means that the component is not replaced but only temporarily fixed and hopefully holds until the next maintenance moment. Because the timing belt is a critical component in the SPO and is constantly moving when the SPO is running, it is not desirable to do a minimal repair but we want to replace it when it fails.

The time until a component is replaced is the random variable X = min (Ď„, T) where Ď„ is the PM threshold and T the moment of failure. The replacement times are renewal points so “we can define the time until replacement as a cycle and then the average costs under this policy can be studied as a renewal reward processâ€? (Arts, 2017, p.30). The expected length of a cycle (ECL) is defined as the expectation of X: đ?œ?

ECL = E[min(Ď„, T)] =âˆŤ0 đ?‘‡đ?‘“đ?‘‡ (đ?‘‡)đ?‘‘đ?‘‡ + đ?œ? ∗ (1 − đ??šđ?‘‡ (đ?œ?))

(2)

If a component fails before Ď„, a cost for unplanned corrective maintenance, Cu, is incurred (Cu >0). On the other hand, if the replacement is done at the usage threshold Ď„, a cost for preventive replacement, 19

Cp, is incurred (0< Cp â&#x2030;¤ Cu). The expected cycle cost (ECC) is defined as: ECC = đ??šđ?&#x2018;&#x2021; (đ?&#x153;?)đ??ś u + (1 â&#x2C6;&#x2019; đ??šđ?&#x2018;&#x2021; (đ?&#x153;?))đ??ś p

(3)

In the ECL and ECC equations, đ??šđ?&#x2018;&#x2021; (đ?&#x153;?) is the distribution function of a random variable T (đ??šđ?&#x2018;&#x2021; (đ?&#x153;?) = P(Tâ&#x2030;¤ đ?&#x153;?)) and đ?&#x2018;&#x201C;đ?&#x2018;&#x2021; (đ?&#x153;?) is the density function of a random variable T. We assume đ?&#x2018;&#x201C;đ?&#x2018;&#x2021; (đ?&#x2018;Ą)=

đ?&#x2018;&#x2018;đ??šđ?&#x2018;&#x2021; (đ?&#x2018;Ą) . đ?&#x2018;&#x2018;đ?&#x2018;Ą

The average cost per time unit, which depend on the usage threshold Ď&#x201E;, is g(Ď&#x201E;) =

đ??¸đ??śđ??ś . đ??¸đ??śđ??ż

Arts (2017)

mentions that the optimal Ď&#x201E; can be found by setting the derivative of g(Ď&#x201E;) equal to zero and solve for Ď&#x201E;.

This is possible because this function is generally convex. Note that if we do this while T has a decreasing failure rate, we see that the derivative is always greater than zero and the optimal replacement moment goes thus to infinity, i.e. the component is replaced when it fails (CM).

4.2.

Using the data and determining cost equations

In this section, we fit a distribution to the data we found in the previous chapter and explain the equations used to determine the preventive and corrective maintenance costs.

4.2.1.

Fitting a distribution to the data

There are several possible distributions that can fit the data and we want to find out which distribution fits best. The distributions that we try to fit to the data are the Weibull distribution and the Gamma distribution because these are used most in reliability engineering. Arts (2017) mentions for example that the Weibull distribution is used a lot in reliability engineering â&#x20AC;&#x153;because it provides a good fit with data in many applications and arises naturally in theoryâ&#x20AC;? (Arts, 2017, p. 19). We use the Akaike Information Criterion (AIC) to compare the models. â&#x20AC;&#x153;The goodness of fit of a model is taken to be: AIC = - 2 log (maximum likelihood of the model) + 2 (number of free parameters of the model)â&#x20AC;?

(Sakamoto, Ishiguro, & Kitagawa, 1986).

(4)

We use MATLAB to fit a Weibull and a Gamma distribution to the data, based on the maximum likelihood estimator, and calculate the AIC for both models. The AIC for the Weibull distribution is 279.2 and the AIC for the Gamma distribution is 279.8. Although the model with the lowest AIC is the model with fits the data best, Burnham and Anderson (2004) mention that when the difference in AICs of two models is below two, there is still some substantial support for the model with the higher AIC. However, we still conclude that the Weibull distribution fits the data better than the Gamma distribution, but encourage Vanderlande to collect more data to check this more carefully.

Now that we are using the Weibull distribution, we want to investigate if the Weibull distribution is a good fit to the data. This is because it might be possible that the data would fit neither the Weibull nor the Gamma distribution well, but still have a better fit to the Weibull distribution. To check if this, we perform a Chi-squared goodness of fit test in MATLAB. This test is used for â&#x20AC;&#x153;testing the goodness of fit of a theoretical distribution to sample dataâ&#x20AC;? (Montgomery & Runger, 2003, p.690). This test has the following null and alternative hypothesis: Ho: The data follows a Weibull distribution with scale parameter Îą and shape parameter β H1: The data does not follow a Weibull distribution with parameter Îą and scale shape parameter β 20

Montgomery and Runger (2003) mention that it can be shown that, if the population follows the hypothesized distribution, the test statistic has a chi-square distribution. Our Chi-squared test returned a p-value of 0.8725. In this case, Montgomery and Runger mention that we are unable to reject H0 with a significance level of 5% and therefore have no strong evidence to indicate that the data is not Weibull distributed. Because of this, we assume that the data follows a Weibull distribution with scale parameter Îą and shape parameter β. Using the â&#x20AC;&#x2DC;wblfitâ&#x20AC;&#x2122;-function in MATLAB, which makes use of the maximum likelihood estimator, we fit a Weibull distribution to the data. This gives the following Îą and β: Scale parameter Îą = 7592.52 Shape parameter β = 1.3688 From the equation for the hazard rate for a Weibull distribution, shown in Appendix I, we can conclude that the Weibull distribution has an IFR when β > 1, which is the case for our data, indicating that PM is a good strategy. Using the Weibull equations from Appendix I, we can formulate g(Ď&#x201E;) for our UBM policy: đ?&#x153;? đ?&#x203A;˝

g(Ď&#x201E;) =

đ?&#x153;? đ?&#x203A;˝

â&#x2C6;&#x2019;( ) â&#x2C6;&#x2019;( ) (1â&#x2C6;&#x2019; đ?&#x2018;&#x2019; đ?&#x203A;ź )â&#x2C6;&#x2014;đ??ś đ?&#x2018;˘ + (đ?&#x2018;&#x2019; đ?&#x203A;ź ) đ??ś đ?&#x2018;? Ď&#x201E;

đ?&#x203A;˝

đ?&#x2018;Ľ đ?&#x203A;˝â&#x2C6;&#x2019;1

â&#x2C6;Ť0 đ?&#x2018;Ľâ&#x2C6;&#x2014;(đ?&#x203A;ź â&#x2C6;&#x2014; (đ?&#x203A;ź)

đ?&#x2018;Ľ đ?&#x203A;˝

đ?&#x153;? đ?&#x203A;˝

â&#x2C6;&#x2019;( ) â&#x2C6;&#x2019;( ) â&#x2C6;&#x2014; đ?&#x2018;&#x2019; đ?&#x203A;ź )đ?&#x2018;&#x2018;đ?&#x2018;Ľ+Ď&#x201E;â&#x2C6;&#x2014; đ?&#x2018;&#x2019; đ?&#x203A;ź

(5)

We want to find the optimal Ď&#x201E;, however, because we use the Weibull distribution, it is very hard to differentiate this function. Because of this, and because the decision to replace is made on a discrete moment, we decide to calculate g(Ď&#x201E;) for Ď&#x201E;, then increase Ď&#x201E; by 1 and calculate g(Ď&#x201E;) again. This is done until g(Ď&#x201E;) > g(Ď&#x201E; -1) and we then declare Ď&#x201E;* = Ď&#x201E;-1. This is possible because g(Ď&#x201E;) is a convex function. Although it is hard to prove for this function, we can see from examples in for example Arts (2017) that this is generally true. When we look at the graphs in Appendix J, we see that g(Ď&#x201E;) looks convex for our cases.

4.2.2.

Equations to determine the relevant maintenance costs

Before we can find the optimal maintenance policy, we need to find the relevant maintenance costs. In our policy there are two kind of costs for component i, the preventive maintenance cost (Cip) and the unplanned corrective maintenance cost (Ciu). The preventive maintenance cost is: Cip = Cisparepart + (tireplacement + ttravel) * WMaintenance,

(6)

with Cisparepart being the cost of the spare part i, WMaintenance the hourly wages for the maintenance engineer who needs to replace the part, tireplacement the time that he needs to perform the replacement of part i, and ttravel the constant travel time.

Ciu is equal to Cip plus the cost that the customer faces for the unavailability of the system, the downtime cost CiDT: Ciu = Cip + CiDT (7) Downtime costs are hard to quantify as they include both tangible and intangible costs. Tangible costs are costs for extra hours that need to be made to finish all orders (CiOT ) and costs for extra trucks that need to be arranged (CiET). Intangible costs are for example costs for customer dissatisfaction and the loss of face for Vanderlande. There has been some research at Vanderlande concerning down time cost. Ă&#x2013;ner et al. (2007) show that downtime cost is approximately 48% of the total costs of a baggage handling system by assuming that each unit of downtime costs a fixed amount of money. Vlasblom (2009) defines 21

an equation to determine the downtime cost for the airports segment based on the moment of failure, the system capacity, the system throughput and the system availability. Aangenendt (2018) defines an equation for downtime cost related to the parcel and postal market as he also focuses on the SPO. His equations are used as basis for the equations we use to determine the CiDT. Aangenendt (2018) takes the tangible costs CiOT and CiET into account and ignores the intangible costs as he sees Vanderlande and the customer as one entity. We also ignore the intangible cost as no information about this is available: CiDT = CiOT + CiET

(8)

CiOT is determined by the multiplying the hours of work that is necessary to process all handling units that arrived too late with the hourly wages of the employees (đ?&#x2018;&#x160;Operational) and the number of employees (q). The hours of work that is necessary to process all handling units that arrived too late are found by dividing the average number of handling units that arrive too late due to failure of component type i (Bi) by the maximum capacity that a SPO can process per hour (Cap): đ??ľ

đ?&#x2018;&#x2013; CiOT = đ?&#x2018;?đ?&#x2018;&#x17D;đ?&#x2018;? â&#x2C6;&#x2014; đ?&#x2018;&#x17E; â&#x2C6;&#x2014; đ?&#x2018;&#x160;Operational

(9)

CiET is determined by multiplying the number of extra truck needed with the number of KM that one truck needs to travel on average (nKM) and the costs per KM for one truck (WKM). The extra number of extra trucks needed is found by multiplying đ??ľđ?&#x2018;&#x2013; with the average weight of the parcels (đ?&#x2018;&#x160;đ??ź Parcel ), divide this by the maximum allowed weight in one truck (đ?&#x2018;&#x160;đ??ź đ?&#x2018;&#x20AC;đ?&#x2018;&#x17D;đ?&#x2018;Ľđ?&#x2018;&#x2021;đ?&#x2018;&#x;đ?&#x2018;˘đ?&#x2018;?đ?&#x2018;&#x2DC; ) and round it up: CiET =

đ??ľđ?&#x2018;&#x2013; â&#x2C6;&#x2014;đ?&#x2018;&#x160;đ??źParcel đ?&#x2018;&#x160;đ??źMaxTruck

* nKM * WKM

(10)

Now we need an equation for Bi. In the time that the system is down, parcels are buffered in front of the system. If the system is repaired, all buffered handling units can be processed again. If the regular throughput of one SPO (Th) is lower than Cap, the system can process the buffered handling units with the maximal capacity until the buffer is empty. This means that đ??ľđ?&#x2018;&#x2013; dependents on the moment of failure and the difference between Th and Cap. We assume that the probability for the moment of failure is uniformly distributed due to the small time window of a shift. Because of this, the availability (Av), defined as the probability that a system is performing its required function at a given point in time when used under stated operating conditions (Ebeling, 2010), of the system can be calculated by dividing the uptime of the system when a failure occurs by the length of a shift (Shi): replacement

Av =

đ?&#x2018; â&#x201E;&#x17D;đ?&#x2018;&#x2013;â&#x2C6;&#x2019;(đ?&#x2018;Ąđ?&#x2018;&#x2013;

+ đ?&#x2018;Ą travel )

(11)

đ?&#x2018; â&#x201E;&#x17D;đ?&#x2018;&#x2013;

There are sites where several SPOs are running in parallel (nSPO). For these sites, it is possible that, when a SPO fails, the other SPOs start running at full capacity. We assume that the throughput and the capacity of the whole system is equally distributed over the SPOs and that the probability that more than one SPO fails in the same shift is neglectable. To adapt the system to this emergency state takes one hour of downtime for all SPOs. This hour also occurs when the system is changed back to the normal state when the failure is fixed. During these two hours, the other SPOs are not running but after that, the system can make up for lost throughput. The number of parcels that should be to late when component i fails but the system can make up for due to redundancy is defined as Ri: Ri = max (0, (đ?&#x2018;&#x203A;SPO â&#x2C6;&#x2019; 1) â&#x2C6;&#x2014; ( 22

(đ?&#x2018;&#x2020;â&#x201E;&#x17D;đ?&#x2018;&#x2013;â&#x2C6;&#x2019;2)â&#x2C6;&#x2014;(đ??śđ?&#x2018;&#x17D;đ?&#x2018;?â&#x2C6;&#x2019;đ?&#x2018;&#x2021;â&#x201E;&#x17D;) 2

â&#x2C6;&#x2019; (2 â&#x2C6;&#x2014; đ?&#x2018;&#x2021;â&#x201E;&#x17D;)))

(12)

Eventually we calculate đ??ľđ?&#x2018;&#x2013; in equation (13) in which the first part calculates the average number of late replacement

parcels when the failure occurs when the remaining time of the shift is more than đ?&#x2018;Ąđ?&#x2018;&#x2013; + đ?&#x2018;Ą travel .

If this happens, the system is repaired before the end of the shift and can operate at full capacity to reduce the number of handling units that miss the truck. Just as Aangenendt (2018), we assume that no extra employees are needed to reach the maximum capacity. The second part adds the average of late replacement

parcels when the failure occurs when the remaining time of the shift is less than đ?&#x2018;Ąđ?&#x2018;&#x2013; + đ?&#x2018;Ą travel .

If this happens, no remaining shift time is left after the repair. At the end, we subtract đ?&#x2018;&#x2026;đ?&#x2018;&#x2013; . It is assumed that đ??ľđ?&#x2018;&#x2013; is completely processed before the next shift starts as the employees complete this in overtime.

Extra explanation about this equation, without đ?&#x2018;&#x2026;đ?&#x2018;&#x2013; , can be found in Section 6.5 of Aangenendt (2018). max(0,đ?&#x2018;&#x2021;â&#x201E;&#x17D;â&#x2C6;&#x2014;đ?&#x2018;&#x2020;â&#x201E;&#x17D;đ?&#x2018;&#x2013;â&#x2C6;&#x2019;đ??śđ?&#x2018;&#x17D;đ?&#x2018;?â&#x2C6;&#x2014;đ?&#x2018;&#x2020;â&#x201E;&#x17D;đ?&#x2018;&#x2013;â&#x2C6;&#x2014;đ??´đ?&#x2018;Ł)+đ?&#x2018;&#x2021;â&#x201E;&#x17D;â&#x2C6;&#x2014;(đ?&#x2018;Ą replacement + đ?&#x2018;Ą travel ) 2 đ?&#x2018;&#x2021;â&#x201E;&#x17D;â&#x2C6;&#x2014;(đ?&#x2018;Ą replacement + đ?&#x2018;Ą travel ) (1 â&#x2C6;&#x2019; Ađ?&#x2018;Ł) â&#x2C6;&#x2014; â&#x20AC;&#x201C; đ?&#x2018;&#x2026;đ?&#x2018;&#x2013; ) 2

đ??ľđ?&#x2018;&#x2013; = max (0 , Ađ?&#x2018;Ł â&#x2C6;&#x2014;

4.3.

+ (13)

Case study: optimal UBM policy

In this section, we state the input values for our scenarios, find the optimal maintenance moments and compare the UBM policy with the current maintenance policies.

4.3.1.

Optimal maintenance policy

The input values used for the UBM policy can be found in Table 6 and an explanation about how we determined the values variables can be found in Appendix K. Because most input values needed to determine the downtime cost are customer specific, we decide to consider three different scenarios: small sites, medium sites and large sites. By doing this we make the distinction between different sites but do not have to gather the values for all customers. An indication for the Cap, q, Th, nSPO and Shi for the three different scenarios is provided by a senior system engineer at Vanderlande. He has a good insight in these values for the three scenarios as he designs these systems. Currently these numbers are only based on the knowledge of this senior system engineer, after he consulted with some colleagues.

He mentions that it is possible to get more specific data if employees would visit sites and the data would be even better if employees could visit multiple sites and take an average. However due to time constraints, this was not possible to do. The system engineer estimates that more validated data would be available within a year. In the future, it would be great if this data is available per customer because then, the cost can be calculated per customer to find an optimal policy specific per customer.

With the input variables from Table 6, we can find the UBM policy for the three different scenarios.

Using MATLAB to calculate the optimal values of Ď&#x201E;, we find the following optimal replacement moments: Ď&#x201E;Small* = 3449 running hours Ď&#x201E;Medium* = 4047 running hours Ď&#x201E;Large* = 81890 running hours

(about 2.65 years) (about 1.20 years) (about 19.68 years)

Note that 19.68 years is longer than the lifetime of the systems of Vanderlande and thus we only replace the belt when it fails. This means that the UBM policy is not useful for timing belts at large sites. The reason is that the other parallel SPOs can compensate for all the lost throughput because of which Cip is equal to Ciu. This may be different for other components at large sites as the repair time differs.

23

Table 6: Input variable for the UBM policy

Variable Scenario Îą β Cisparepart WMaintenance tireplacement ttravel đ?&#x2018;&#x160;Operational Cap per sorter q per sorter Shi Th per sorter WIParcel WIMaxTruck #KM â&#x201A;Ź/KM N 4.3.2.

Small 7592.52 1.3688 â&#x201A;Ź16.93 â&#x201A;Ź54 1.88 hours 2 hours â&#x201A;Ź26 3000 pph 3 workers 5 hours 2000 pph 8 KG 1200 KG 100 KM â&#x201A;Ź0.59/KM 1

Input parameters Medium 7592.52 1.3688 â&#x201A;Ź16.93 â&#x201A;Ź54 1.88 hours 2 hours â&#x201A;Ź26 6000 pph 21 workers 13 hours 3842 pph 8 KG 1200 KG 100 KM â&#x201A;Ź0.59/KM 2

Large 7592.52 1.3688 â&#x201A;Ź16.93 â&#x201A;Ź54 1.88 hours 2 hours â&#x201A;Ź26 2400 pph 8 workers 16 hours 1563 pph 8 KG 1200 KG 100 KM â&#x201A;Ź0.59/KM 10

Comparison UBM policy with current maintenance policy

Looking at the maintenance manuals for the SPO, Vanderlande advices to do periodic inspections on the timing belt entry. These inspections are advised every three months. During these inspections, the maintenance engineer checks if the timing belt is worn out and once per year they need to check if the tension of the timing belt meets the requirements. At the end, the maintenance engineer decides if the belt gets replaced This type of CBM can be modelled using delay time degradation (see Arts, 2017, Chapter 5). However, there is no data available about when a maintenance engineer inspects a specific belt and whether or not it is replaced. Although Vanderlande advises inspections for the timing belt, the SPO expert mentions that it is hard to detect the wear-out with the eye. Because of the lack of data and the experience of the SPO expert, we assume that the window to detect a possible failure is very short, so it is impossible to detect a defect belt. Thus, we decide to compare the UBM policy with a failurebased policy. Note that there are replacements of timing belts that happen during a periodic inspection but these replacements are probably based on the knowledge of the maintenance engineer in place.

A failure-based policy means that the component is replaced when it fails and the cost Cu are incurred.

The costs up to time t form a renewal reward process. The ECL in this case is the mean time to failure, E[T] and the ECC under are Cu. Therefore the expected costs per time unit, g(â&#x2C6;&#x17E;), can be found by: g(â&#x2C6;&#x17E;) đ??śu

= đ??¸[T] (Arts, 2017). E[T] of the Weibull distribution with the Îą and β from Section 4.2 can be calculated with the equation from Appendix I and Cu is calculated by Equation (7).

For the three scenarios considered in the previous section, we compare the value of g(â&#x2C6;&#x17E;) for the failurebased policy with the value of g(Ď&#x201E;) for the UBM policy with Ď&#x201E; being Ď&#x201E;Small*, Ď&#x201E;Medium* and Ď&#x201E;Large*, respectively.

The values of g(â&#x2C6;&#x17E;) and g(Ď&#x201E;) can be found in Table 7. We can conclude that that the UBM policy is indeed better than a failure-based policy for the small and medium scenario but performs equally well for the large scenario. Using a UBM policy for the timing belt for small and medium scenario saves respectively 24

16.2% and 13.1% (€986 and €1734 per timing belt for the lifetime of the system) in cost in the long run.

This also makes sense as we already concluded that PM should be beneficial compared to a CM policy as our Weibull distribution has a β > 1, indicating an IFR. The reason why the two policies perform equally well for the large scenario is because the parallel SPOs that have not failed can completely compensate the lost throughput. Because of this, no downtime occurs and Cip is equal to Ciu. If doing PM is just as expensive as doing CM, we want to do CM because we use more of the components lifetime. We thus show that the value of UBM is not only dependent on the component but also on the customer site.

Note that this UBM policy never provides a worse solution than a failure-based policy as the UBM policy becomes a failure-based policy when the component does not have an IFR or Cip is equal to Ciu. Table 7: Comparison UBM policy vs failure-based policy

Scenario UBM policy: g(τ) Failure-based policy: g(∞) Small 0.2612 0.3118 Medium 0.2263 0.2605 Large 0.0326 0.0326 Compared to the current periodic inspection policy, the UBM policy has a few benefits for Vanderlande.

First, there are currently components with an IFR, like the timing belt, for which it is hard to see the state the condition during an inspection, so periodic inspections are not useful. UBM might be the strategy that better matches the degradation of the component. It is recommended to investigate how different components degrade and if this is based on usage, do UBM or possibly connect the inspection interval to this. Second, UBM can be very useful as a service offering for small customer sites. When Vanderlande has more data available, it can make a UBM policy for more components and incorporate it in their service proposition. With this UBM policy, they do not need to go to the customer for inspections but only go to the customer when the part need to be replaced preventively or correctively. This would save the inspection cost for the customer, which is especially beneficial for small customers who do not have a lot of money for maintenance services and have more time available to de maintenance.

4.4.

Conclusions

In this chapter, we answered RQ3: What is a good UBM policy for Vanderlande? with the sub-question RQ3a: What are the optimal maintenance moments under this UBM policy? and RQ3b: What are the benefits of the UBM policy compared to the current maintenance policy?

For RQ3a, we defined a single-component age-based policy that determines the optimal replacement moment based on the PM cost, CM cost and the lifetime distribution of the component. We fitted a Weibull distribution to the, in Chapter 3, collected data and defined equations for the PM and CM cost.

Furthermore, we find the optimal replacement moment for the timing belt for three different scenarios, which represent a small, a medium and a large SPO site. For answering RQ3b, we compared the UBM policy with a failure-based policy and find that the UBM policy saves 16.2%, 13.1%, and 0% in maintenance costs for the timing belt for the small site, medium site and large site scenario, respectively.

We show that, although the component has an IFR, it is not always beneficial to do UBM as the redundancy in the system can make up for lost capacity. Thus, the value of UBM is not only dependent on the component but also on the customer site. This is something that should be taken into account when using the MPS-model of Alcorta (2017). The MPS-model considers a component and an equipment level but does not take the complete system with its redundancy into account.

25

INVENTORY CONTROL MODEL In this chapter, we answer RQ4. In Section 5.1 and 5.2, we describe the model and how to solve it.

Section 5.3 shows the optimal stock levels of this model and in Section 5.4, we state our conclusions.

In this research, we want to use the ADI from the developed UBM policy in Vanderlandeâ&#x20AC;&#x2122;s inventory control. However, before developing such a model, we first develop a basic spare parts inventory model because Vanderlande does not have such a model in place. As discussed in Section 1.3.2, Vanderlande currently sells the spare parts to its customers, who then take the ownership of the spare parts. When the customer is out of stock, they can ask Vanderlande for a replenishment, but for more general parts the customer can also buy the items somewhere else. When Vanderlande moves to selling spare parts as a service, most spare parts are probably stocked at a quick response stocks (QRS) instead of at the customer. Note that for critical, fast moving parts it is still a good strategy to have a safety stock at the customer but the critical, slow moving parts should be stored in a QRS to reduce the number of parts in the supply chain and still be able to deliver a certain service level to all customers. Due to time limitations, we only develop an inventory control policy for the QRS as we assume that the central warehouse always has stock available to deliver the QRS within a certain lead time.

5.1.

Multi-item, single-location inventory model with emergency shipments

The model discussed in this section is largely based on the model in Chapter 2.9 of van Houtum and Kranenburg (2015). This is a multi-item, single-location model that makes use of emergency shipments in case of a stock out and takes the aggregate mean waiting time as service measure. They mention that this model is especially fit for a local warehouse when it is assumed that the central warehouse has infinite stock. We refer to the local warehouse as a QRS. In this section, we explain this model with the variables and the assumptions. Because the model is largely based on van Houtum and Kranenburg (2015), we mention where the differences between our model and their model are, but where no differences are mentioned, the models are the same.

In the model, a QRS keeps stock of several spare parts to serve multiple customerâ&#x20AC;&#x2122;s machines of the same type. When a critical spare part fails at the customer, a new spare part is needed as soon as possible to replace the failed one (repair by replacement). We refer to these critical spare parts as stock keeping units (SKUâ&#x20AC;&#x2122;s). We denote the set of SKUâ&#x20AC;&#x2122;s by I and the number of SKUâ&#x20AC;&#x2122;s is denoted by |I| Đ&#x201E; â&#x201E;&#x2022; = {1, 2,â&#x20AC;Ś}. We denote the set of customers served by a QRS as J and the number of customers is denoted by |J| Đ&#x201E; â&#x201E;&#x2022;. One of the assumptions of this model is that the demand for different SKUâ&#x20AC;&#x2122;s follows an independent Poisson process with a constant (demand) rate mi (â&#x2030;Ľ0). This assumption should be checked for every SKU i and for every customer j and how we checked this assumption is explained in Section 5.3. The demand rate that the QRS is facing for the SKU i is calculated with the following equation: đ?&#x2018;&#x161;đ?&#x2018;&#x2013; = â&#x2C6;&#x2018;đ?&#x2018;&#x2014;Đ&#x201E;đ??˝ đ?&#x2018;&#x203A;đ?&#x2018;&#x2013;,đ?&#x2018;&#x2014; â&#x2C6;&#x2014; đ?&#x2018;&#x161;đ?&#x2018;&#x2013;,đ?&#x2018;&#x2014; ,

â&#x2C6;&#x20AC;đ?&#x2018;&#x2013;Đ&#x201E;đ??ź

(14)

with đ?&#x2018;&#x203A;đ?&#x2018;&#x2013;,đ?&#x2018;&#x2014; being the number of times that SKU i exists in the system of customer j and đ?&#x2018;&#x161;đ?&#x2018;&#x2013;,đ?&#x2018;&#x2014; the demand rate for one SKU i at customer j. This equation assumes that all the same SKUs i at customer j have the same demand rate. This equation is not defined in the model by van Houtum and Kranenburg (2015) as they assume that đ?&#x2018;&#x161;đ?&#x2018;&#x2013; is given, however they mention that this can be any value larger or equal to zero.

The total demand rate for all SKUâ&#x20AC;&#x2122;s is defined as M = â&#x2C6;&#x2018;đ?&#x2018;&#x2013;Đ&#x201E;đ??ź đ?&#x2018;&#x161;đ?&#x2018;&#x2013; and it is assumed that M >0.

26

The stock in the QRS is controlled by a continuous-review base stock policy. This means that when one part is sent to the customer, a new one is ordered immediately. This part is delivered to the QRS after a deterministic replenishment lead time, indicated by Li (>0) for SKU i. We assume that the replenishment lead times of different SKUâ&#x20AC;&#x2122;s are independent and that the replenishment lead times for the same SKU are independent and identically distributed. We assume that an emergency shipment can be done when a part is not on stock at the QRS. An emergency shipment means that the part is shipped directly to the customer from the central warehouse or the external supplier. This means that the demand is observed as a lost sale at the QRS. Emergency shipments are more expensive than the normal shipments due to their unexpected and fast delivery, but they are very useful to prevent downtime. We assume that an emergency shipment is possible because backordering is not preferable as we only consider critical spare parts, so the customer does not want to wait for the part as its system is down. According to the spare part manager, this is a valid assumption as an emergency shipment should be possible. The physical stock at the QRS for SKU i plus the number parts for this SKU on their way to the QRS is a constant number (Si). Si is called the base-stock level for SKU i and the base-stock levels are the decision variables in the model. A graphical representation of the inventory control system is given in Figure 5.

Central warehouse

Customer

QRS

Emergency shipments Normal shipments Demand

1

CW (Best)

. . . .

QRS 1

2

. . . .

. . . .

QRS 59

I-1

I

Figure 5: graphical representation of the inventory control system

The objective of the model is to minimize the total inventory holding cost and emergency shipment cost, subject to the constraint on the aggregate mean waiting time. We use the aggregate mean waiting time because the model of Van den Bosch (2017), used to determine the position of the QRS, is also based on the expected time to reach a customer, which makes these two models align. We first elaborate on how we find the costs for the model and then we explain how we find the aggregate mean waiting time.

The inventory holding cost for one part of SKU i is denoted as đ??śđ?&#x2018;&#x2013;h (>0) and the cost for an emergency shipment for one part of any SKU for a specific customer j is denoted đ??śđ?&#x2018;&#x2014;em (>0). The đ??śđ?&#x2018;&#x2013;h is assumed to be the acquisition cost of a SKU. Vanderlande needs to buy this SKU and put it in stock. The more items they put in stock, the more investment in spare parts they need to make but the probability that a stock out occurs becomes lower. Next to that, there are the one-time investment cost for a building to store the spare parts but this cost is not incorporated in our model because it is fixed and needs to be made anyway. The đ??śđ?&#x2018;&#x2014;em is the cost for a fast delivery procedure of any spare part from the central warehouse to customer j. The spare parts manager mentions that the cost for an emergency shipment are not dependent on the SKU but on the distance between the central warehouse in Best and customer j. It is also possible that for more important customers, the emergency cost will be higher in the future than for less important customers. Having the emergency shipment cost is different per customer and not per SKU is a difference compared to the model of van Houtum and Kranenburg (2015). To still use their model, we calculate a weighted average emergency cost (đ??śđ?&#x2018;&#x2013;e ) for each SKU i based on the percentage of demand that the QRS expects for SKU i for customer j and the emergency cost per customer j: 27

đ??śđ?&#x2018;&#x2013;e =â&#x2C6;&#x2018;đ?&#x2018;&#x2014;Đ&#x201E;đ??˝

đ?&#x2018;&#x203A;đ?&#x2018;&#x2013;,đ?&#x2018;&#x2014; â&#x2C6;&#x2014; đ?&#x2018;&#x161;đ?&#x2018;&#x2013;,đ?&#x2018;&#x2014; đ?&#x2018;&#x161;đ?&#x2018;&#x2013;

â&#x2C6;&#x2014; đ?&#x2018;?đ?&#x2018;&#x2014;em

â&#x2C6;&#x20AC;đ?&#x2018;&#x2013;Đ&#x201E;đ??ź

(15)

Now that we have đ??śđ?&#x2018;&#x2013;e , we need to find the expected amount of emergency shipments needed for SKU i.

This is the probability that an arbitrary demand for a SKU cannot be fulfilled from stock, which is the same as one minus the probability that there is at least one item of SKU i on stock. Because we assume that the demand for a SKU occurs according to a Poisson process, each failed SKU i stays a deterministic time Li in the replenishment pipeline, and emergency shipments that bounds the pipeline stock of SKU i to a maximum of Si, makes the system act like a M|G|c|c queue with c = Si parallel servers, arrival rate mi and service time Li. The M|G|c|c queue is also called an Erlang loss system. We can obtain the fill rate βi(Si) for SKU i with the Erlang loss probability. â&#x20AC;&#x153;The fill rate is equal to the fraction of time that there is at least one part on stock. This is equal to the fraction of time that at least one server is free in the corresponding Erlang loss system. The latter probability is equal to 1 minus the fraction of time that all servers are occupiedâ&#x20AC;? (van Houtum & Kranenburg, 2015, p.41). The equation for the fill rate βi(Si) is: βi(Si) = 1 â&#x20AC;&#x201C;

1 (đ?&#x2018;&#x161;đ?&#x2018;&#x2013; đ??żđ?&#x2018;&#x2013; )đ?&#x2018;&#x2020;đ?&#x2018;&#x2013; đ?&#x2018; đ?&#x2018;&#x2013; ! đ?&#x2018; đ?&#x2018;&#x2013; 1 â&#x2C6;&#x2018;đ?&#x2018;&#x2014;=0 (đ?&#x2018;&#x161;đ?&#x2018;&#x2013; đ??żđ?&#x2018;&#x2013; )đ?&#x2018;&#x2014; đ?&#x2018;&#x2014;!

â&#x2C6;&#x20AC;đ?&#x2018;&#x2013;Đ&#x201E;đ??ź

(16)

Combining the cost for holding and emergency shipments results into the total cost for SKU i: Ci(Si) = đ??śđ?&#x2018;&#x2013;h â&#x2C6;&#x2014; đ?&#x2018; đ?&#x2018;&#x2013; + đ?&#x2018;&#x161;đ?&#x2018;&#x2013; * (1- βi(Si)) * đ??śđ?&#x2018;&#x2013;e

â&#x2C6;&#x20AC;đ?&#x2018;&#x2013;Đ&#x201E;đ??ź

(17)

The total cost connected to the QRS is the sum of the total cost for all SKUâ&#x20AC;&#x2122;s đ?&#x2018;&#x2013; Đ&#x201E; đ??ź: C(S) = â&#x2C6;&#x2018;đ?&#x2018;&#x2013;Đ&#x201E;đ??ź đ??śđ?&#x2018;&#x2013; (đ?&#x2018;&#x2020;đ?&#x2018;&#x2013; ) where S is the vector consisting of all base stock levels, S = (S1, â&#x20AC;Ś , SI).

(18)

Next, we explain the equation for the aggregated mean waiting time (W(S)). In our model, we assume two possible waiting times for the customer. The first is the normal waiting time (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;&#x;đ?&#x2018;&#x17D;đ?&#x2018;Łđ?&#x2018;&#x2019;đ?&#x2018;&#x2122; ), when a part is available from stock. We also assume đ?&#x2018;Ą travel to be constant and not depending on SKU i or customer j. This is because van den Bosch (2017) determines the locations of these QRSâ&#x20AC;&#x2122;s in a way that any part to any customer should always be delivered within a certain time. Van Houtum and Kranenburg (2015) assume that, when a part is available on stock, the delivery of the part is instant and thus đ?&#x2018;Ą travel is equal to zero. Second, there is the emergency waiting time (đ?&#x2018;Ą em ), when a part is not available from stock. The đ?&#x2018;Ą em is al not dependent on the SKU i or customer j. In the model of van Houtum and Kranenburg (2015), the emergency shipment time is depending on the SKU, which is thus a difference with our model. Using the fill rates, we can determine the average mean waiting time per SKU i, Wi(Si): Wi(Si) = (1- βi(Si)) * đ?&#x2018;Ą em + βi(Si) * đ?&#x2018;Ą travel

â&#x2C6;&#x20AC;đ?&#x2018;&#x2013;Đ&#x201E;đ??ź

(19)

The aggregated mean waiting time for all SKUâ&#x20AC;&#x2122;s is equal to: W(S) = â&#x2C6;&#x2018;đ?&#x2018;&#x2013; â&#x2C6;&#x2C6;đ??ź

đ?&#x2018;&#x161;đ?&#x2018;&#x2013; đ?&#x2018;&#x160;đ?&#x2018;&#x2013; (đ?&#x2018;&#x2020;đ?&#x2018;&#x2013; ) đ?&#x2018;&#x20AC;

(20)

Vanderlande does not want the customer to wait for, on average, more than a maximum amount of waiting time until the required spare parts are on site (Wobj). Thus, we want to find the optimal Si levels, for which we minimise C(S) while keeping W(S) below or equal to Wobj. This gives optimization problem (P). There is a related multi-objective problem (Q) where C(S) and W(S) are both minimised: 28

Problem (P): Min Subject to

5.2.

Problem (Q): Min Min Subject to

C(S) W(S) â&#x2030;¤ Wobj S Đ&#x201E; Solution space

C(S) W(S) S Đ&#x201E; Solution space

Greedy algorithm

This section is based on the work of van Houtum and Kranenburg (2015, Chapter 2.9), which state that we can find efficient solutions for problem (Q). A solution is defined as efficient if and only if there is no other solution in the solution space where C(Sâ&#x20AC;&#x2122;) â&#x2030;¤ C(S) and W(Sâ&#x20AC;&#x2122;) â&#x2030;¤ W(S) and the strict inequality for at least one of these inequalities holds. These solutions are found by a greedy algorithm where all the efficient solutions together form the efficient frontier. An optimal solution for problem P can be picked from this efficient frontier by taking the first solution where W(S) â&#x2030;¤ Wobj. A greedy algorithm is possible because Ci(Si) is convex on its whole domain for each i and Wi(Si) is concave and decreasing on its whole domain for each i. This is because βi(Si) is strictly concave and increasing on its whole domain for each i. Note that Ci(Si) is not always increasing in Si because of the presence of the emergency cost and we have a lower bound on Wi(Si), which is equal to ttravel. With these properties, we can formulate the greedy algorithm shown in Algorithm 1 (Algorithm 2.3 from van Houtum and Kranenburg (2015)).

Algorithm 1 works as follows: the first efficient solution is found by finding the Si values for each SKU where the cost Ci(Si) is the lowest. Ci(Si) may be decreasing for the lower values of Si and Wi(Si) is always decreasing in Si (until the lower bound ttravel). Because of this, increasing Si to get a lower Ci(Si) and lower Wi(Si) is always a good idea. Per SKU, the Si where Ci(Si) is at its minimum becomes the Si,min and the values of Si < Si,min are excluded from the solution space. Next, the algorithm increases Si by one for each SKU and computes Î&#x201C;i, which is the highest decrease in W(S) relatively to the increase in cost C(S): Î&#x201D;đ?&#x2018;&#x2013;đ?&#x2018;&#x160;(đ??&#x2019;)

Î&#x201C;i := â&#x2C6;&#x2019; Î&#x201D;iđ??ś(đ??&#x2019;)

â&#x2C6;&#x20AC;đ?&#x2018;&#x2013;Đ&#x201E;đ??ź

(21)

with Î&#x201D;iW(S) =

đ?&#x2018;&#x161;đ?&#x2018;&#x2013; Î&#x201D;Wi(Si) đ?&#x2018;&#x20AC;

=

đ?&#x2018;&#x161;đ?&#x2018;&#x2013; (Wi(Si+1) đ?&#x2018;&#x20AC;

â&#x2C6;&#x2019;Wi(Si))

Î&#x201D;iC(S) = Î&#x201D;Ci(Si) = Ci(Si+1) â&#x2C6;&#x2019; Ci(Si).

After doing this for all SKUs, we find the highest Î&#x201C;i and increase the base stock of this SKU by one. We keep doing this step until a stop criterion is reached. This stop criterion is W(S) â&#x2030;¤ Wobj.

Algorithm 1: Greedy Algorithm Step 1: Si,min := arg min Ci(Si) for all i â&#x2C6;&#x2C6; I; Set Si := Si,min for all i â&#x2C6;&#x2C6; I, and S = (S1,min, . . ., S|I|,min); E := {S}; Compute C(S) and W(S).

Step 2: Î&#x201C;i := â&#x2C6;&#x2019;

đ?&#x2018;&#x161;đ?&#x2018;&#x2013;â&#x2C6;&#x2014;Î&#x201D;đ?&#x2018;&#x160;đ?&#x2018;&#x2013;(đ?&#x2018;&#x2020;đ?&#x2018;&#x2013;) đ?&#x2018;&#x20AC;â&#x2C6;&#x2014;Î&#x201D;đ??śđ?&#x2018;&#x2013;(đ?&#x2018;&#x2020;đ?&#x2018;&#x2013;)

for all i â&#x2C6;&#x2C6; I;

k := arg max {Î&#x201C;i : i â&#x2C6;&#x2C6; I}; S := S+ek; E := E â&#x2C6;Ş {S}.

Step 3: Compute C(S) and W(S); If â&#x20AC;&#x2DC;stop criterionâ&#x20AC;&#x2122;, then stop, else go to Step 2.

29

5.3.

Results

In this section, we first define the parameter setting that we used to run the model of Section 5.1 and after that we present the solution found using Algorithm 1.

5.3.1.

Parameter settings

An overview of the parameter settings is given in Table 8. In our case, we only focus on components that could provide five or more data points. As we do not have usage information for all the considered customer sites, we decide to use the days between failures to find the failure distribution. The considered components are three timing belts that have five data points after our search for failure data.

This means that |I| = {1,2,3} and the decision variables are S1, S2 and S3. The set J considered in this research is deducted from the research of Van den Bosch (2017). In his research, he makes a model to determine where Vanderlande should place their QRSâ&#x20AC;&#x2122;s. We use his positioning of the QRSâ&#x20AC;&#x2122;s in a way that the customers can always be reached within two hours after a demand occurs (ttravel). He takes European customers in the parcel and postal market into account. We select the customers from van den Bosch (2017) that use at least one of the three timing belts in their SPO. This results into 152 customer sites, which are served by 59 different QRSâ&#x20AC;&#x2122;s. The considered customer sites, together with the number of times SKU i occurs in their SPO (nij) and the QRS allocation, can be found in Appendix L. Table 8: Variable settings for the inventory control model

Variable |I| |J| nij mij

Setting {1,2,3} Different per QRS, can be found in Appendix L Different per customer j, can be found in Appendix L 1

1

1

{920 , 616 , 1549} â&#x2C6;&#x20AC;jĐ&#x201E;đ??˝

Li {15,15,15} days travel t 1/12 days (2 hours) tem 1 day h Ci {â&#x201A;Ź12.03, â&#x201A;Ź15.93, â&#x201A;Ź17.93} Cjem Different per customer j, can be found in Appendix L obj W 3/24 days (3 hours) Before we can determine values for mij, we need to check the assumption that the demand follows an independent Poisson process with a constant (demand) rate mij (â&#x2030;Ľ0). If this is true, we can add up all the demand rates for the same SKU i at customer j. This is because nij is a multiplier for the times that a SKU i is in the system of customer j and the distribution of multiple independent Poisson distributions together is still Poisson distributed with a Lambda equal to the individual Lambdas added together.

The failures of all the timing belts are independent processes as a failure of the timing belt does not lead to a failure of another component in the SPO. It does lead to a failure of the SPO itself, which makes it a critical component. Furthermore, Van Houtum and Kranenburg (2015) mention that the assumption of a Poisson process is justified when the lifetime distribution is exponential or generally distributed and the number of machines that is served by the warehouse is sufficiently large. Due to the low data availability about the failures of components (i.e. the demand for spare parts), it was hard to check this assumption. We did this by looking at the times between failure of the data points that were also available for the UBM policy. These times can be found in Appendix F. We perform a Chi-squared test in MATLAB for all three components and we do not reject the null hypothesis stating that the data follows 30

an exponential distribution with mean đ?&#x2018;&#x161;đ?&#x2018;&#x2013;đ?&#x2018;&#x2014; on a significance level of 5% (p-value = 0.7937 for S1, 0.1903 for S2 and 0.6647 for S3). Because there is no strong evidence to indicate that the data is not exponentially distributed, we assume that it is. We find that đ?&#x2018;&#x161;đ?&#x2018;&#x2013;đ?&#x2018;&#x2014; is 920 days for i=1, 616 days for i=2 and 1549 days for i=3. In our case, đ?&#x2018;&#x161;đ?&#x2018;&#x2013;,đ?&#x2018;&#x2014; is the same for each customer j but if it can be measured in usage, it is possible than this value can differ per customer j. Unfortunately, the number of machines that is served by a QRS is not sufficiently large and for some QRSâ&#x20AC;&#x2122;s it is even below ten. However, because there is no other data available to validate Poisson distributed demand, we assume that this assumption is correct. When more data about the spare parts demand is available, this assumption should be justified.

For the replenishment lead time Li, we took the lead time that Vanderlande currently uses as indicator for how long it takes from ordering a part until it is delivered to the customer. This is a constant number that can be found in the spare parts list and is equal to 15 days for all these items. Cih for SKU i is equal to the purchasing price of the SKU and Cjem per customer j are determined by the distance between the central warehouse in Best and the location of the customer as the spare parts manager mentions that the emergency cost is about â&#x201A;Ź1/KM. The difference in KMs is shown in Appendix L. He also mentions that using an emergency shipment should mean that the product is available for the customer within 24 hours. Looking at the information about the Express delivery of DHL in van den Bosch (2017), this indicates that a next day delivery is possible within Europe. Because of this, we set tem to be one day.

Last, we need to decide on the objective mean aggregated waiting time (Wobj). This is discussed with the spare parts manager and he determines that the average waiting time should be about three hours.

5.3.2.

Optimal base stock levels for the QRSâ&#x20AC;&#x2122;s

In this section, we run algorithm 1 for all 59 QRSâ&#x20AC;&#x2122;s to solve the inventory control model with the input values from Table 8. Table 9 shows the Si for the three timing belts and the W(S) and C(S) for each QRS. In total, there are 205, 111 and 137 parts running of SKU 1, SKU 2 and SKU 3, respectively, at all 152 customer sites together. Looking at the result, our model stocks respectively 67, 61 and 55 parts of these three timing belts in all the QRSâ&#x20AC;&#x2122;s. Currently, Vanderlande calculates the number of spare parts to be stocked at the customer by looking at the number of units of a spare part in a system and multiply it by a percentage determined by R&D. This number is compared with a predetermined minimum and maximum number to come up with final number. For the three timing belts, the predetermined percentage is 5%, the minimum number of stock spare parts is one and the maximum amount of spare parts stocked is four. If we use the current policy, we find that there are respectively 140, 93 and 137 parts of the three SKUs stocked at the 152 different customers, respectively. Our model results in a reduction of respectively 52.14%, 34.41% and 59.85% for these three spare parts stocked at the end of the supply chain. This reduction is because the stock is pooled to serve multiple customers from a single location. The expected cost for the long run for these three items for all the QRSâ&#x20AC;&#x2122;s is â&#x201A;Ź2774.59: â&#x201A;Ź2763.89 holding cost and â&#x201A;Ź10.70 emergency shipment cost. The fact that the holding cost is so high compared to the emergency shipments cost makes sense because we have Wobj close to the lower bound. Having an emergency shipment would increase W(S) to much and the model tries to avoid it. In the current model, Vanderlande has no cost as the customer owns the spare parts but the holding costs for the components that are stocked at the customer is â&#x201A;Ź5622.10. If we assume no emergency shipments in the current situation, the new model results into a reduction of 50.64% in costs for only these three spare parts.

Note that we only use three spare parts that are all low value products, if this model is executed with a larger set of products and incorporates high value spare parts, the cost savings will be even higher.

31

Table 9: Output of the inventory control model

QRS 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 5.4.

S1 S2 S3 1 2 4 2 2 1 2 2 2 1 1 1 2 1 2 1 2 1 1 1 1 1 1 1 0 0 1 1 1 1 0

1 1 0 1 1 0 2 1 1 1 1 1 2 1 1 1 2 1 1 1 1 1 1 2 1 1 0 1 0 2 1

1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1

W(S) (Hours) 2.80 2.76 2.69 2.69 2.58 2.59 2.67 2.78 2.90 2.41 2.41 2.79 2.81 2.80 2.81 2.41 2.56 2.41 2.41 2.78 2.41 2.41 2.41 2.49 2.43 2.43 2.35 2.56 2.58 2.33 2.43

C(S) (â&#x201A;Ź)

QRS

S1

S2

S3

46.03 58.35 48.94 58.09 58.16 30.04 73.96 58.06 58.43 45.91 45.93 45.95 74.01 46.05 58.14 45.94 74.15 45.96 45.93 46.03 45.94 45.94 45.94 61.97 33.92 33.91 12.05 46.01 30.04 62.02 33.94

32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59

0 1 0 1 0 1 1 1 1 1 2 2 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 0 Sum S1 67

1 2 0 1 1 0 1 0 2 0 0 2 1 1 1 1 2 2 2 0 2 0 2 1 1 1 1 1 Sum S2 61

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 Sum S3 55

Total

W(S) (Hours) 2.43 2.23 2.21 2.75 2.43 2.58 2.92 2.30 2.85 2.30 2.13 2.44 2.41 2.80 2.80 2.41 2.35 2.66 2.44 2.30 2.96 2.69 2.23 2.89 2.80 2.41 2.80 2.43 Average W(S) 2.56

C(S) (â&#x201A;Ź) 33.94 61.91 17.94 46.13 33.91 30.04 46.22 30.01 62.32 30.01 42.05 74.06 45.96 46.16 46.24 45.93 74.20 62.71 61.83 29.96 61.94 12.04 61.83 28.22 46.80 46.12 46.41 33.96 Sum C(S) 2774.59

Conclusion

In this chapter, we answered RQ4: What should the basic inventory control model of Vanderlande look like for the component(s) in this research and how large is the benefit compared to the current model?

We defined a multi-item, single-location inventory model with emergency shipments in case of a stock out, based on the model of Chapter 2.9 of van Houtum and Kranenburg (2015), that can be used for the QRS. The model minimises the expected holding and emergency costs while meeting a service level constraint, which is the mean aggregate waiting time. Using the proposed model for only three components and 152 customers in Europe results in a reduction of 50.64% in holding cost and emergency cost compared to the current policy of Vanderlande. If this model is executed with a larger set of products and incorporates high value spare parts, the cost savings will be even higher.

32

INVENTORY CONTROL MODEL WITH ADI FROM THE UBM POLICY In this section, we answer RQ5. In Section6.1, we explain the PMAO and PMAO-extension policy of Coumans (2017). In Section 6.2, we define our own ADI policy and in Section 6.3, we compare our ADI policy and some ADI policies in literature. In Section 6.4, we state our conclusions.

6.1.

PMAO and PMAO-extension policy

As part of the ProSeLoNext project, research has been done at Océ in Venlo on the use of ADI contained in the UBM and CBM planning, to improve spare parts inventory planning. The results are in the master thesis by Coumans (2017). He uses the aging information and the PM threshold in a single-location, multi-item inventory system that is periodically reviewed. The author first develops the so-called Preventive-Maintenance-based Advance Order (PMAO) policy and after that he makes an extension to that, which he names the PMAO-extension policy. We shortly explain the two policies in this section.

6.1.1.

Two demand streams and advance order threshold

Coumans (2017) develops two inventory policy that “make use of part-age information to improve the matching of supply with demand for service parts and thus decreases costs” (p.20). He mentions that his policies can be used for spare parts that are maintained using a PM strategy. The idea is as follows: because a usage threshold τ is defined for the components, it is possible to determine when the replacement takes place and thus when the part is needed. However, it is possible that the part fails before this threshold is reached and when this happens, we perform CM. This results into two demand streams: PM demand that can be forecasted based on the age information (imperfect ADI) and CM demand that cannot be forecasted and is random. We explain how the demand streams are controlled.

The CM demand stream is controlled by the model from Section 2.9 of van Houtum and Kranenburg (2015), which is a base stock policy that uses emergency shipment in case of a stock out. This is the same model on which we base our inventory control model in Chapter 5. Note that the demand rates for the items are lower compared to the demand rate in the model of Chapter 5 as that model considers all demand to be corrective and this model also processes demand as preventive.

Advance order triggered for PM action

Advance order triggered for PM action

Part Age

PM delay PM action

PM action

PM threshold Advance order threshold

If CM demand occurs in this interval, satisfy from CM stock

Time

Figure 6: Part aging, allocation rules and ordering decisions (Coumans, 2017)

For the PM demand stream, there is no base stock at the QRS but these parts are ordered when the advance order threshold is reached. The first moment that the company observes that the usage of the component is above the advanced order threshold, the part is shipped from the central warehouse to 33

the QRS, at which it arrives after a deterministic lead time. A PM demand is fulfilled when the company observes that the component has reached the usage threshold Ď&#x201E; and there is a part on stock. It would be ideal if the aging rate is fully deterministic because then we can make sure that the PM parts arrive in a just-in-time fashion. Unfortunately, the aging of most parts is not fully deterministic but faces variance. If the PM action cannot be executed, the PM is delayed. This means that the demand for this PM action is backordered and not executed when the PM was planned initially. In Figure 6, the graphical representation of the part aging, allocation rules and ordering decisions is shown.

6.1.2.

PMAO policy

The sequence of events per period of this policy is visualized by Coumans (2017) and shown in Figure 25 in Appendix M. First, the replenishment orders for the CM and PM inventory pool arrive that have been ordered the lead time periods ago and the in-transit inventory moves one period closer to the QRS. Second, the outstanding backorders for the PM demand are directly satisfied. The age of these items is set back to zero. After this, it is checked if an item has passed the PM threshold in the current period and if this is the case and sufficient parts are available in the PM inventory pool, the PM actions are done in the current period. After performing a PM action on an item, the age is set to zero. If insufficient PM parts are available, the PM action is delayed and the PM parts are backordered. After this step, the advance order signals are counted and replenishment orders are placed for both stocks. During the period, corrective demand may arrive and is satisfied from the CM inventory pool if possible. Coumans (2017) mentions that the age of the item is only set to zero after a CM action when the corrective demand matches the number of times this item is in the machine. This is because PM actions are performed for all the same components in the system (block replacement) and setting the age back to zero due to a CM action would change this. If insufficient CM parts are available on stock, an emergency procedure is used. At the end of the period, the age of the parts is increased and the cost for this period is calculated based on the on-hand inventory, emergency shipments and the PM delays.

6.1.3.

PMAO-extension

Coumans (2017) extends the PMAO policy to a policy where the inventory is no longer labelled for CM or PM but the demand is fulfilled from one common inventory pool using a FCFS allocation rule. This can be beneficial when the PM threshold is already reached but a PM part has not arrived yet. In this case, no PM delay is needed but when a CM demand occurs, it can happen that there is no inventory available to satisfy this CM demand and we need to perform an emergency procedure. This policy can also be beneficial when a CM demand occurs that we cannot fulfil from the CM inventory pool and there is PM stock available that is not allocated yet. However, the probability that this occurs is relatively small. Next to these benefits, this policy is easier to implement in practice as a part is simply be delivered when inventory is available. This is clearer for the warehouse employees who just wants to satisfy a demand.

The sequence of events, which occur every period, are shown in Figure 25 in Appendix M. 6.2.

PMAO-CM-priority policy

In this section, we discuss the PMAO-CM-priority policy, which is based on Coumans (2017) and Basten and Ryan (2015). In Section 6.2.1, we explain the sequence of events and in Section 6.2.2, we explain the used variables and equations.

34

6.2.1.

Sequence of events PMAO-CM-priority policy

The sequence of events of this policy is shown in Figure 7. First, the replenishment orders arrive, which are ordered the deterministic lead time ago and the in-transit inventory moves one period closer to the QRS. After that, we satisfy any PM backorders. When this is done, the advanced order signals are observed and new replenishment orders for the PM and CM stock are placed. The PM orders are based on the advanced order signals and the CM orders are based on the inventory control model defined in Chapter 5. After this is done, corrective demand may occur. When this happens, it is satisfied from the CM inventory pool if possible. If the CM inventory pool is empty, the demand is possibly satisfied from the PM inventory pool if a part is available. When a replacement happens, the age of the maintained components is set back to zero. If there is no stock available in both inventory pools, an emergency shipment is done and the age is reset as well. At the end of the period, the PM actions are planned if there are still parts available in the PM stock pool. If this is not the case, the demand is not being fulfilled from the CM stock pool but the part is backordered and the PM action is rescheduled to when the part arrives. Because the backorders are satisfied before the corrective demand occurs, a PM action can only be delayed once. After the PM demand is fulfilled or backordered, the costs for the parts on hand, emergency shipments, PM delays, PM actions and CM actions are calculated.

Increase age of the parts Satisfy PM Back orders t

Replenishment orders arrive

Corrective demand occurs which is satisfied from the corrective inventory pool if possible. Otherwise it is satisfied from the preventive inventory pool if possible. Last option is to perform an emergency shipment. Reset the age of the replaced part

Calculate cost t+1

If component has reached the usage threshold and preventive inventory is available, replace part preventively and reset age. If no PM inventory is available when a part hits the usage threshold, delay PM action and back order PM demand.

Count advance order signals and place corrective and preventive replenishment orders

Figure 7: Sequence of events of the PMOA-CM-priority policy

6.2.2.

Variable and equations

In this section, we describe the variables and equations that are relevant for the PMAO-CM-priority model. An overview of all variables is given in the List of variables in the beginning of the report.

General We consider the single-location, multi-item model in which a QRS keeps stock of several spare parts to serve multiple customersâ&#x20AC;&#x2122; machines of the same type. Just as in Chapter 5, we denote the set of SKUâ&#x20AC;&#x2122;s

by I and the number of SKUâ&#x20AC;&#x2122;s is denoted by |I| Đ&#x201E; â&#x201E;&#x2022;. The set of customers served by a QRS is denoted by J and the number of customers is denoted by |J| Đ&#x201E; â&#x201E;&#x2022;. Furthermore, we denote đ?&#x2018;&#x203A;đ?&#x2018;&#x2013;,đ?&#x2018;&#x2014; as the total number of times that SKU i exists in the system of customer j. When a part is ordered, it arrives at the QRS after CM (đ?&#x2018;Ą), which is the sum a deterministic lead time Li. Every period, we observe the corrective demand, đ??ˇđ?&#x2018;&#x2013;đ?&#x2018;&#x2014; PM (đ?&#x2018;Ą), of the number of failed SKU i at customer j, and preventive demand for SKU i at customer j, đ??ˇđ?&#x2018;&#x2013;đ?&#x2018;&#x2014;

which is the sum of the number of SKU i at customer j that reached the PM threshold that period. The đ??˝

value of these demands cannot be more than the number of times SKU i is served by the QRS (â&#x2C6;&#x2018;1 đ?&#x2018;&#x203A;đ?&#x2018;&#x2013;đ?&#x2018;&#x2014; ) 35

per period as we assume that the part does not fail in the period it is replaced. This is reasonable to assume as the periods we consider are very small compared to the lifetime of a component. We model the periodic review model over a finite time horizon consisting of T periods, indexed by t Đ&#x201E; {1, 2,â&#x20AC;Ś, T}.

We do not model over an infinite time horizon as it is very hard to determine the steady states for the PM demand stream, because the advance order signals are not constant over time. We simulate the model over a finite time horizon with the length of the lifetime of a system. An advantage of this is that it keeps the model simple. The downside of this is that for example at the end of the time horizon, Vanderlande is probably going to do less PM as the end of the lifetime system is coming closer. Our model does not take this into account, which means that a PM action can be done on for example the day before the end of the time horizon. Thus, the cost can be lower if this is incorporated in the model.

Age information All considered parts age with a certain rate. This rate is in terms of the usage measurement, which fits the degradation best, and can be different for all number đ?&#x2018;&#x203A;đ?&#x2018;&#x2013;,đ?&#x2018;&#x2014; of SKU i Đ&#x201E; I at customer j Đ&#x201E; J. We define đ?&#x2018;&#x;đ?&#x2018;&#x2013;đ?&#x2018;&#x2014;đ?&#x2018;&#x203A; (đ?&#x2018;Ą) as the realized aging at period t Đ&#x201E; T for number n Đ&#x201E; {1, â&#x20AC;Ś , đ?&#x2018;&#x203A;đ?&#x2018;&#x2013;,đ?&#x2018;&#x2014; } of SKU i Đ&#x201E; I at customer j Đ&#x201E; J and is equal to zero when đ?&#x2018;&#x203A;đ?&#x2018;&#x2013;,đ?&#x2018;&#x2014; = 0. We assume, just as Coumans (2017), that đ?&#x2018;&#x;đ?&#x2018;&#x2013;đ?&#x2018;&#x2014;đ?&#x2018;&#x203A; (đ?&#x2018;Ą) follows a normal distribution with đ?&#x153;&#x2021;đ?&#x2018;&#x2013;đ?&#x2018;&#x2014;đ?&#x2018;&#x203A; and standard deviation đ?&#x153;&#x17D;đ?&#x2018;&#x2013;đ?&#x2018;&#x2014;đ?&#x2018;&#x203A; . Unfortunately, it is not possible to verify this assumption with data as there is not enough data available for the usage degradation of different components. The age of number n Đ&#x201E; {1, â&#x20AC;Ś , đ?&#x2018;&#x203A;đ?&#x2018;&#x2013;,đ?&#x2018;&#x2014; } of SKU i Đ&#x201E; I at customer j Đ&#x201E; J for period t+1 is defined as đ??´đ?&#x2018;&#x2013;đ?&#x2018;&#x2014;đ?&#x2018;&#x203A; (đ?&#x2018;Ą + 1) = đ??´đ?&#x2018;&#x2013;đ?&#x2018;&#x2014;đ?&#x2018;&#x203A; (đ?&#x2018;Ą) + đ?&#x2018;&#x;đ?&#x2018;&#x2013;đ?&#x2018;&#x2014;đ?&#x2018;&#x203A; (đ?&#x2018;Ą) and is equal to zero if đ?&#x2018;&#x203A;đ?&#x2018;&#x2013;,đ?&#x2018;&#x2014; = 0. The preventive maintenance threshold for SKU i Đ&#x201E; I at customer j Đ&#x201E; J is denoted as Ď&#x201E;ij and is determined with the UBM policy defined in Chapter 0. When đ??´đ?&#x2018;&#x2013;đ?&#x2018;&#x2014;đ?&#x2018;&#x203A; (đ?&#x2018;Ą) â&#x2030;Ľ Ď&#x201E;ij, a PM demand occurs and we want the PM action to be done. The PM demand in period t Đ&#x201E; T for SKU i Đ&#x201E; I at customer j Đ&#x201E; J is defined as: đ?&#x2018;&#x203A;

PM (đ?&#x2018;Ą) = â&#x2C6;&#x2018;1 đ?&#x2018;&#x2013;đ?&#x2018;&#x2014; 1đ??´đ?&#x2018;&#x2013;đ?&#x2018;&#x2014;đ?&#x2018;&#x203A; (đ?&#x2018;Ą)â&#x2030;Ľđ?&#x153;?đ?&#x2018;&#x2013;đ?&#x2018;&#x2014; & đ??ˇđ?&#x2018;&#x2013;đ?&#x2018;&#x2014;

đ??´đ?&#x2018;&#x2013;đ?&#x2018;&#x2014;đ?&#x2018;&#x203A; (đ?&#x2018;Ąâ&#x2C6;&#x2019;1)<đ?&#x153;?đ?&#x2018;&#x2013;đ?&#x2018;&#x2014;

(22)

The part is ordered at the central warehouse when đ??´đ?&#x2018;&#x2013;đ?&#x2018;&#x2014;đ?&#x2018;&#x203A; (đ?&#x2018;Ą) â&#x2030;Ľ đ?&#x2018;&#x2021;đ?&#x2018;&#x2013;đ?&#x2018;&#x2014;đ?&#x2018;&#x203A; . đ?&#x2018;&#x2021;đ?&#x2018;&#x2013;đ?&#x2018;&#x2014;đ?&#x2018;&#x203A; is the advance order threshold for number n Đ&#x201E; {1, â&#x20AC;Ś , đ?&#x2018;&#x203A;đ?&#x2018;&#x2013;,đ?&#x2018;&#x2014; } of SKU i Đ&#x201E; I at customer j Đ&#x201E; J and is equal to infinity if đ?&#x2018;&#x203A;đ?&#x2018;&#x2013;,đ?&#x2018;&#x2014; = 0 . We set the value of đ?&#x2018;&#x2021;đ?&#x2018;&#x2013;đ?&#x2018;&#x2014;đ?&#x2018;&#x203A; in the same way as Coumans (2017): â&#x20AC;&#x153;The threshold is set such that the part is on stock in the QRS with probability βPM when đ??´đ?&#x2018;&#x2013;đ?&#x2018;&#x2014;đ?&#x2018;&#x203A; (đ?&#x2018;Ą) â&#x2030;Ľ Ď&#x201E;ijâ&#x20AC;? (p.23). By doing this, Vanderlande can offer the customer a PM service level meaning it performs the PM in the first moment when đ??´đ?&#x2018;&#x2013;đ?&#x2018;&#x2014;đ?&#x2018;&#x203A; (đ?&#x2018;Ą) â&#x2030;Ľ Ď&#x201E;ij in βPM times of the cases. Increasing βPM reduces the probability that a PM action is delayed but also increases the holding cost as the parts are in stock earlier. Because we know the deterministic lead time Li and assume that the aging occurs according to a normal distribution, we can calculate the expected aging during this lead time and calculate the value of đ?&#x2018;&#x2021;đ?&#x2018;&#x2013;đ?&#x2018;&#x2014;đ?&#x2018;&#x203A; to make sure that βPM is guaranteed: đ?&#x2018;&#x2021;đ?&#x2018;&#x2013;đ?&#x2018;&#x2014;đ?&#x2018;&#x203A; = đ?&#x153;?đ?&#x2018;&#x2013;đ?&#x2018;&#x2014; â&#x2C6;&#x2019; đ??żđ?&#x2018;&#x2013; đ?&#x153;&#x2021;đ?&#x2018;&#x2013;đ?&#x2018;&#x2014;đ?&#x2018;&#x203A; â&#x2C6;&#x2019; đ?&#x2018;&#x2DC;đ?&#x153;&#x17D;đ?&#x2018;&#x2013;đ?&#x2018;&#x2014;đ?&#x2018;&#x203A; â&#x2C6;&#x161;đ??żđ?&#x2018;&#x2013;

(23)

Where k is the safety factor from the standard normal loss function, set to reach βPM. Inventory control The stock level for the corrective demand stream for SKU i Đ&#x201E; I are base stock levels and are determined via the inventory control model of Chapter 5. All variables that are used in that model are thus also used in this model. When a part is used, it is reordered at the next possible moment and in case of a stock out, an emergency shipment is used. Note that we now have periodic review instead of continuous 36

review. However, because the periodic interval is short compared to the lifetime of a component, this is about the same as continuous review and the ordering delay is never more than one period. The stock levels of the PM demand for SKU i Đ&#x201E; I are dependent of the number of parts with an age is above the advance order threshold. The number of advance order alarms đ?&#x2018;&#x17D;đ?&#x2018;&#x2013; (đ?&#x2018;Ą) for SKU i Đ&#x201E; I at period t Đ&#x201E; T is: đ?&#x2018;&#x17D;đ?&#x2018;&#x2013; (đ?&#x2018;Ą) = â&#x2C6;&#x2018;đ?&#x2018;&#x2014;â&#x2C6;&#x2C6;đ??˝ â&#x2C6;&#x2018;đ?&#x2018;&#x203A;â&#x2C6;&#x2C6;đ?&#x2018; 1 (đ?&#x2018;Ą)â&#x2030;Ľđ?&#x2018;&#x2021; (đ?&#x2018;Ą) (24) đ??´đ?&#x2018;&#x2013;đ?&#x2018;&#x2014;đ?&#x2018;&#x203A;

đ?&#x2018;&#x2013;đ?&#x2018;&#x2014;đ?&#x2018;&#x203A;

The inventory for the two demand streams are controlled separately, but as mentioned, it is possible to use PM stock for CM demand. We first discuss the inventory variables for the corrective demand stream and then the inventory variables for the preventive demand stream.

Let đ?&#x2018;&#x201A;đ??ťđ?&#x2018;&#x2013;CM (đ?&#x2018;Ą) be the number of parts for CM demand of SKU i Đ&#x201E; I physically on-hand at period t Đ&#x201E; T. đ?&#x2018;&#x201A;đ??ťđ?&#x2018;&#x2013;CM (đ?&#x2018;Ą) is always greater than or equal to zero because CM demand that cannot be satisfied due to stock-outs, is satisfied in the same period using an emergency procedure. đ??źđ?&#x2018;&#x2021;đ?&#x2018;&#x2013;CM (đ?&#x2018;Ą) is denoted as the number of parts for CM demand of SKU i Đ&#x201E; I that are in-transit to the QRS at the end of period t Đ&#x201E; T. At the moment of ordering, we increase the đ?&#x2018;&#x201A;đ??ťđ?&#x2018;&#x2013;CM (đ?&#x2018;Ą) + đ??źđ?&#x2018;&#x2021;đ?&#x2018;&#x2013;CM (đ?&#x2018;Ą) to the set base stock level Si for SKU i.

Again, we assume that there is always sufficient stock at the central warehouse so ordered parts can immediately be shipped. When we are not able to meet a demand for CM from the đ?&#x2018;&#x201A;đ??ťđ?&#x2018;&#x2013;CM (đ?&#x2018;Ą), we can meet it from the đ?&#x2018;&#x201A;đ??ťđ?&#x2018;&#x2013;PM (đ?&#x2018;Ą), the number of parts for PM demand of SKU i Đ&#x201E; I physically on hand at period t Đ&#x201E; T. If we still cannot meet the CM demand, an emergency shipment is used. The number of emergency shipment for SKU i Đ&#x201E; I in period t Đ&#x201E; T is defined as: đ?&#x2018;&#x203A;

CM (đ?&#x2018;Ą) â&#x2C6;&#x2019; đ?&#x2018;&#x201A;đ??ťđ?&#x2018;&#x2013;CM (đ?&#x2018;Ą) â&#x2C6;&#x2019; đ?&#x2018;&#x201A;đ??ťđ?&#x2018;&#x2013;PM (đ?&#x2018;Ą)) đ?&#x2018; đ?&#x2018;&#x2013;em (đ?&#x2018;Ą) = đ?&#x2018;&#x161;đ?&#x2018;&#x17D;đ?&#x2018;Ľ(0, â&#x2C6;&#x2018;đ?&#x2018;&#x2014;â&#x2C6;&#x2C6;đ??˝ â&#x2C6;&#x2018;1 đ?&#x2018;&#x2013;đ?&#x2018;&#x2014; đ??ˇđ?&#x2018;&#x2013;đ?&#x2018;&#x2014;đ?&#x2018;&#x203A;

(25)

For the PM demand stream, we have something similar. Let đ??ľđ?&#x2018;&#x201A;đ?&#x2018;&#x2013;PM (đ?&#x2018;Ą) be the number of backorders of SKU i Đ&#x201E; I at the end of period t Đ&#x201E; T. đ??ľđ?&#x2018;&#x201A;đ?&#x2018;&#x2013;PM (đ?&#x2018;Ą) can be calculated by equation 26. In this equation, we first add the number of PM parts that are needed in the period and then subtract the PM parts that we have available for PM at the end. The parts needed for PM in period t are the parts needed to satisfy the PM demand. The part available for PM are calculated in equation 26, which subtracts the outstanding backorders and the PM parts needed to meet CM demand from the PM parts on hand at the beginning of the period. If the available parts are more than the needed parts, the backorders are zero.

CM Ě&#x201A; đ?&#x2018;&#x2013;PM (đ?&#x2018;Ą) = max(0, đ?&#x2018;&#x201A;đ??ťđ?&#x2018;&#x2013;PM (đ?&#x2018;Ą) â&#x2C6;&#x2019; đ??ľđ?&#x2018;&#x201A;đ?&#x2018;&#x2013;PM (đ?&#x2018;Ą â&#x2C6;&#x2019; 1) â&#x2C6;&#x2019; max(0, â&#x2C6;&#x2018;đ?&#x2018;&#x2014;â&#x2C6;&#x2C6;đ??˝ â&#x2C6;&#x2018;đ?&#x2018;&#x203A;đ?&#x2018;&#x2013;đ?&#x2018;&#x2014; đ??ˇđ?&#x2018;&#x2013;đ?&#x2018;&#x2014;đ?&#x2018;&#x203A; (đ?&#x2018;Ą) â&#x2C6;&#x2019; đ?&#x2018;&#x201A;đ??ťđ?&#x2018;&#x2013;CM (đ?&#x2018;Ą))) (26) đ?&#x2018;&#x201A;đ??ť 1

PM Ě&#x201A; đ?&#x2018;&#x2013;PM (đ?&#x2018;Ą) ) (đ?&#x2018;Ą) â&#x2C6;&#x2019; đ?&#x2018;&#x201A;đ??ť đ??ľđ?&#x2018;&#x201A;đ?&#x2018;&#x2013;PM (đ?&#x2018;Ą) = max(0, â&#x2C6;&#x2018;đ?&#x2018;&#x2014;â&#x2C6;&#x2C6;đ??˝ đ??ˇđ?&#x2018;&#x2013;đ?&#x2018;&#x2014;

(27)

If an SKU i Đ&#x201E; I is backordered in period t Đ&#x201E; T, the number of PM delay for that SKU in that period, đ?&#x2018;&#x192;đ?&#x2018;&#x20AC;đ??ˇđ?&#x2018;&#x2019;đ?&#x2018;&#x2122;đ?&#x2018;&#x17D;đ?&#x2018;Śđ?&#x2018;&#x2013; (đ?&#x2018;Ą), is increased by one. Because we allow backorders, the net inventory for PM demand of SKU đ?&#x2018;&#x2013; â&#x2C6;&#x2C6; đ??ź at the end of period đ?&#x2018;Ą â&#x2C6;&#x2C6; đ?&#x2018;&#x2021; is equal to đ??źđ?&#x2018; đ?&#x2018;&#x2013;PM (đ?&#x2018;Ą)= đ?&#x2018;&#x201A;đ??ťđ?&#x2018;&#x2013;PM (đ?&#x2018;Ą) â&#x2C6;&#x2019; đ??ľđ?&#x2018;&#x201A;đ?&#x2018;&#x2013;PM (đ?&#x2018;Ą). Note that it is not possible to have preventive inventory on-hand and backorders at the same time, so one of them is always equal to zero. The number of parts for PM demand SKU i Đ&#x201E; I that are in-transit to the QRS at the moment of ordering in period t Đ&#x201E; T is denoted as đ??źđ?&#x2018;&#x2021;đ?&#x2018;&#x2013;PM (đ?&#x2018;Ą). At the moment of ordering, we increase đ?&#x2018;&#x201A;đ??ťđ?&#x2018;&#x2013;PM(đ?&#x2018;Ą) + đ??źđ?&#x2018;&#x2021;đ?&#x2018;&#x2013;PM (đ?&#x2018;Ą) to the number of advance order alarms đ?&#x2018;&#x17D;đ?&#x2018;&#x2013; (đ?&#x2018;Ą) for SKU i Đ&#x201E; I at period t Đ&#x201E; T. Note that the backorders are not taken into account in the inventory position as having a backorder does still require a part to be in transit but does not increase or decrease the advance order alarms.

The

complete

state

of

the

system

at

time

t

(đ?&#x2018;&#x201A;đ??ťđ?&#x2018;&#x2013;CM (đ?&#x2018;Ą), đ??źđ?&#x2018;&#x2021;đ?&#x2018;&#x2013;CM (đ?&#x2018;Ą), đ?&#x2018;&#x201A;đ??ťđ?&#x2018;&#x2013;PM (đ?&#x2018;Ą), đ??źđ?&#x2018;&#x2021;đ?&#x2018;&#x2013;PM (đ?&#x2018;Ą)). The values of đ?&#x2018;&#x201A;đ??ťđ?&#x2018;&#x2013;CM (đ?&#x2018;Ą) and

by Si, because an emergency shipment is used in case of a stock out, 37

can

be

described

using

đ??źđ?&#x2018;&#x2021;đ?&#x2018;&#x2013;CM (đ?&#x2018;Ą) are bounded from above and it must hold that đ?&#x2018;&#x201A;đ??ťđ?&#x2018;&#x2013;CM (đ?&#x2018;Ą) +

đ??źđ?&#x2018;&#x2021;đ?&#x2018;&#x2013;CM (đ?&#x2018;Ą) = đ?&#x2018;&#x2020;đ?&#x2018;&#x2013; . The values of đ?&#x2018;&#x201A;đ??ťđ?&#x2018;&#x2013;PM (đ?&#x2018;Ą) and đ??źđ?&#x2018;&#x2021;đ?&#x2018;&#x2013;PM (đ?&#x2018;Ą) are bounded from above by â&#x2C6;&#x2018;đ??˝1 đ?&#x2018;&#x203A;đ?&#x2018;&#x2013;đ?&#x2018;&#x2014; and it must hold that đ?&#x2018;&#x201A;đ??ťđ?&#x2018;&#x2013;PM (đ?&#x2018;Ą) + đ??źđ?&#x2018;&#x2021;đ?&#x2018;&#x2013;PM (đ?&#x2018;Ą) = đ?&#x2018;&#x17D;đ?&#x2018;&#x2013; (đ?&#x2018;Ą). Because đ?&#x2018;&#x17D;đ?&#x2018;&#x2013; (đ?&#x2018;Ą) varies over time, the states can be defined for all values of đ?&#x2018;&#x17D;đ?&#x2018;&#x2013; (đ?&#x2018;Ą) but no general description can be given. If we look at the state definition, we can see that it is theoretically possible that there are more spare parts of SKU i at the QRS than there are parts of SKU i in the installed base (IB) served from the QRS (â&#x2C6;&#x2018;đ??˝1 đ?&#x2018;&#x203A;đ?&#x2018;&#x2013;đ?&#x2018;&#x2014; ). This happens when đ?&#x2018;&#x201A;đ??ťđ?&#x2018;&#x2013;CM (đ?&#x2018;Ą) is equal to Si, đ?&#x2018;&#x17D;đ?&#x2018;&#x2013; (đ?&#x2018;Ą) is greater than â&#x2C6;&#x2018;đ??˝1 đ?&#x2018;&#x203A;đ?&#x2018;&#x2013;đ?&#x2018;&#x2014; â&#x2C6;&#x2019; đ?&#x2018;&#x2020;đ?&#x2018;&#x2013; and all the preventive parts are at the QRS before any of them is needed. Although the probability that this happens is very small, it can happen when the served IB is small, the part is stocked for CM demand and đ?&#x203A;˝ PM is high. When this happens, a warehouse employee could question the correctness and optimality of this policy, what can cause resistance. Although, it is possible to change the base stock levels for CM demand to a state dependent base stock level, which take this problem into account, we decided not to incorporate this in the policy as this increases the complexity significantly as we need to find that state dependent base stock levels per state.

Costs At the end of the period, the costs for that period are calculated. The costs for SKU i Đ&#x201E; I are build up out of five parts: holding cost (đ??śđ?&#x2018;&#x2013;h ), emergency shipment cost (đ??śđ?&#x2018;&#x2013;e , see Section 5), PM delay cost (đ??ś PMDelay), PM cost (đ??śđ?&#x2018;&#x2013;P ) and CM cost (đ??śđ?&#x2018;&#x2013;U ).

The holding cost is taken for all on-hand components of SKU i Đ&#x201E; I at the end of the period t Đ&#x201E; T. This holding cost is a percentage of the cost for the spare part. This percentage is equal to one divided number of running days of a system. The reasoning behind this is that Vanderlande faces the acquisition cost of the component as cost, even when the part is in the warehouse for the complete lifetime of the system. The emergency shipment cost is paid over the number of emergency shipments and the PM delay cost is paid for the number of PM delays, which both occur for SKU i Đ&#x201E; I in the period t Đ&#x201E; T. The PM delay cost is for example the cost for rescheduling the PM and it is a fixed cost that occurs once per delay. Thus, it does not matter how much period ahead we need to delay the PM demand, the cost for this is always the same. However, it is possible to let this cost depend on how many periods the demand is delayed without increasing the complexity of the model. Furthermore, the PM cost is paid for all PM actions for SKU i Đ&#x201E; I in the period t Đ&#x201E; T. The number of PM actions for SKU i Đ&#x201E; I in the period t Đ&#x201E; T, đ?&#x2018;&#x192;đ?&#x2018;&#x20AC;đ?&#x2018;&#x2013; (đ?&#x2018;Ą), is increased by one when a PM backorder is fulfilled and when a PM action is done. Per period, đ?&#x2018;&#x192;đ?&#x2018;&#x20AC;đ?&#x2018;&#x2013; (đ?&#x2018;Ą) can take three different forms:

(28)

Furthermore, CM cost is paid for all CM actions for SKU i Đ&#x201E; I in the period t Đ&#x201E; T. This cost is made for CM actions done from the CM inventory, the PM inventory or via an emergency shipment. So, when an emergency shipment is needed, both the cost for CM as cost for the emergency shipment are considered. The total cost for SKU i Đ&#x201E; I in the period t Đ&#x201E; T is defined as: đ??śđ?&#x2018;&#x2013; (đ?&#x2018;Ą) = đ??śđ?&#x2018;&#x2013;h * (đ?&#x2018;&#x201A;đ??ťđ?&#x2018;&#x2013;CM (đ?&#x2018;Ą) + đ?&#x2018;&#x201A;đ??ťđ?&#x2018;&#x2013;CM (đ?&#x2018;Ą)) + đ??ś PMDelay â&#x2C6;&#x2014; đ?&#x2018;&#x192;đ?&#x2018;&#x20AC;đ??ˇđ?&#x2018;&#x2019;đ?&#x2018;&#x2122;đ?&#x2018;&#x17D;đ?&#x2018;Śđ?&#x2018;&#x2013; (đ?&#x2018;Ą) + đ??śđ?&#x2018;&#x2013;e * đ?&#x2018; đ?&#x2018;&#x2013;em (đ?&#x2018;Ą) + CM (đ?&#x2018;Ą) đ??śđ?&#x2018;&#x2013;P â&#x2C6;&#x2014; đ?&#x2018;&#x192;đ?&#x2018;&#x20AC;đ?&#x2018;&#x2013; (đ?&#x2018;Ą) + đ??śđ?&#x2018;&#x2013;U â&#x2C6;&#x2014; â&#x2C6;&#x2018;đ?&#x2018;&#x2014;â&#x2C6;&#x2C6;đ??˝ đ??ˇđ?&#x2018;&#x2013;đ?&#x2018;&#x2014;

(29)

The total cost for the QRS is equal to: TCQRS = â&#x2C6;&#x2018;đ?&#x2018;&#x2021;đ?&#x2018;Ą=0 â&#x2C6;&#x2018;đ??źđ?&#x2018;&#x2013;=1 đ??śđ?&#x2018;&#x2013; (đ?&#x2018;Ą).

38

(30)

6.3.

Comparison to other literature

Our policy has similarities to the PMAO-extension policy of Coumans (2017). He uses the model of Section 2.9 of van Houtum and Kranenburg (2015) to set the base stock levels for corrective demand and our model to set these base stock levels is strongly based on that model of van Houtum and Kranenburg (2015). Furthermore, Coumans also consideres two demand streams, corrective and preventive, and he determines the advance order threshold in the same way. Another paper that makes use of an advance order threshold is the paper of Deshpande et al. (2006) but they only consider one demand stream, the corrective demand. There are also some differences between our policy and the PMAO-extension policy. The first difference is that the PMAO-extension policy uses a block replacement policy when it executes preventive maintenance. We do not follow a block replacement policy but a single component preventive maintenance policy as designed in Chapter 4. We do not want to use a block replacement policy because the usage of similar components can be very different and it is very strange to block replace a component relatively short after it has been correctively replaced. Another difference is that we allow PM stock to be used for CM demand but not the other way around, which is the case for the PMAO-extension policy. Last, we give more priority to CM demand because we changed the series of events so that the CM demand is faced before we allocate PM stock to PM demand.

A paper that uses the same sequence of events is that of Basten and Ryan (2015). They also observe the state of the system, place their orders, face unplanned demand, meet planned demand if possible and calculated the costs per period. They mainly consider a case where the replenishment lead time is zero but also present an extension with a positive lead time. In one of the three policies with zero lead time, they assume that a planned demand can be delayed at most once. This also happens in our model as we incur a fixed PM delay cost that is independent of the length of the delay. The delay can however be multiple periods but it occurs at most once per component as the PM backorders are fulfilled before we allocated the rest of the stock. This is done to keep the customers satisfied. The main difference between our policy and the policy of Basten and Ryan (2015) is that they assume that the planned demand is deterministic while we assume it to be stochastic. Another difference is that they can delay unplanned demand (backorder) and we use an emergency shipment in case of a stock out.

6.4.

Conclusion

In this chapter, we answered RQ5: How can ADI from the UBM policy be used in the spare parts inventory control model? In Section 6.1, we elaborated about the PMAO and PMAO-extension policy of Coumans (2017). In these two policies, the QRS faces two types of demand steams, a preventive demand steam and a corrective demand stream. For the preventive demand steam, it is possible to use the imperfect ADI from the UBM policy by ordering the spare parts for PM when an advance order threshold is reached. The difference between the two policies is that the PMAO policy controls the two demand streams separately and the PMAO-extension policy combines the inventory pools and satisfies the demand by a first-come-first-served allocation rule. In Section 6.2, we explain another ADI policy, the PMAO-CM-priority policy. In this policy, the PM inventory pool can be used to satisfy CM demand but not the other way around. Also, the PM is executed at the end of the period instead of the beginning to increase the possibility that there is PM stock available in case of a CM stock out. This policy gives more priority to the CM demand stream and should avoid expensive emergency shipments.

39

NUMERICAL EXPERIMENTS In this chapter, we answer RQ6: How large are the benefits of using the policies of Research Question 5 compared to policies without ADI? In Section7.1, we explain the considered policies without ADI and in Section 7.2, we elaborate about the input variables for the numerical experiments. In Section 7.3, we show the results of the experiments and in Section 7.4 we conclude this chapter.

7.1.

Policies without ADI

In this chapter, we compare the three ADI models (PMAO policy, PMAO-extension policy and PMAOCM-priority policy) with policies that do not take ADI into account. We consider two non-ADI policies: one policy uses the spare parts inventory control model of Chapter 5 and uses a failure-based maintenance policy (called the non-UBM policy) and the second non-ADI policy uses the spare part inventory control model of Chapter 5 and the UBM policy of Chapter 4 (called the non-ADI policy).

We mentioned that the proposed UBM policy and the spare parts inventory control model provide optimal solutions, when they are used for the right components. This is true if we observe the service and spare parts department separately. However, both departments are part of Vanderlande and if the two departments do not work together, we can see that the two policies do not perfectly align. Looking at the UBM policy from Chapter 4, we see that this policy relies on the assumption that there is always a spare part available when we need to perform CM or PM. The inventory control model of Chapter 5, on the other side, limits the amount of spare parts stocked at the QRS and sees all demand as corrective that follows a Poisson distribution. Observing only corrective demand reduces the probability that multiple of the same component need to be replaced in the same period because of which we can stock for multiple customers. However, when we use a UBM policy, and components age with the same rate, it is more likely that multiple of the same components do need to be replace at the same time, which then results into a stock out. The two departments need to communicate as their decisions influence the total solution for Vanderlande. A way to combine the two policies is via the proposed ADI policies.

There are two interesting things to investigate. First, as mentioned, it is interesting to compare the nonADI policy with the ADI policies because this shows the benefit when service and spare parts department within Vanderlande work together by using ADI. Second, it is interesting to compare the non-UBM policy with the best ADI policy to see if UBM is still valuable compared to a failure-based policy when we loosen the assumption that there is always a part in stock when maintenance is needed.

7.2.

Input values for the numerical experiments

In this section, we present input values for the ADI models in Table 10. We vary the spare parts on three component specific variables: demand rate (low, medium, high), price (low, medium, high) and replenishment lead time (low, high). This results into 18 different theoretical spare parts, which all differ from each other on at least one aspect. An overview of these spare parts is given in Appendix N. We consider nine different experiments based on the different component specifications. In the first eight experiments, we consider the spare parts that have one specific variable the same, e.g. the first experiment considers only the six spare parts with a low demand rate, the second experiment considers the six spare parts with a medium demand rate and so on. In the ninth experiment, we consider all the 18 different spare parts. Next, we explain the input values of these three component specific variables.

40

The different demand rates are based on the experience of the spare parts manager. He mentions that components that fail less than once per two years (520 days) are considered to have a low demand rate, components that fail about once per year (260 days) have a medium demand rate and components that fail once per quarter (65 days) have a high demand rate. Note that this demand rate is adjusted for the ADI policies as these rates are lower because we also do PM. The different price categories are based on Van den Bosch (2017). He mentions that “the team leader Logistical Support and the Spare Parts manager both agreed that the low-value parts should cover approximately 80% of its spare parts”. He considers the amount of spare parts per price groups (Figure 20 in Appendix E). From this, we decide that a low price is €50,-, medium price is €200,- and a high price is €500,-. We also did this for the different values of the lead time. From Figure 8, we can see that about 50% of all components have a lead time equal or below 22 days and 20% of the components have a lead time more than 43 days.

Because of this, we define a low lead time as 22 days and a high lead time as 43 days.

Figure 8: Number of product with a certain lead time and the cumulative percentage

Furthermore, we need to define a Weibull distribution for the lifetime distribution of the considered spare parts to determine the optimal maintenance moment using the UBM policy from Chapter 4.

Because no specific data about this is available, we find an α and β for a theoretical Weibull distribution by looking at coefficient of variance (CV), which is the standard deviation divided by the expected value, of the Weibull distribution fitted to the data in Section 3.2 and the demand rates for the component.

With the α and β from Section 3.2 and the equations for the expected value and standard deviation, found in Appendix I, we calculated the CV of this distribution, which is equal to 0.74. Next, we set the expected value of the Weibull distributions for our spare parts equal to the demand rate in terms of usage by using the shift length of the small scenario from Chapter 4 (5 hours per day). So, he expected value for the three different demand rate levels is equal to 2600 (520*5), 1300 (260*5) and 325 (65*5) running hours, respectively. The found α and β for these theoretical lifetime distributions are given in Table 10. Because we also want to show the impact of the variance in the lifetime distribution to the policies and show the value of having good quality data, we also fit an α and β using the same expected values but use a CV of 0.50. These values are also provided in Table 10.

The nine different experiments based on the spare parts specifics are executed three time, resulting in 27 different experiments. The first nine experiments use a Weibull distribution fitted to a CV of 0.74 (called high variance), the second nine experiments used a Weibull distribution fitted to a CV of 0.50 (called low variance) and the last nice experiments use the Weibull distribution fitted to a CV of 0.74 to determine the optimal UBM policy and inventory stock levels but the components actually have a lifetime distribution equal to Weibull distribution fitted to a CV of 0.50 (called unexpected low variance).

These last nine experiments are done to show the value of having the right data available instead of having the wrong data. The different experiments are numbered and shown in Appendix O. 41

Table 10: Input variables for numerical experiments

Variable Weibull distribution (CV = 0.74):

Values {2842, 1421, 355} 1.368 Weibull distribution (CV = 0.50): {2936, 1468, 367} 2.101 Demand rate CM demand without PM: {1/520, 1/260, 1/65} Price: CiSparePart {50, 200, 500} Lead time: Li {22, 43} obj Objective aggregate mean waiting time: W {3/24} Safety factor for βPM (95%): k 1.64 Customer site scenario: Small scenario WMaintenance, WOperational, Cap, Th, WIMaxTruck, #KM, €/KM, n, Shi (see Table 6) Variance in hours per shift: var(Shi) 1 Number of customers served from QRS: J 3 Number of time SKU i occurs at customer j: nij 5 Time (hours) to deliver item from QRS: ttravel 2 em Time (hours) to deliver item via emergency shipment: t 24 Time (hours) to replace the component: treplacement 1.88 Cost for emergency shipment: Cie 753 PMDelay Cost for delaying PM maintenance action: C 100 Lifetime of a SPO: T 3900 days Next, we present the variables that are constant for every spare part and experiment. We only discuss the input variable that are not yet discussed and Appendix P explains the values of variables based on previous data. First, we set the fill rate for the PM demand to 95% (which gives a k of 1.64) and assume the cost for a PM delay to be €100,-. These assumptions are not based on any data or knowledge at Vanderlande as nothing is known about this, but these are the same values as Coumans (2017) assumes.

We assume that a system runs five days per week, 52 weeks per year over a lifetime of 15 year. This means the system runs (5*52*15=) 3900 days and this is what we used as time horizon for the model as we see one day as one period. For all numerical experiments, we assume that the number of times that a SKU occurs in the system of the customer is equal to five for all SKUs and all customers. This assumption is not based on data as nothing about this is available, because these are theoretical spare parts.

Furthermore, we assume that the three customers sites that are served are completely new or just had a revision because of which all components are observed as new and thus all start with an age of zero.

Next, we assume that Vanderlande just started to use the QRS and the stock levels at the QRS are thus equal to the optimal base stock levels for the considered policy. The warm-up period is equal to zero.

Because we consider a finite time horizon, the costs are not constant every simulation run but can deviate. To cover for this, we run all experiments 101 times and present the average cost, maximum cost, minimum cost and a 95% confidence interval of the cost based on 101 runs. These statistics for all the experiments and all the policies are shown in Appendix Q. 7.3.

α β α β mi

Results of the numerical experiments

In this section, we present the results of the numerical experiments. In Section 7.3.1, we compare the ADI policies with the non-ADI policy. In Section 7.3.2, we vary the spare part specific variables comparing the best ADI policy with the non-ADI policy. In Section 7.3.3, we compare the non-ADI policy with the non-UBM policy. Last, in Section 7.3.4, we show the value of having correct data.

42

7.3.1.

ADI policies vs non-ADI policy

In this section, we investigate the value of the ADI policies compared to the non-ADI policy. By comparing these, we show the benefit, in terms of cost, if the service and spare part department work together via ADI compared to if they do not. In Figure 9 and Figure 10 (where the x-axis mentions the experiment number show in Appendix O), we shown the proportional cost savings of the ADI policies compared to the non-ADI policy for the numerical experiments with high and low variance, respectively. We can see that the ADI policies always outperform the non-ADI policy. Looking at these 18 experiments, we see that the best ADI policy results into, on average, 3.65% cost savings compared to the non-ADI policy for high variance and 7.76% for low variance. Thus, we conclude that have a lower variance in the lifetime distribution results into 4% more saving for all ADI-policies compared to the non-ADI policy. Thus, knowing more precisely when a part fails, is beneficial. Noticeable is the high saving of about 14% when we only consider components with a low price. This is because the PM threshold is lower when the price is lower as the difference between PM cost and CM cost is bigger. This results into more stock outs if we use the non-ADI policy and these are covered for by the ADI policies, hence the cost savings are higher.

Cost savings ADI policies vs non-ADI policy: CV=0.74

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Figure 10: Savings ADI policies vs non-ADI policy: CV=0.50

Furthermore, we, just as Coumans (2017), conclude from Figure 9 and Figure 10 that the PMAO policy is the worst of the ADI-policies for all 18 numerical experiments. The PMAO-extension policy performs best in ten experiments and the PMAO-CM-priority policy performs best in eight experiments. Although the average difference between the best policy and the PMAO is only 0.74% (maximum is 1.53% and minimum is 0.21%), we advise Vanderlande to go with one of the other two ADI policies.

Table 11: Advantages and disadvantages of the PMAO-extension policy and the PMAO-CM-priority policy

Policy PMAO-extension policy

+ The lowest probability of PM delays - The highest probability of emergency shipments + The easiest to implement PMAO-CM-priority policy + The lowest probability of emergency shipments - The highest probability of PM delays - Harder to implement because there are separate stocks Which of the two remaining policies to choose is a decision the management should take based on the advantages and disadvantages of both policies in Table 11. The PMAO-extension policy is the easiest to implement as the different demand is served from one stock. This means that a warehouse employee can use a part if it is available. Using this policy gives the lowest probability of PM delays but the highest probability of emergency shipments. The PMAO-CM-priority policy, on the other side, gives the highest probability of PM delays but the lowest probability of emergency shipments. This policy is less practical as it is only allowed to use PM stock for CM demand but not the other way around.

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7.3.2.

Numerical experiments: vary in demand rate, lead time and price

In this section, we compare the numerical experiments where we vary the demand rate, lead time and price of the considered spare parts. We focus on these component specific variables to see if they influence the cost savings of the best ADI policy compared to the non-ADI policy.

Figure 11 shows the experiments where we only consider spare parts with a specific demand rate. We conclude that the cost savings become more when the demand rate increases. The reason for this is because the ADI policy results into a higher reduction in the CM stock levels for higher demand rates compared to the lower demand rate. Figure 12 shows the cost savings of the experiments where we only consider spare parts with the same lead time. We conclude that the cost savings are higher for a higher lead time. This is because the lead time only slightly influences the cost for the ADI policy, which is also found by Coumans (2017), but the lead time does affect the costs for the non-ADI policy. As the cost for the non-ADI policy increases and the cost for the ADI-policy stays about the same, the savings become higher. In Figure 13, we see the cost savings of the experiments where we only consider spare parts with the same price. We conclude that the cost savings decrease when we price becomes higher.

This is because higher prices result into a higher PM threshold for spare parts with the same lifetime distribution. Because the PM actions occur later, there is a higher probability that a component fails and thus a CM action is needed. Because less PM is executed and thus less failures are covered, ADI provides less value as it is less used and thus the savings are less.

Cost savings best ADI policy vs non-ADI policy: Vary lead time

Cost savings best ADI policy vs non-ADI policy: Vary demand rate 10,00% 9,00% 8,00% 7,00% 6,00% 5,00% 4,00% 3,00% 2,00% 1,00% 0,00%

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Figure 11: Savings based ADI policy vs non-ADI policy, vary demand rate

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Figure 12: Savings best ADI policy vs non-ADI policy, vary lead time

Cost savings best ADI policy vs non-ADI policy: Vary prices 16,00% 14,00% 12,00% 10,00% 8,00% 6,00% 4,00% 2,00% 0,00% 4.1 5.1 6.1 (Low, high (Medium, (High, high variance) high variance) variance)

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Figure 13: savings best ADI policy vs non-ADI policy, vary price

7.3.3.

Best ADI policy vs non-UBM policy

In this section, we compare the best ADI policy with the non-UBM policy to see if UBM is also beneficial compared to a failure-based policy when we loosen the assumption that there is always a spare part on 44

stock. The non-UBM policy is compared with the best ADI policy as we showed that the ADI policy always outperforms the non-ADI policy. In Figure 14 and Figure 15, we show the proportional cost savings of the best ADI policy vs the non-UBM policy on the y-axis while the x-axis mentions the considered experiment (corresponding with Appendix O). The reason for this is because a higher the price results into a higher the PM threshold as the difference between the PM cost and CM cost becomes relatively smaller. We conclude that for a high variance and medium or high prices, the maintenance threshold becomes too high because of which the PM action are less executed but the stock levels are still lowered.

Because of this, number of CM stock outs, and thus needed emergency shipments increases. The extra costs for this cannot be countered by the lower holding costs and slightly less CM costs resulting in the fact that a failure-based policy is beneficial. In the other scenarios with high variation in the lifetime distribution, the best ADI policy outperforms the non-UBM-policy with 4.7% to 8.1% in terms of cost.

For the experiments with a lower variation in the lifetime distribution, we see that the cost savings are much higher. Here, the cost savings vary from 20% up to 40%. This makes sense because having less variation in the lifetime distribution results into a more accurate PM threshold and advance order threshold. So, having components with a lower variance in their lifetime results into more cost savings and results into the fact that the best ADI policy always outperforms the non-UBM policy, i.e. UBM is beneficial.

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Figure 14: Cost savings best ADI policy vs non-UBM policy: CV=0.74

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The value of correct failure data

In this section, we focus on numerical experiments with unexpected low variance in the lifetime of the components to show the benefit of having the correct data. Figure 16 shows the cost savings of the ADI policies compared to the non-ADI policy and we again see that the ADI policies always outperform the non-ADI policy. However, if we compare the cost savings from Figure 16 with the cost savings in Figure 10, where we did have the right lifetime distribution, we see that the cost savings are, on average, 4% lower when we have the incorrect data. Thus, having the incorrect data reduces the possible cost savings of the ADI policies over the non-ADI policy.

Figure 17 shows the benefit of the best policy for the nine experiments with low variance in the lifetime distribution with the best policy for the nine experiments with the unexpected low variance in the lifetime distribution. All but one experiment show the results are as we would expect: having the right data results into lower costs when using the best policy, average of 7.81%. Remarkable is the case where we only consider components with a low price, as we see that having incorrect data results into a lower cost than the right data. Having the wrong data results into higher stock levels, a later PM threshold, and thus also a later advance order threshold, and apparently, when we do not always have a spare part 45

on stock, it is beneficial to increase the stock and PM threshold compared to the value that the separate optimal policies would indicate. However, when these values become much higher, which happens for medium and higher prices, the PM actions do not cover enough CM actions anymore and the optimal values of the real data indicate to be better again. Thus, we expect that there is a joint optimisation policy that results into lower costs compared to the current ADI policies, by finding the PM threshold and stock levels based on each other instead of determining them by separate individual policies.

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Conclusion

In this chapter, we present the results of the numerical experiments that compare a non-UBM policy, non-ADI policy and the three ADI policies from Chapter 6. Hereby, we answer RQ6: How large are the benefits of using the ADI policies of Research Question 5 compared to policies without ADI? We define 18 theoretical spare parts and via numerical experiments, we conclude that the ADI policies always outperform the non-ADI policy. We see that the PMAO policy is always the worst of the ADIpolicies, but the other two differ not that much. Which ADI policy to use is a management decision that can be based on the advantages and disadvantages in Table 11. Furthermore, we conclude that the cost savings increase when the demand rate increases, because of a higher reduction in inventory levels, the cost savings increase for a higher lead time, because the lead time has almost no effect for the ADI policies but does have an effect for the non-ADI policy, and the cost savings decrease when we price increases as this results into a higher PM threshold and thus more CM actions.

Furthermore, we compare the best ADI policy with the non-UBM policy to see if UBM is also beneficial compared to a failure-based policy when we loosen the assumption that there is always a spare part on stock. It turns out that this is not always the case as we see that for a high variance combined with medium or high prices, the maintenance threshold becomes too high because of which the PM action are less executed but the stock levels are still lowered. Because of this, number of CM stock out, and thus needed emergency shipments increases resulting in the fact that a failure-based policy is beneficial.

We find that having a lower variation in the lifetime distribution of the components results into more cost savings as the PM threshold and advance order threshold are more accurate. Last, we find that having the incorrect data reduces the cost savings of the ADI policies over the non-ADI policy with about 4% and we observe in one experiment that the incorrect data results into a lower cost. We expect that there is a joint optimisation policy that results into lower costs by finding the PM threshold and stock levels based on each other instead of determining them by separate individual policies.

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CONCLUSIONS, RECOMMENDATIONS AND FUTURE RESEARCH In this final chapter, we conclude the research. In Section 8.1, we state the conclusion of our research by answering the main research question and stating the contribution to the literature. In Section 8.2, we present the recommendations for Vanderlande and in Section 8.3, we elaborate on the limitations of this research and future research topics.

8.1.

Conclusions

We conclude this research by answering the main research question: How can UBM be applied as preventive maintenance strategy and how can the information resulting from the UBM policy be used in the spare parts inventory control? We presented a single-component UBM policy that calculates the optimal replacement moment of a component. Furthermore, we defined a spare parts inventory control model that can be modified to take the ADI from the UBM policy into account to control demand for PM as a second demand stream. We elaborate on this by answering each of the research questions.

To answer RQ1: What is the available failure and usage data at Vanderlande and what is its quality?, we found that there was no specific data available concerning the failures of the components. We investigated several data sets but it was hard to find failure data on a component level. We set some requirements and made some assumptions because of which it was possible to use the spare part sales data as failure data. Also, usage data was very hard to get at Vanderlande, especially covering the complete lifetime of a system. It was already hard to find when a system started running. The main conclusion was that the combination of failure data for components and usage data for sites is very hard to gather. For example, we mainly focus on relatively small customer sites due to our requirements and assumptions for the failure data, because of which almost no usage data was available.

RQ2 is: Given the availability of data, what are the possible components to apply UBM on? Based on the data gathered in RQ1, a list of components was made for which UBM is possible. For these components, we checked if UBM is a good policy using the MPS-model of Alcorta (2017). We conclude that the timing belt in the entry of the SPO is the only component for which enough data is available and UBM is a suitable strategy. Based on a SPO expert, we concluded that running hours of the SPO is the best usage indicator for a timing belt failure.

RQ3 is: What is a good UBM policy for Vanderlande? We defined a single-item UBM policy that finds the optimal moment to replace a component based on the costs for preventive and corrective maintenance and the lifetime distribution of the components. We did a scenario analyses that takes a small, medium and large SPO site into account and found that, compared to a failure-based policy, the UBM policy for the timing belt can save 16%, 13% and 0% in these scenarios, respectively. We thus show that the value of UBM is not only dependent on the component but also on the customer site.

RQ4 is: What should the basic inventory control model of Vanderlande look like for the component(s) in this research? We defined a multi-item, single-location inventory model with emergency shipments. This model finds the optimal number of items to put on stock at a QRS to minimise the expected cost while meeting the aggregate mean waiting time objective. Using this model for three different timing belts and for 152 SPO sites in Europe, we already showed that the number of the parts at the end of the supply chain decreases with on 50%.

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RQ5 is: How can ADI from the UBM policy be used in the spare parts inventory control model? We elaborated on the PMAO and the PMAO-extension policy developed by Coumans (2017) and developed our own PMAO-CM-priority policy. In these policies, the QRS faces two demand streams, one for CM and one for PM. There is a CM inventory pool that is controlled by a base stock policy and a PM inventory pool that is controlled by ordering the amount of parts that have past the advanced order threshold.

The PMOA-CM-priority policy prioritizes the CM demand as it checks if PM stock is needed for CM demand before allocating the PM stock to a PM action.

RQ6 is: How large are the benefits of using the policiess of Research Question 5 compared to a policies without ADI? We define 18 theoretical spare parts and via numerical experiments, we conclude that the ADI policies always outperform the non-ADI policy in terms of costs for maintenance and spare parts.

We see that the PMAO policy is always the worst of the ADI-policies, but the other two differ not that much. Furthermore, we conclude that the cost savings are increasing in the demand rate and lead time and decreasing in price. Next, we compare the best ADI policy with the non-UBM policy to see if UBM is beneficial compared to a failure-based policy when we loosen the assumption that there is always a spare part on stock. It turns out that this is not always the case as two experiments show that the nonUBM policy provides lower cost. Next, we find that having a lower variation in the lifetime distribution of the components results into more cost savings as the PM threshold and advance order threshold are more accurate. Last, we find that having the incorrect data reduces the cost savings of the ADI policies over the non-ADI policy. We observe one experiment where the incorrect data results into a lower cost, which makes us expect that there is a better joint optimisation policy that finds the PM threshold and stock levels based on each other instead of determining them by separate individual policies.

Contribution to literature Our first scientific contribution is that we use a broad view where we define a UBM policy and a spare parts inventory model in a way for them to be combined into an ADI policy. UBM policies, spare parts inventory models and ADI models are topics that are considered in literature but are, to the authorâ&#x20AC;&#x2122;s best knowledge, never developed together in the same research. Furthermore, we developed a new policy that takes ADI from the UBM policy into account in spare parts inventory control. A similar policy is used by Basten and Ryan (2015) but they do not explicitly consider stochastic aging of the components.

Thirdly, the developed models are tested in the company environment of Vanderlande. As literature mainly focuses on developing new models, these models are often not tested in practice. We try to close the gap between literature and practice.

8.2.

Recommendations

The recommendations presented in this section are needed if Vanderlande want to move into the direction of UBM, spare parts inventory control and ADI. Collect data about the lifetime of components The main problem with the failure data was that we could not match it to a specific component in the system. If this data is collected and stored in a structural way, Vanderlande benefits from this as it can optimise its services. We recommend that the maintenance engineers keep track of their maintenance actions in more detail. If all service engineers record exactly which components have been replace, the MTTFs can be easily subtracted. As a maintenance engineer already receives a work order with parts he needs to inspect, it is not much extra effort to also store when he replaces a specific part. This might be 48

documented in DOS Maximo as this is the current program used to store and coordinate maintenance actions.

Collect data about the usage of the components It is recommended that Vanderlande tries to store usage data regularly. This can be done via for example the Flow System Controller (FSC). The FSC is used as equipment control but also records some information like throughput and running hours. A program should be developed that makes sure that the FSC writes this information to a database like VIDI to keep it centrally stored. This program can be developed by R&D on initiative from the service department who should be the problem owner. What should be considered, is that the data is not be lost when a software update or an error occurs. If Vanderlande wants to do something with UBM, it must invest in this automatic data acquisition. It is also possible that a service engineer writes down the running hours that are recorded via a time counter.

Implement UBM maintenance for the right components It is recommended that Vanderlande reconsiders their maintenance strategy, finds the best maintenance strategy per components and defines clear measurable rejection criteria if deciding to do CBM. The MPS-model of Alcorta (2017) is a good way to do this but they can also use a more general way like reliability centered maintenance (Rausand, 1998). For the UBM components, it is recommended to use the UBM policy from Chapter 4. This extra PM service is a good addition to the current service proposition of Vanderlande as it improves the uptime of the systems but decreases maintenance costs.

However, before Vanderlande can move forward with this, it needs to develop a clear business case to make UBM a priority and get the required funding. We recommend to evaluate more components and customer sites to determine the benefits for the customer and Vanderlande. Also, investigate how the future maintenance programs for complete customer sites should be designed.

When providing spare parts as a service, use the spare parts inventory control model for the QRS The spare parts department wants to move to selling spare parts as a service. When this happens, it is advised to move to a multi-echelon inventory model and we recommend using (a version of) the developed spare parts inventory control model for the QRSâ&#x20AC;&#x2122;s as this results into less spare parts at the end of the supply chain due to a pooling effect. Before moving to spare parts as a service, it is advised to investigate how long a customer is willing to wait for a component and consider the work of van den Bosch (2017) to decide which spare parts are stocked at which location in the supply chain.

When a spare parts inventory control model and predictive maintenance policies are in place, investigate the possible cost savings of an ADI policy at Vanderlande We recommend Vanderlande to consider ADI policies when a spare parts inventory control model and PM policies are in place. This is because we found that ADI policies always outperform a way of working where the departments do not exchange information, i.e. a non-ADI policy. At this moment there is a lack of data on the lifetime of a component at Vandelande. Therefore we recommend a more specific case study, as we see that UBM combined with spare parts inventory control may not be suitable when the variation of the lifetime distribution is high. Next to that, we recommend that they also think about the use of a shared information dashboard between the cooperating departments because clear information exchange is needed and it needs to be clear who is responsible for the delivery of which type of information. Last, to use ADI, Vanderlande needs to monitor the usage of a system for example every day, their systems and IT infrastructure should facilitate this data exchange between the systems at the customer site and the IT at Vanderlande.

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8.3.

Critical assumptions, limitations and future research

In this section, we identify the limitations to our research and present some future research directions.

First, there are some limitations regarding the data availability. To use spare parts sales data as failure data, we made assumptions regarding the inventory control policies at the customers but never checked these assumptions as it was too time consuming to do this for all customers. Next to that, a few decisions are based on the knowledge of experts and not on data. The loyal customers are based on the knowledge of the spare parts manager and the fact if components have an IFR and the best usage measurement for a component is based on the knowledge of a SPO expert. For the usage data, we needed to assume that the usage of the systems is constant over their lifetime as only a few months of data was available. Next, the lifetime distribution of the timing belt is based on only 14 data points. Although we have checked if the data fits the Weibull distribution, more data would give a more reliable lifetime distribution.

Furthermore, we assumed that the demand rate of the components is Poisson distributed. However, we were not able to confirm this due to the lack of available data. Furthermore, we were only able to consider three components in the spare parts inventory control model for which we could at least determine a MTTF based on five data points. If more components are considered, we could really show the possible benefits for Vanderlande. The last limitation due to missing data is that, for the numerical experiments, we needed to make some assumptions for certain variables like the cost for delaying a PM action and lifetime distribution of the parts. As more information becomes available, Vanderlande should perform a case study that would indicate what the expected values of the ADI policies are.

For the UBM policy, we developed a single components UBM policy but scope it to a single component policy. How Vanderlande should incorporate this into a complete maintenance program for a complete customer site with multiple components is not investigated. This is a topic for future research at Vanderlande. We already give some examples on how to do this in Appendix G. For the spare parts inventory control model, we only consider one echelon, the QRS, and assume that the central warehouse always has enough parts on stock. This model should eventually be expanded to a multi-echelon model that also determines stock levels for the central warehouse. Next to that, we did not consider lateral transhipments between QRSâ&#x20AC;&#x2122;s when a part is needed during a stock out. These are two options for future research at Vanderlande.

There are also some limitations and future research directions for the ADI model. First, these policies only consider a single echelon and do not take lateral transhipments into account. Also, we did not consider state dependent stock levels for the CM demand because of which it is possible that there are more parts on stock than there are parts to be served. Furthermore, we only consider information from the developed UBM policy for ADI. Vanderlande might also use information from the CBM actions, i.e. the periodic inspections or the CBM model of Alcorta (2015), as ADI. Next to that, we did not investigate how the information needs to be transferred between different departments within Vanderlande and who is responsible for collecting certain information. This information exchange is a direction for future research a Vanderlande. The main academic future research topic is the joint optimisation of the UBM policy and the spare parts inventory model, possible via ADI, as these policies are currently not optimised together. Doing this results in a model where the PM threshold and stock levels are based on each other instead of determined by separate individual policies. This can be the reason why we observe once that lower costs are achieved when wrong data about the lifetime distribution.

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from https://www.nwo.nl/onderzoek-en-resultaten/onderzoeksprojecten/i/92/14292.htmlNo Title Peijnenburg, J. (2016). Vanderlande Company presentation. Veghel.

Rausand, M. (1998). Reliability centered maintenance. Reliability Engineering and System Safety, 60, p.121-132. https://doi.org/10.1007/978-1-84882-472-0_16 Sakamoto, Y., Ishiguro, M., & Kitagawa:, G. (1986). Akaike Information Criterion Statistics. Dordrecht, Netherlands: Kluwer Academic Publishers Group.

Schwering, B. (2017). BPI - System Overviews. Retrieved September 25, 2017, from https://vikipedia.vanderlande.com/display/SER/BPI+-+System+Overviews Sherwin, D. J. (1999). Age-based opportunity maintenance. Journal of Quality in Maintenance Engineering, 5, p.221-235. https://doi.org/10.1108/13552519910282674 Tan, T., GĂźllĂź, R., & Erkip, N. (2007). Modelling imperfect advance demand information and analysis of optimal inventory policies. European Journal of Operational Research, 177, p.897-923. https://doi.org/10.1016/j.ejor.2005.12.031 Topan, E., Tan, T., & van Houtum, G. J. (2016). Using imperfect advance demand information in lostsales inventory systems Using Imperfect Advance Demand Information in Lost-Sales Inventory Systems. van Asseldonk, J. W. (2017). Control visualization (ESC-V). Retrieved September 25, 2017, from https://vikipedia.vanderlande.com/pages/releaseview.action?pageId=8749677 van den Bosch, S. (2017). Spare parts network design optimization. Tilburg University (master thesis). van der Heijden, I. (2017). JD Edwards Enterprise ONE (E1). Retrieved September 25, 2017, from https://vikipedia.vanderlande.com/pages/viewpage.action?pageId=120586410 van Dijkhuizen, G., & van Harten, A. (1997). Optimal clustering of frequency-constrained maintenance jobs with shared set-ups. European Journal of Operational Research, 99, p.552-564. https://doi.org/10.1016/S0377-2217(96)00320-7 Van Horenbeek, A., & Pintelon, L. (2013). A dynamic predictive maintenance policy for complex multicomponent systems. Reliability Engineering and System Safety, 120, p.39-50. https://doi.org/10.1016/j.ress.2013.02.029 van Houtum, G. J., & Kranenburg, A. A. (2015). Spare parts inventory control under system availability constraints. Springer. https://doi.org/10.1007/978-1-4899-7609-3 van Neerrijnen, M. (2017). DHL DP MechZB. Retrieved March 20, 2018, from https://vikipedia.vanderlande.com/display/public/CUS/DHL+DP+MechZB van Schijndel, F. (2016). Vanderlande Spare Parts: a study on which services to offer in the year 2020.

TIAS (Master thesis).

Vanderlande. (2017a). Annual Report CY2016. Retrieved from https://www.vanderlande.com/aboutvanderlande/annual-report/ Vanderlande. (2017b). History. Retrieved September 18, 2017, from https://www.vanderlande.com/about-vanderlande/history 52

Wang, H., & Pham, H. (2006). Reliability and Optimal Maintenance. Springer.

Wildeman, R. E., Dekker, R., & Smit, A. C. J. M. (1997). A dynamic policy for grouping maintenance activities. European Journal of Operational Research, 99, p.530-551. https://doi.org/10.1016/S0377-2217(97)00319-6

53

APPENDIX A â&#x20AC;&#x201C; OTHER CONSIDERED DATA SETS FOR FAILURE DATA In this appendix we discuss three other data sets that we considered to use for the extraction of failure data. These data sets are Scada, DOS Maximo and specific data collected by the Bartolini sites.

A.1. Scada data A possible data set that can be used for the collection of failure data are the alarms in Scada.

Vanderlande uses Scada to get real-time information about the availability of the system and to control the system. If there are alarms available that indicate a failure, these errors can be used as failure data.

Usage of the Scada alarms for failure data causes some problems. First, the alarms are mostly stored for a period of about three months. This is a limiting factor because the systems of Vanderlande mostly run for about ten to fifteen years. Especially because we want to make the connection to spare parts control, we focus on spare parts, which are most likely not to fail twice in three months. Second, Scada mostly reports operational alarms. These alarms do not necessarily indicate a failure. Instead, it can be that an item fell from the conveyer or is not scanned correctly. Also, we need the alarms to be that specific that we also know which component has failed. If an alarm indicates a failure but it can be one of multiple components, it is not possible to trace that alarm back to a specific component. This means that we cannot use all the alarms, but we need to find alarms that specifically indicate that a failure of a component has occurred. Furthermore, the Scada alarms are not completely the same at each site. They are configured to the requirements of the customer, so inconstancies between sites can occur.

Currently, Scada alarms are not useful as failure data. If Vanderlande can standardise the errors, write down which actions need to be done when an error occurs (for example replace or not), store the errors that indicate a failure for a longer period and can link the errors to a specific component, than this can be a useful dataset in the future.

A.2. DOS Maximo There is also information about spare parts usage in DOS Maximo. Inhere, the spare parts consumption is entered with the maintenance orders. There are a few problems with Maximo. First, the reliability and quality of the data highly depends on the customers. Some customers enter the data very specifically per work order and on equipment level but other might combine work orders or just enter the spare parts on area level. Because of this, it is hard to find which components are used at what place and when the components are exactly used. Second, Maximo is only running now for about one year and mostly at sites where Vanderlande has a site based team present. This reduces the available data significantly as only a year of data is available and only sites that use DOS Maximo can be considered.

It is possible to use this data in the future when data over more years is available and customers enter their spare parts usage on a component level. When this happens, it is also possible to use data from components that exist more than once in the system because it is still know which component has failed.

This increases number the components to do UBM on.

A.3. The Bartolini dataset Another option that was considered as is data from the 23 Bartolini sites in Italy. These are all SPO sites with about the same layout. In 2009, the Bartolini sites started to collect data about their maintenance 54

activities. Every time a maintenance action was performed, they recorded the type of maintenance (corrective or preventive), who did the maintenance, the used parts and the time it took. Unfortunately, they do not record exactly which component is replaced when a part occurs multiple times in the system.

Because of this, we again can only focus on components that occur only once in the system. However, because these are the real used parts, the other assumptions and requirements from Table 1 are not necessary anymore.

During this data collection, some notable things are observed. First, components that occur once in the systems are sometimes used multiple times on the same date on the same site. This should not be possible because this means that a component, which occurs once in the system, is replaced twice on the same date. Possible explanations for this are that the information at Vanderlande is wrong and the components occurs more than once in the system, they have done maintenance at multiple sites and record it as one, they also record the parts they put in the inventory, the first spare parts they wanted to use was already broken, or something went wrong in entering the paper sheets. Another issue was that, most useful maintenance actions were recorded as preventive. This means that not the complete lifetime of the component is used and no actual failure has occurred. These data points are not useful unless we assume that when a component is replaced preventively, it was very close to failure and the replacement can be seen as â&#x20AC;&#x2DC;correctiveâ&#x20AC;&#x2122;. Another notable thing was that for some cases, maintenance actions for the same components occurred very close to each other. For example, there has been a corrective maintenance action for a component and within a week, there was again a preventive maintenance action for the same component. This does not really make sense. After discussing this, it turned out that it was possible that the maintenance engineer did not have enough time to do the complete maintenance the first time and needed to come back later that week to finish it. However, this action was again recorded as a new maintenance action.

Eventually not enough useful data points could be collected to fit a failure distribution. Besides that, we only focus on specific components, they only started to record this data from 2009 onwards. Most sites however were older than 2009, which means that the first replacement could not be used as a data point because we do not know how long the part was already in the SPO before they started to collect data. The fact that these 23 sites could not result into enough data points was the reason why this set was not used.

55

APPENDIX Bâ&#x20AC;&#x201C; PRODUCT SPECIFICATIONS FOR COMBINED DATA POINTS In this appendix, we present the product specifications of different components for which we decided to combine the failure data points. These are only the products that also, combined, provided more than five data points. We provide a picture of the component, a technical drawing (is available), the important parameters and mention what the difference is between the products.

B.1. Timing belts The timing belts that are considered are the item numbers 004885-92030, 004885-12003 and 004886-88030. The difference between these timing belts is the length of the belt and the position in the machine.

The first two timing belts are used in the entry of the SPO and the last timing belt is used in the end of the SPO. Therefore, the data points for the last timing belt is not used in the combined data points for the entry timing belts.

The parameters for the different item numbers are given below. The length in mm is indicated with the letter L. Parameters 004885-92030: entry

Parameters 004885-12003: entry

Parameters 004886-88030: end

56

B.2. Assy merge The assy merges that are considered are the item numbers 0L855100001, 0L8552-00001 and 0L8554-00001. The difference between these assy merges is the angle which it can move (20 or 30 degrees) and the direction it moves (left or right).

For this item, we give the technical drawings because they give more information about the differences. The angle can be found in the red box.

Technical drawing 0L8551-00001: assy merge, right, angle=20 degrees

57

Technical drawing 0L8552-00001: assy merge, right, angle = 30 degrees

Technical drawing 0L8554-00001: assy merge, left, angle = 30 degrees.

58

B.3. Drive pulley Ø75 cylindrical The drive pulleys Ø75 cylindrical that are considered are the item numbers 0L3636-00650, 0L3636-00750, 0L3636-00850 and 0L3636-00950. The drive pulley Ø75 cylindrical differ from each other in term of length of the steel ring and the key rounded 8x7x20 ISO R 773/DIN6885 (Form A) Ck 45 DIN1652.

The parameters for the different item numbers are given below. The length of the steel ring in mm is indicated with the letter B, the length of the key rounded 8x7x20 ISO R 773/DIN6885 (Form A) Ck 45 DIN1652 in mm is indicated with the letter A. For this item, we give one technical drawings because the other once look the same but only with different parameters.

Technical drawing for the drive pulley Ø75 cylindrical

Parameters 0L3636-00650

59

Parameters 0L3636-00750

Parameters 0L3636-00850

Parameters 0L3636-00950

B.4. Cables The cables that are considered are the item numbers 006002-13655, 006002-13671, 006002-13684 and 006002-13695. The cables differ from each other in term of length of the cable and the fact if it is a male or female connection.

The parameters for the different item numbers are given below. The length of the cable in mm is indicated with the letter L and the difference between male and female can be found by M/F. For this item, no technical drawing is given because it is not a mechanical component.

Parameters 006002-13655

Parameters 006002-13671

60

Parameters 006002-13684

Parameters 006002-13695

61

APPENDIX C – NUMBER OF DATA POINTS PER ITEM NUMBER PER CONSIDERED GROUP The item numbers of the components that are combined, together with the number of data points available per item number and the number of useful data points per group of components can be found in Table 12.

Item numbers starting with ‘0L’ are made by Vanderlande itself. Other components are bought by Vanderlande via an external supplier. For components that are bought from an external supplier it is interesting to investigate how the failure distributions of the components from different suppliers perform and test if one performs significantly better or worse than the others. However, in Section 0, we get limited to only the Timing Belt Entry as component due to the leak of usage data. This also makes it not possible anymore to compare different timing belts and get some information about the different suppliers. However, this is one of the things that would be beneficial to investigate when the data is available.

Table 12: Useful components based on available failure data on item number level

Item number

Description

004885-92030 Timing Belt 920-RPP-SLV8-30 004885-12003 Timing Belt 1200-RPP-SLV8-30 Timing Belt entry 004886-88030 Timing Belt 880-RPP8-30 Timing Belt end 0L8551-00001 Assy merge Angle=20° right 0L8552-00001 Assy merge Angle=30° right 0L8554-00001 Assy merge Angle=30° left Assy merge 006002-13655 Cable M8 female 4p. wire H.F.L=5m 006002-13671 Cable M12 male 4p.M8 female 4p.H.F.L=7m 006002-13683 Cable M12 male 4p./M12 female 006002-13684 Cable M12 male 4p.M12 female 4p.H.F.L=3m 006002-13695 Cable M12 male 4p. wire H.F.L= 2m Cable 0L3636-00650 Drive pulley Ø75 cylindrical 0L3636-00750 Drive pulley Ø75 cylindrical 0L3636-00850 Drive pulley Ø75 cylindrical 0L3636-00950 Drive pulley Ø75 cylindrical Drive pulley Ø75 cylindrical

62

Individual data points 13 6

Combined data points

19 5 5 3 4 3 10 2 2 1 1 1 7 1 1 2 1 5

APPENDIX D â&#x20AC;&#x201C; MPS-MODEL BY ALCORTA (2017) The MPS-model is shown in Figure 18. The criteria included as decision points are selected based on a questionnaire that was conducted at Vanderlande by Alcorta. The criteria included in this questionnaire are based on literature about MPS and are complemented with criteria that were specifically important for Vanderlande. In the questionnaire, employees mention how important a criterion is according to them and eventually, the most important criteria are used in the decision trees. The final tree is shown in Figure 18, where the dotted lines indicate a split between the smaller trees and the orange boxes indicate end The first part of the decision tree, called the CM vs. PM decision tree, is to determine if PM is a good option based on specific customer site factors (safety and legislation) and based on the failure rate of the component. The decision about safety is to make sure that no maintenance action is recommended that is not safe for the maintenance engineers. After that, the decision tree makes sure that the legislation within a country is obeyed regardless of which maintenance policy is best for the component.

The last split in the first part of the decision tree checks if the component has an increasing failure rate (IFR). If a component does not have an IFR, the component does not wear over time and replacing the component preventively makes no sense.

The second part of the decision tree, called the PM equipment decision tree, takes the piece of equipment in which the component is installed into account. This decision tree checks if the equipment is critical for the system of the customer. If this is not the case, a failure of the component does not affect the availability of the systems thus it is better to use the complete lifetime of the component (CM). If the equipment is critical to the customer, the third part of the decision tree is executed.

The last part of the decision tree, called the PM component decision tree, checks criteria for the specific component. First, it is check if the component is critical for the equipment it is placed in. Again, if the component is not critical, the component can be maintained correctively. If the component is critical, it is checked if the failure of the component is predictable. If this is not the case, we are not able to predict when PM actions are needed and thus CM is the best option. When the failure of the component is predictable for the component, we are going to do PM, but we need to decide if we do UBM or CBM. First, the model checks if the spare parts cost is high. CBM is more expensive than UBM, since sensors are needed to do CBM. If the spare parts costs are high, the customer is more willing to pay these higher costs to lose less of the useful lifetime of the component. When the spare parts costs are low, the customer rather replaces the component a little earlier and does not want to pay the higher costs needed for CBM (resulting in UBM). The last criteria in the decision tree is if a degradation pattern can be indicated. If this is not possible, CBM is not possible and UBM is the best policy. If the degradation pattern can be identified, CBM is the best maintenance policy.

63

Figure 18: MPS-model (Alcorta, 2017)

64

APPENDIX E – COMPONENT CRITICALITY BY VAN DEN BOSCH (2017) In this appendix we elaborate on how van den Bosch (2017) determined the criticality levels for components. He based the criticality on two factors: the spare part criticality and the location criticality.

For the spare part criticality he wanted to investigate the seven factors described in Botter and Fortuin (2000). However, due to time limitations, getting an exact value for these factors was not possible and he got an approximation from experts (spare parts coordinator and R&D engineer). This approximation was in three different levels: (1) high, (2) medium and (3) low critical levels. These levels are defined as follows: “1. High: The failure has to be corrected and the spares should be supplied immediately, because these parts cause high losses due to non-availability of equipment, in case they are needed while not in stock.

2. Medium: The failure can be tolerated with temporary arrangements for a short period of time, during which the spare can be supplied, or because these items cause moderate losses due to non-availability of equipment 3. Low: The failure is not critical for the process and causes only minor disruptions, it can be corrected and spares can be supplied after a longer period of time“ (van den Bosch, 2017).

For the location criticality he looked at the place of the part in the system. Van den Bosch (2017) mentions that “due to the complexity of the products delivered by Vanderlande, just the criticality of the part is not enough. It is also important to know where the part is located in the conveyor system”.

For the location in the system Vanderlande uses three categories that are defined as below and are visualised by Figure 19.

A. Main line, no redundancy: high impact on system uptime B. Not in main line, some redundancy: medium impact on system uptime C. Not in main line, redundant: little impact on system uptime

Figure 19: System layout including location criticality from van Schijndel (2016)

65

Eventually, he defined the criticality of the component based on the spare parts criticality and the location criticality in the following three categories: 1. “If the spare part criticality is 1 and the location criticality is A, 2. If the spare part criticality is 2 or when the spare part criticality is 1 and the location criticality is B or C, 3. If the spare part criticality is 3 “ (van den Bosch, 2017).

After that he determined if a spare part was considered as high value or as low value. Van den Bosch (2007) mentions that “the team leader Logistical Support and the Spare Parts manager both agreed that the low-value parts should cover approximately 80% of its spare parts”. To find this he considered the amount of spare parts in certain price groups (Figure 20) and decided that low value spare parts are spare parts with a price between €0,- and €250,- and high-value spare parts have a price more than €250,-.

Figure 20: Price groups spare parts from van den Bosch (2017)

Eventually, with the criticality levels of the components and the fact if they have a high or a low value, he created the criticality scale as depicted in Table 13.

Table 13: Criticality scale created by van den Bosch (2017)

1

2

3

4

5

6

7

8

user specific, low criticality

userspecific, middle or high criticality

standard part, low value, low criticality

standard part, low value, middle criticality

standard part, low value, high criticality

standard part, high value, low criticality

standard part, high value, middle criticality

standard part, high value, high criticality

66

APPENDIX F â&#x20AC;&#x201C; AVAILABLE DATA POINTS In this Appendix, we show the available data points which are used in this research.

Table 14: Used data points

Customer 2193867 Amazon France Logistique SAS 2240061 Amazon Pforzheim GmbH 2101818 - OZ Export BV 2101953 Syncreon Netherlands BV 2102159 DHL Freight (Sweden) AB 2193861 DHL Express (Schweiz) AG 2101806 DPD (Nederland) B.V. 2101806 DPD (Nederland) B.V. 2101806 DPD (Nederland) B.V. 2101806 DPD (Nederland) B.V. 2101806 DPD (Nederland) B.V. 2101806 DPD

Business Unit 140017004 Amazon FR Saran

Item Number 00488512003

Description

start date 1-10-2011

Order Date 6-8-2015

Time (days) 1463

Usage (run. Hr.) n.a.

Timing belt RPPSLV8-30 L=1200

140249106 Amazon Pforzheim STR1 145559906 Oz export 145567807 Syncreon Technologies

00488512003

Timing belt RPPSLV8-30 L=1200

1-8-2013

20-4-2017

1283

n.a.

00488512003 00488512003

Timing belt RPPSLV8-30 L=1200 Timing belt RPPSLV8-30 L=1200

1-10-2007

15-4-2015

1302

10509

18-10-2007

1-4-2016

2157

16948

145573505 DHL Goteborg 148642806 DHL Regensdorf 1455554 DPD Best

00488512003

Timing belt RPPSLV8-30 L=1200

1-12-2010

18-6-2014

1205

13255

00488512003

11-10-2011

9-9-2016

1887

n.a.

00488592030

Zahnriemen 1200-RPP-HPR830 Timing Belt 920RPP-SLV8-30

1-3-2010

17-4-2012

717

8246

1455554 DPD Best

00488592030

Timing Belt 920RPP-SLV8-30

1-3-2010

19-2-2013

308

3542

1455554 DPD Best

00488592030

Timing belt RPPSLV8-30 L=920

1-3-2010

16-7-2014

512

5888

1455554 DPD Best

00488592030

Timing belt RPPSLV8-30 L=920

1-3-2010

7-8-2014

22

253

145555407 DPD Best

00488592030

Timing belt RPPSLV8-30 L=920

1-3-2010

16-6-2015

335

3853

145555408 DPD Best

00488592030

Timing belt RPPSLV8-30 L=920

1-3-2010

8-9-2015

84

966

67

(Nederland) B.V. 2101818 - OZ Export BV 2101818 - OZ Export BV 2101818 - OZ Export BV 2102159 DHL Freight (Sweden) AB 2102117 Schenker NV 2102117 Schenker NV 2102139 TNT Express (België) 2204403 Amazon France Logistique SAS 2211225 Amazon Koblenz GmbH 2102139 TNT Express (België) 2101914 FleuraMetz B.V. 2101914 FleuraMetz B.V.

1455599 - Oz export 1455599 - Oz export 145559906 Oz export 145573505 DHL Goteborg 147813506 Schenker Mechelen BV 147813508 Schenker Mechelen BV 147814707 TNT Express Benelux Antwerpen 140027206 Amazon FR Montelimar

00488592030 00488592030 00488592030 00488592030

Timing Belt 920RPP-SLV8-30 Timing Belt 920RPP-SLV8-30 Timing belt RPPSLV8-30 L=920 Timing belt RPPSLV8-30 L=920

17-10-2007

21-9-2011

432

3487

17-10-2007

14-1-2013

481

3882

17-10-2007

15-4-2015

821

6627

1-12-2010

18-6-2014

1174

12914

00488592030

Timing belt RPPSLV8-30 L=920

1-6-2011

19-1-2015

1328

n.a.

00488592030

Timing belt RPPSLV8-30 L=920

1-7-2011

26-102016

646

n.a.

00488592030

Timing belt RPPSLV8-30 L=920

1-3-2009

2-3-2015

964

7643

00488688030

Timing belt RPP8-30 L=880

1-8-2011

3-7-2017

2156

n.a.

1402490 Amazon Koblenz CGN1 140964701 TNT Milmort BE 145565705 Fleura Export BV 145565706 Fleura Export BV

00488688030

Timing Belt 880RPP8-30

1-9-2012

24-102013

418

n.a.

00488688030

Timing belt RPP8-30 L=880

1-8-2016

29-8-2017

393

2931

00488688030

Timing belt RPP8-30 L=880

24-11-2011

10-9-2014

1021

n.a.

00488688030

Timing belt RPP8-30 L=880

24-8-2011

17-5-2016

615

n.a.

68

APPENDIX G â&#x20AC;&#x201C; WAYS TO DESIGN AN FUTURE MAINTENANCE PROGRAM As briefly mentioned in the introduction of Chapter 4, Vanderlande want to create a maintenance program for a complete customer site considering CM, UBM and CBM strategies for different components. These different strategies should be aligned to make sure that with the lowest amount of maintenance visits, the most maintenance actions are executed. Although we focus on a single component maintenance policy, we want to encourage Vanderlande to also do research on this for the future. The goal of this chapter is to give some examples of how this can be done. Note that we do not want to suggest one direction but only inform some possibilities for maintenance programs.

One way to design a maintenance program is to use the framework of Gits (1992). He formulates a procedure based model to design a maintenance program that consists of seven steps. The model of Gits (1992) is based on multiple research projects and tested in different settings. In this framework, clear and autonomous steps are developed and it is a good way to start designing a maintenance program. Something that needs to be considered is that Gits (1992) does not take modification into account in his model. He mentions that his model does not focus on the possibility to modify the system to prevent failures but only tries to control the consequences of failure. In step 1, Gits specifies the appropriate maintenance policy per component. In this step, the MPS-model of Alcorta (2017) can be used. In the second step, Vanderlande needs to specify the maintenance actions per component, i.e. repair the component, replace the component or do an inspection. In step 3, we need to find the optimal maintenance interval per component that would be optimal if this was the only component in the system. In step 4, the preventive maintenance actions are clustered to save set-up cost. This can for example be done by the algorithm of van Dijkhuizen and van Harten (1997). They define five properties, which the optimal clustering solution must satisfy. With these properties in mind, they define a problem to find the lowest maintenance cost. Next, the maintenance intervals from different clusters are harmonised to save more set-up cost in step 5 of Gitsâ&#x20AC;&#x2122; framework. In step 6, Gits allocates the maintenance clusters to maintenance time instants to make sure that the workload of maintenance engineers is smoothed and in step 7, the maintenance rules are evaluated in term of for example costs, failures, satisfaction and implementation issues.

Another way to design a maintenance program for a system is by defining an optimization problem that minimises the cost for all different types of maintenance policies together. This is done in Chapter 6 of Arts (2017). Inhere, he defines an optimization problem, which is a multi-variable non-linear non-convex integer program. Unfortunately, it is hard to get an efficient algorithm to solve it because it is non-linear and non-convex. Wang and Pham (2006) elaborate on multiple maintenance policies for multi-unit systems in Chapter 3.3 of their book. Example of these group maintenance policies are a T-age group replacement policy, in which a group replacement is done when the system is of age T, an m-failure group replacement policy, in which inspections are done after m failures have occurred, and a combination of both policies, referred to as an (m,T)-group replacement policy. Another group maintenance policy that is discussed is the one from Wildeman, Dekker and Smit (1997). In this policy, maintenance activities are carried out on a technical system that involves a system dependent set-up cost that is the same for all maintenance activities carried out on that system. Grouping these activities saves costs since execution of a group of activities requires only one set-up. â&#x20AC;&#x153;Under this policy, a rollinghorizon approach is proposed that takes a long-term tentative plan as a basis for a subsequent adaptation according to information that becomes available in the short term. This policy makes it easy 69

to incorporate short-term circumstances such as opportunities or a varying use of components because these are either not known beforehand or make the problem intractableâ&#x20AC;? (Wang & Pham, 2006, p.4647). More research about this policy is done by van Horenbeek and Pintelon (2013) where they for example consider non-zero maintenance downtimes and include predictive information about the component remaining useful life.

If we include CM actions in the maintenance program, it is possible to save costs by applying opportunity maintenance. â&#x20AC;&#x153;In opportunity maintenance, the preventive work (PM) that is due and overdue, is done only or mainly when failures force the system to stopâ&#x20AC;? (Sherwin, 1999). Examples of opportunistic maintenance policies can be found in Chapter 3.3.2 and Chapter 6 of Wang and Pham (2006).

Again, these are just some examples of policies and frameworks that can be used to come to a multi component maintenance program. These books and papers can be used in future research by Vanderlande to develop these kinds of programs.

70

APPENDIX H â&#x20AC;&#x201C; SHORT OVERVIEW OF RENEWAL REWARD THEORY We explain some background required to understand the model used for UBM in Section 0. We discuss some basic reliability theory in Section C.1. and renewal (reward) theory in Section C.2. Most of this Appendix is based on the work of Arts (2017). For more derivations of the equations, we refer to his paper.

H.1. Reliability theory First, let T be a random variable that indicates the time to failure of a component. T is required to be bigger than zero, which means that the component has not failed before it has been used. If T is a continuous variable, its distribution is given by FT(t) = P(Tâ&#x2030;¤t) and its density is given by fT(t) =

đ?&#x2018;&#x2018; FT(t). đ?&#x2018;&#x2018;đ?&#x2018;Ą

Note that when T is a discrete random variable instead of a continuous random variable, the following equations can easily be adapted by changing the integrals to summations.

The reliability of a component at time t, R(t), is the probability the component survives beyond time t.

This is given by the equation: â&#x2C6;&#x17E;

R(t) = P(Tâ&#x2030;Ľt) = 1- FT(t) = â&#x2C6;Ťđ?&#x2018;Ą đ?&#x2018;&#x201C;đ?&#x2018;&#x2021; (đ?&#x2018;Ą â&#x20AC;˛ )đ?&#x2018;&#x2018;đ?&#x2018;Ą â&#x20AC;˛

(31)

With this reliability function, the mean time to failure (MTTF) can be calculated. This is the expectation of T, given by: â&#x2C6;&#x17E;

MTTF = E[T] = â&#x2C6;Ť0 đ?&#x2018;&#x2026;(đ?&#x2018;Ą)đ?&#x2018;&#x2018;đ?&#x2018;Ą

(32)

The next important function in reliability theory is the failure rate (also referred to as hazard rate). This is defined as the â&#x20AC;&#x153;instantaneous expected number of failures per time unit at time tâ&#x20AC;?(Arts, 2017, p.13).

This function (for a continuous random variable) is defined as: h(t) =

đ?&#x2018;&#x201C;đ?&#x2018;&#x2021; (đ?&#x2018;Ą) đ?&#x2018;&#x2026;(đ?&#x2018;Ą)

(33)

The failure rate shows us some interesting features about the degradation of components. When the component has an increasing failure rate (IFR),

đ?&#x2018;&#x2018;â&#x201E;&#x17D;(đ?&#x2018;Ą) > 0, the component degrades over time. This means đ?&#x2018;&#x2018;đ?&#x2018;Ą

that the chance that the component fails increases when the component is in use. This is mostly the case for mechanical components. On the other side, when a component has a decreasing failure rate (DFR),

đ?&#x2018;&#x2018;â&#x201E;&#x17D;(đ?&#x2018;Ą) đ?&#x2018;&#x2018;đ?&#x2018;Ą

< 0, it means that the component becomes more reliable over time when it has not failed

yet. Typically, electronic components have a DFR. Furthermore, there are components that have a constant failure rate (CFR),

đ?&#x2018;&#x2018;â&#x201E;&#x17D;(đ?&#x2018;Ą) = 0. đ?&#x2018;&#x2018;đ?&#x2018;Ą

It is also possible that a component has a failure rate that alternates

from being decreasing to being increasing during the lifetime of the component. One important failure rate function is the bathtub curve. Ebeling (1997) mentions that the components that follow a bathtub curve experience a DFR in the beginning of their life cycle, followed by an CFR during the life use and face an IFR in the wear-out (ending) phase of the component.

The equations in this section can be used for different distributions. Commonly used distributions are the exponential, uniform, Erlang, gamma, Weibull, Poisson, geometric, negative binomial and logarithmic distribution. If the reader wants more specific equations and properties per distribution, we refer to Chapter 2.2 of Arts (2017).

71

H.2. Renewal (reward) theory â&#x20AC;&#x153;A renewal process is a counting process in which the time between events (also called renewals) are independently and identically distributed (i.i.d.)â&#x20AC;? (Arts, 2017, p.23). X1, X2 ,â&#x20AC;Ś is defined as a sequence of non-negative i.i.d. random variables with a common distribution F(x), a density f(x) and a positive mean.

In this sequence, Xi is defined as the time between the (i-1)-th and the i-th renewal. The time until the ith renewal is defined as Si: Si = â&#x2C6;&#x2018;đ?&#x2018;&#x2013;đ?&#x2018;&#x2DC;=1 đ?&#x2018;&#x2039;đ?&#x2018;&#x2DC; , S0 = 0.

(34) Instead of defining Xi as the time between renewals, it can also be defined as the time until a failure occurs, the time to failure. In this case, Si is the time until the i-th failure. The renewal process indicates how many renewals (failures) have occurred until time t. This is denoted as N(t): N(t) = max {i Đ&#x201E; â&#x201E;&#x2022;0 | Si â&#x2030;¤ t}, t â&#x2030;Ľ 0.

(35) The expected number of renewals up until the time t, E[N(t)], is called the renewal function and is denoted with M(t): đ?&#x2018;Ą

M(t) = F(t) + â&#x2C6;Ť0 đ?&#x2018;&#x20AC;(đ?&#x2018;Ą â&#x2C6;&#x2019; đ?&#x2018;Ľ)đ?&#x2018;&#x201C;(đ?&#x2018;Ľ)đ?&#x2018;&#x2018;đ?&#x2018;Ľ,

tâ&#x2030;Ľ0

(36)

Unfortunately, this equation is not immediately helpful for computing M(t) because solving this equation is very difficult. A way to do this is to make a guess for M(t) under some f(x) and F(x) and plug these into the equation to check if the guess is correct. To do this correctly, it is needed to have a lot of understanding of the context, as Arts (2017) mentions.

Last, if there is a reward (cost), Wi, associated with each renewal i, the total reward (cost) up until time t, Y(t), is denoted as: đ?&#x2018; (đ?&#x2018;Ą)

Y(t) = â&#x2C6;&#x2018;đ?&#x2018;&#x2013;=1 đ?&#x2018;&#x160;đ?&#x2018;&#x2013; (37) Note that it is assumed that W1, W2, â&#x20AC;Ś is an i.i.d. sequence of random variables with |E[Wi]| < â&#x2C6;&#x17E;.

Y(t) is called a renewal reward process. The average reward (cost) per time unit of a renewal process, g, is given by: g=

đ??¸[đ?&#x2018;&#x160;đ?&#x2018;&#x2013; ] đ??¸[đ?&#x2018;&#x2039;đ?&#x2018;&#x2013; ]

(38)

The expected length of a renewal, đ??¸[đ?&#x2018;&#x2039;đ?&#x2018;&#x2013; ], is also referred to as the expected cycle length (ECL) and the average cost per renewal, đ??¸[đ?&#x2018;&#x160;đ?&#x2018;&#x2013; ], is also called the expected cycle cost (ECC). Including these definitions in the last equation, â&#x20AC;&#x153;the renewal reward theorem says that the expected cost per time is simply ECC/ECLâ&#x20AC;?(Arts, 2017, p.26).

72

APPENDIX I â&#x20AC;&#x201C; THE WEIBULL DISTRIBUTION In this appendix, we given the basic equations for the cumulative distribution function (CDF), the probability distribution function (PDF), the reliability function and the failure (hazard) rate of the Weibull distribution. We also enter these equations into the ECC and ECL equations from Section 4.1. đ?&#x153;? đ?&#x203A;˝

CDF:

F (đ?&#x153;?) = 1- đ?&#x2018;&#x2019; â&#x2C6;&#x2019;(đ?&#x203A;ź)

PDF:

f (đ?&#x153;?) = đ?&#x203A;ź â&#x2C6;&#x2014; (đ?&#x203A;ź)

Reliability Function:

R (đ?&#x153;?) = đ?&#x2018;&#x2019; â&#x2C6;&#x2019;(đ?&#x203A;ź)

Failure rate:

h (đ?&#x153;?) =

Expected value:

E(đ?&#x153;?) = Î&#x201C;(1+ ) â&#x2C6;&#x2014; đ?&#x203A;ź

Variance:

Var(đ?&#x153;?) = đ?&#x203A;ź 2 â&#x2C6;&#x2014; Î&#x201C;(1+đ?&#x203A;˝ ) - E(đ?&#x153;?)2

(44)

Standard deviation:

â&#x2C6;&#x161;đ?&#x2018;&#x2030;đ?&#x2018;&#x17D;đ?&#x2018;&#x;(đ?&#x153;?)

(45)

(39)

đ?&#x153;? đ?&#x203A;˝â&#x2C6;&#x2019;1

đ?&#x203A;˝

đ?&#x153;? đ?&#x203A;˝

â&#x2C6;&#x2014; đ?&#x2018;&#x2019; â&#x2C6;&#x2019;(đ?&#x203A;ź)

(40)

đ?&#x153;? đ?&#x203A;˝

đ?&#x203A;˝ đ?&#x203A;źđ?&#x203A;˝

(41)

â&#x2C6;&#x2014; đ?&#x153;? đ?&#x203A;˝â&#x2C6;&#x2019;1

(42)

1 đ?&#x203A;˝

(43) 2

As arts (2017) mentions, we can conclude that this distribution has an increasing failure rate (IFR) for β > 1, a decreasing failure rate (DFR) for 0 < β < 1 and a constant failure rate (CFR) for β = 1. Note that if β = 1 the Weibull distribution becomes an exponential distribution.

Entering these equations into the equations of the ECC and ECL from Section 4.1, we get the following equations: đ?&#x153;? đ?&#x203A;˝

đ?&#x153;? đ?&#x203A;˝

ECC = (1- đ?&#x2018;&#x2019; â&#x2C6;&#x2019;(đ?&#x203A;ź) )*Cu + (đ?&#x2018;&#x2019; â&#x2C6;&#x2019;(đ?&#x203A;ź) ) Cp â&#x2C6;&#x17E;

(46) đ?&#x203A;˝

đ?&#x2018;Ľ đ?&#x203A;˝â&#x2C6;&#x2019;1

ECL = E[min(T, Ď&#x201E;)] = â&#x2C6;Ť0 min(x, Ď&#x201E;) â&#x2C6;&#x2014; ( đ?&#x203A;ź â&#x2C6;&#x2014; (đ?&#x203A;ź) Ď&#x201E;

đ?&#x203A;˝

đ?&#x2018;Ľ đ?&#x203A;˝â&#x2C6;&#x2019;1

= â&#x2C6;Ť0 đ?&#x2018;Ľ â&#x2C6;&#x2014; (đ?&#x203A;ź â&#x2C6;&#x2014; (đ?&#x203A;ź)

73

đ?&#x2018;Ľ đ?&#x203A;˝

đ?&#x2018;Ľ đ?&#x203A;˝

â&#x2C6;&#x2014; đ?&#x2018;&#x2019; â&#x2C6;&#x2019;(đ?&#x203A;ź) )đ?&#x2018;&#x2018;đ?&#x2018;Ľ đ?&#x153;? đ?&#x203A;˝

â&#x2C6;&#x2014; đ?&#x2018;&#x2019; â&#x2C6;&#x2019;(đ?&#x203A;ź) ) đ?&#x2018;&#x2018;đ?&#x2018;Ľ + Ď&#x201E; â&#x2C6;&#x2014; đ?&#x2018;&#x2019; â&#x2C6;&#x2019;(đ?&#x203A;ź)

(47)

APPENDIX J â&#x20AC;&#x201C; CONVEXITY OF THE AVERAGE COST PER TIME UNIT In this appendix, we shown the figure of g(Ď&#x201E;) (y-axis) against time unit t (x-axis) for the three considered scenarios: small, medium and large. For every scenario, there are two pictures. The first picture shows g(t) over the time, starting from zero. However, because this does not give a clear image of the convexity, we zoom in on this graph in the second one. In the second one, is clearly seen that the function is convex.

For the small and medium scenario, there is a minimum that is shown in the second picture of both cases. For the large scenario, there is no minimum as this minimum goes to infinity. As explained in Section 4.3, for this case are the cost for preventive maintenance equal to the cost for corrective maintenance, which makes a UBM policy not useful.

Scenario small:

Figure 21: Convexity of g(t) over time for the small scenario, second graph is a zoom in of the first

74

Scenario medium:

Figure 22: Convexity of g(t) over time for the medium scenario, second graph is a zoom in of the first

75

Scenario large:

Figure 23: Convexity of g(t) over time for the large scenario, second graph is a zoom in of the first

76

APPENDIX K â&#x20AC;&#x201C; EXPLANATION INPUT VALUES FOR THE UBM POLICY In this appendix, we elaborate on how we determined the values for the input variables for the UBM policy in Section 4.3.

For the parameter values ι and β for the Weibull distribution, we use the determined values of Section 4.2.

Next, we need the cost for preventive maintenance. The cost of the timing belt entry is for the 00488592030 timing belt (4 data points) â&#x201A;Ź15.93 and for the 004885-12003 timing belt (10 data points) â&#x201A;Ź17.93.

This gives an average cost for the timing belt entry of â&#x201A;Ź16.93. This is the value used for Cisparepart. The time it takes to replace a timing belt is deducted from the Bartolini dataset. In this dataset mentions how long the maintenance engineer was working on a job. We considered jobs where only a timing belt entry is replaced. We only considered call-out job because in the current situation, the maintenance engineer knows what needs to be replaced during a call-out and thus only spends his time on replacing this one timing belt entry. When a preventive maintenance action is done in the current situation, the maintenance engineer needs to inspect the system and determine if something needs to be replaced.

Because in this case he does not know beforehand what to replace and needs to inspect the system, it takes longer. There were 11 call-out cases where only a timing belt was replaced and the average time needed to replace the timing belt (tireplacement) was 1.88 hours (with a standard deviation of 0.97 hours).

We also need to take the travel time of the maintenance engineer into account. Because later in the research, we use quick response stocks (QRS) that are about two hours away from customers, we also assume that the maintenance engineer needs two hours of travel time (ttravel) to reach his destination.

The hourly wages of a maintenance engineer (WMaintenance) is extracted from CAP8. This is the pricing and proposal verification tool in which they store key figures about for example hours wages. Wages is â&#x201A;Ź54 per hour. Eventually we find that the preventive maintenance cost is equal to: Cip = â&#x201A;Ź16.93 + (1.88 hours + 2 hours) * â&#x201A;Ź54 per hour = â&#x201A;Ź226.45.

Most input values in the equation to determine the downtime cost are customer specific. Later, these costs can be calculated per customer if the information is available but now this is not the case. Because we do want to make some difference between downtime cost, we do a scenario analyses where we take scenarios for small, medium and large POSISORETR sites into account. An indication for the Cap, q, Th, nSPO and Shi for the three different scenarios is given by a senior system engineer at Vanderlande. He has a good insight in what these values approximately are for the three scenarios as he designs these systems. The values for đ?&#x2018;&#x160;operational is extracted from CAP8, which is equal to â&#x201A;Ź26.

Finally, we need the costs for an extra truck. Looking at the tender from a same day carrier in the thesis of Van den Bosch (2017, p.53), a transporter can move a weight of 1200 KG (WIMaxTruck) against a cost of 0.59 â&#x201A;Ź/KM (WKM). An average package in the parcel and postal industry (WIParcel) is around 15 KG (van Neerrijnen, 2017) and we assume that the truck should be able to drive by all addresses within 100 KM of the distribution centrum (nKM).

77

APPENDIX L - CUSTOMERS CONSIDERED FOR INVENTORY CONTROL Table 15: Considered customers with their warehouse allocation, their number of timing belts and the distance to the central warehouse

Customer site

DPDHL MECH-ZB - Erlangen DPDHL MECH-ZB - Nürnberg DPDHL MECH-ZB - Aschheim DPDHL MECH-ZB - Germering DPDHL MECH-ZB - München CLZ DPDHL MECH-ZB - München Neuaubing DPDHL MECH-ZB - München Neubruch DPDHL MECH-ZB - München Riesenfeld DPDHL MECH-ZB - Ottobrunn DPDHL MECH-ZB - Unterschleißheim DHL Leipzig DE Hermes Fulfilment - Ohrdruf DPDHL MECH-ZB - Darmstadt DPDHL MECH-ZB - Frankfurt DPDHL MECH-ZB - Ginsheim DPDHL MECH-ZB - Hanau DPDHL MECH-ZB - Hattersheim DPDHL MECH-ZB - Kassel DPDHL MECH-ZB - Mainz Post Österreich - Wolfurt DHL - Graben (ASC) Post Österreich - Linz Post Österreich / Salzburg DHL - Euskirchen DPDHL MECH-ZB - Bonn DPDHL MECH-ZB - Brühl DPDHL MECH-ZB - Düsseldorf DPDHL MECH-ZB - Köln Oskar-Jäger Str. DPDHL MECH-ZB - Neuss DPDHL MECH-ZB - Ratingen DPDHL MECH-ZB - Schwelm DPDHL MECH-ZB - Wuppertal DPDHL MECH-ZB - Würselen DPDHL MECH-ZB - Hannover PZ DPDHL MECH-ZB - Bielefeld

QRS Allocation, delivery within 2 hours

Number of timing belt 00488688030 (n1,j)

Number of timing belt 00488592030 (n2,j)

Number of timing belt 00488512003 (n3,j)

Distance from the central warehouse in Best (KM)

1 1 2 2 2 2 2 2 2 2 3 3 4 4 4 4 4 4 4 5 5 6 6 7 7 7 7 7 7 7 7 7 7 8 8

1 1 1 1 1 1 1 2 1 1 43 2 1 1 1 1 1 1 1 2 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 2 0 0 0 1 0 1 0 0 1 0 0 0 1 0 1

1 1 1 1 1 1 1 2 1 1 0 2 1 1 1 1 1 1 1 2 3 1 1 1 1 1 1 1 1 1 1 1 1 0 1

557 569 735 715 733 733 717 733 751 720 581 511 362 354 346 374 335 325 342 756 714 897 884 174 185 165 128 159 124 133 184 163 119 376 277

78

DPDHL MECH-ZB - Braunschweig DE DPDHL MECH-ZB - Hannover DPDHL MECH-ZB - Berlin Gasag DPDHL MECH-ZB - Berlin Gradestrasse DPDHL MECH-ZB - Berlin Nord DPDHL MECH-ZB - Berlin Orlopp DPDHL MECH-ZB - Berlin Pankow DPDHL MECH-ZB - Berlin Suedost DPDHL MECH-ZB - Berlin Zentrum MECH-ZB - Kleinmachnow DPDHL MECH-ZB - Oldenburg DPDHL MECH-ZB - Freiburg DPD - Föhren DPDHL MECH-ZB - Koblenz DHL - Rheinberg (ASC) DPDHL MECH-ZB - Bochum DPDHL MECH-ZB - Dinslaken DPDHL MECH-ZB - Essen DPDHL MECH-ZB - Hamm DPDHL MECH-ZB - Kamen DPDHL MECH-ZB - Moers DPDHL MECH-ZB - Oer-Erkenschwick DPDHL MECH-ZB - Osnabrück MECH-ZB - Essen Steele DHL - Regensdorf MECH-ZB - Lörrach DPDHL MECH-ZB - Hamburg Billbrook DPDHL MECH-ZB - Lübeck DPDHL MECH-ZB - Norderstedt DPDHL MECH-ZB - Tornesch DHL Prague DPDHL MECH-ZB - Heilbronn DPDHL MECH-ZB - Holzgerlingen DPDHL Mech-ZB - Karlsruhe 2 DPDHL MECH-ZB - Leimen DPDHL MECH-ZB - Mannheim Nord DPDHL MECH-ZB - Mannheim Süd DPDHL MECH-ZB - Stuttgart DPDHL MECH-ZB - Waiblingen DPDHL MECH-ZB - Würzburg DPD Edinburgh DPD Cardiff DPD Stoke Hermes (94276)

8 8 9 9 9 9 9 9 9 9 10 11 12 12 13 13 13 13 13 13 13 13 13 13 14 14 15 15 15 15 16 17 17 17 17 17 17 17 17 17 18 19 20 20 79

1 1 1 1 1 1 1 1 1 1 1 1 2 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2

1 1 0 0 0 1 0 1 1 0 1 1 0 1 0 0 1 0 0 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 0 0 0 1 1 1 1 1 1 0

1 1 1 1 1 1 1 1 1 1 1 1 2 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0

438 376 672 659 659 671 685 669 655 636 365 575 278 247 114 147 128 132 206 187 108 164 257 137 706 634 480 541 492 500 859 457 521 442 408 381 381 511 512 464 1098 718 749 644

DPD Exeter DPD Leeds SPO DPD Liverpool DPD Dagenham DPD Dunstable FedEx Milton Keynes Bartolini Pisa Bartolini Genova DHL Express Katowice Ozarowice PL Bartolini Brescia Bartolini Parma DHL HUB - Graz AT Post Österreich - Graz Bartolini S.P.A. BRT Perugia Bartolini Roma Bartolini Caserta Bartolini Bari BRT Rovereto Trento TNT Padova Bartolini Ancona Bartolini Gatteo MTN Bologna Bartolini Gorizia DHL HUB - Wien AT DHL Bratislava Bartolini Landriano Bartolini Torino GLS - San Giuliano Milanese ad Estatal Correos Y Teleg Malaga Ciblex Lyon Mions FR Geopost Baune (Exapaq) UPS Lyon Jonage FR SEUR ESPAÑA OPERACIONES, S.A. Correos Express Coslada / Madrid ES TNT Express Worldwide San Fernando RAMONEDA CARGO, S.L. Calberson Paris Gonesse FR Ciblex Chilly FR Ciblex Roissy FR XP Lieusaint PNL Jönköping DHL Express Goteborg SE DHL Goteborg

21 22 23 24 24 24 25 26 27 28 28 29 29 30 30 30 31 32 33 33 34 35 35 36 37 37 38 38 38 39 40 40 40 41 42 42 42 43 43 43 43 44 45 45 80

1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 0 0 0 1 0 0 1 0 0 1 1 1 0 2 1 1 2 2 1 1 2 1 5 1 1 1 1 1 1

1 1 1 1 1 2 1 1 0 1 0 0 0 1 1 1 1 1 1 2 0 1 1 1 0 0 1 1 0 0 1 2 2 0 0 0 0 5 1 1 0 1 1 1

1 1 1 1 1 2 1 1 0 1 0 0 1 1 1 1 1 1 1 2 1 1 1 1 0 1 1 1 0 1 1 3 2 1 0 2 0 5 1 1 0 1 1 1

732 773 834 461 535 566 1249 1107 1142 1054 1095 1057 1057 1536 1418 1540 1715 1852 1014 1203 1409 1281 1182 1223 1060 1146 990 1042 990 2225 833 611 829 1976 1707 1701 1720 427 459 421 473 1131 1110 1110

DHL Express Vastberga DHL Vastberga SE Post Danmark - Kolding DHL Oslo Skedsmokorset NO Posten Norge Alnabru NO Posten Norge Drammen NO Posten Norge Fredrikstad NO Matkahuolto Helsinki FI Posten logistik Schenker Helsinki Vantaa CEVA - Oostrum DHL Beek NL DHL Eindhoven DPD Nederland B.V. Best TNT Milmort BE P&T Luxemburg DHL Aviation Brussel Schenker Mechelen TNT Express Antwerpen TNT Zulte UPS Diegem GLS Services Leidsche Rijn DHL Drachten NL DHL Zwolle Interlink Ireland Correos Las Palmas ES Correos Santa Cruz de Tenerife ES Urgent Currier Bucharest - Romania Estonian Post

46 46 47 48 48 48 48 49 49 49 50 50 50 50 51 51 52 52 52 52 52 53 54 54 55 56 57 58 59

81

1 1 1 1 3 1 1 2 1 1 1 1 1 0 1 0 2 1 1 1 1 2 0 1 2 2 1 2 0

1 1 1 1 3 0 0 2 1 2 1 1 1 1 0 0 2 1 1 1 1 0 1 2 2 2 1 2 1

1 1 1 1 3 1 1 2 1 2 1 1 1 0 0 1 2 1 1 1 1 0 1 2 0 2 1 2 1

1443 1443 715 1283 1294 1244 1319 1931 1763 1931 53 89 14 2 126 312 136 117 95 176 132 85 226 147 1206 3717 3649 2136 2153

APPENDIX M â&#x20AC;&#x201C; SEQUENCE OF EVENTS PMAO POLICY AND PMAO-EXTENSION POLICY In this appendix, the sequence of events for the PMAO policy and PMAO-extension policy of Coumans (2017) are shown in Figure 25 and figure 26.

Figure 24: Sequence of events PMOA policy (Coumans, 2017)

Figure 25: Sequence of events PMOA-extension policy (Coumans, 2017)

82

APPENDIX N â&#x20AC;&#x201C; DIFFERENT SPARE PARTS IN THE NUMERICAL EXPERIMENTS In this appendix, we show the different spare parts considered in the numerical experiments. These are 18 different spare parts that all differ from each other on at least one aspect (demand rate, price or lead time).

Table 16: different spare parts considered in the numerical experiments

Spare part

Demand rate: High - Medium - Low

Price: High - Medium - Low

Lead time: Low - High

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Low Low Low Low Low Low Medium Medium Medium Medium Medium Medium High High High High High High

Low Low Medium Medium High High Low Low Medium Medium High High Low Low Medium Medium High High

Low High Low High Low High Low High Low High Low High Low High Low High Low High

83

UBM threshold: high variance (Running Hours) 1440 1440 2082 2082 3357 3357 721 721 1042 1042 1680 1680 165 165 262 262 421 421

UBM threshold: low variance (Running Hours) 1089 1089 1360 1360 1785 1785 545 545 681 681 894 894 130 130 172 172 225 225

APPENDIX O â&#x20AC;&#x201C; DIFFERENT NUMERICAL EXPERIMENTS This appendix shows the different numerical experiments that we have performed. There are nice different experiments based on the spare parts specification from Appendix P and these nice experiments are done three times, following a different Weibull distribution for the spare parts.

Table 17: different numerical experiments

Experiment

Demand rate

1.1

All Low demand All medium demand All high demand

2.1 3.1 4.1

Price

All low price All medium price All high price

5.1 6.1 7.1 8.1 9.1 1.2 2.2 3.2

Lead time

All All Low demand All medium demand All high demand

4.2

All

All low Lead time All High Lead time All

All low price All medium price All high price

5.2 6.2 7.2 8.2 9.2 1.3

All All Low demand

2.3

All medium demand

All

All low Lead time All High Lead time All

84

Weibull distribution

Number of items

Data-based

6

Data-based

6

Data-based

6

Data-based

6

Data-based

6

Data-based

6

Data-based

9

Data-based

9

Data-based Lower

18 6

Lower

6

Lower

6

Lower

6

Lower

6

Lower

6

Lower

9

Lower

9

Lower Expect databased but face lower Expect databased but face lower

18 6

6

3.3

All high demand

4.3

All low price

5.3

All medium price

6.3

All high price

7.3

All low Lead time

8.3

All High Lead time

9.3

All

All

All

85

Expect databased but face lower Expect databased but face lower Expect databased but face lower Expect databased but face lower Expect databased but face lower Expect databased but face lower Expect databased but face lower

6

6

6

6

9

9

18

APPENDIX P â&#x20AC;&#x201C; DETERMINATION OF INPUT VALUES FOR ADI POLICIES In this appendix, we elaborate on the used input values for the ADI models that are based on data or decision earlier on.

First, for the customer site specific parameters, we decided to focus on small customer sites (one of the scenarios in Section 4.3) because most SPO sites fall in this category and we did not have enough time to run all experiments for all customer sites. Next to that, we set the variance in shift length to 1 hour, based on the interview with the system engineer.

The following numbers are based on the input values of Chapter 5. The number of customer served from the QRS is equal to 3, average number of customer served in Chapter 5. The Cem is equal to 753, which is average emergency costs over all customers considered in Chapter 5. The ttravel is equal to 2 hours, the tem is equal to 24 hours, both based on Chapter 5, and the treplacement is equal to 1.88 hours, based on the time it takes to replace a timing belt, assuming this is about the same for all components.

Lastly, the Wobj is set to 3 hours just as in Chapter 5. Note that we did not vary on the PM fill rate or this objective for the aggregate mean waiting time as this is done by Coumans (2017).

86

APPENDIX Q â&#x20AC;&#x201C; OUTCOME STATISTICS OF THE NUMERICAL EXPERIMENTS This appendix shows the average cost, maximum cost, minimum cost and a 95% confidence interval of the cost for all numerical experiments and all policies based on 101 runs. The 95% confidence interval is đ?&#x2018;&#x2020;đ?&#x2018;Ąđ?&#x2018;&#x17D;đ?&#x2018;&#x203A;đ?&#x2018;&#x2018;đ?&#x2018;&#x17D;đ?&#x2018;&#x;đ?&#x2018;&#x2018; đ?&#x2018;&#x2018;đ?&#x2018;&#x2019;đ?&#x2018;Łđ?&#x2018;&#x2013;đ?&#x2018;&#x17D;đ?&#x2018;Ąđ?&#x2018;&#x2013;đ?&#x2018;&#x153;đ?&#x2018;&#x203A;(101 đ?&#x2018;&#x;đ?&#x2018;˘đ?&#x2018;&#x203A;đ?&#x2018; )2 ..

101

calculated by Average(101 runs) Âą t100,0.975â&#x2C6;&#x161;

In this equation, t100,0.975 is the

critical value of the Student t-distribution with 100 degrees of freedom and Îą equal to 0.025.

Table 18: Outcome of the numerical experiments for the non-UBM policy

Experiment: Non-UBM

Average

Max

Min

95% confidence interval: lower bound

1.1 2.1 3.1 4.1 5.1 6.1 7.1 8.1 9.1

1586683 1732287 1477951 3211814 3376348 3031120 12900959 13221996 12551101 4883211 5062061 4740727 5227841 5443346 5065462 5904265 6112331 5675683 8842868 9074726 8546508 8834404 9113059 8515274 17659702 18049025 17247856

1576129 3198747 12873104 4867834 5212802 5885056 8820328 8812113 17628263

95% confidence interval: upper bound 1597238 3224881 12928814 4898588 5242879 5923475 8865408 8856696 17691141

1.2 2.2 3.2 4.2 5.2 6.2 7.2 8.2 9.2

1553926 1636570 1463170 3174151 3270646 3082840 12829018 13037464 12617881 5366407 5525224 5244884 5724375 5860823 5580474 6458951 6639336 6295209 8778916 9019784 8569914 8784506 9033881 8609523 17559913 17881862 17305338

1547447 3165512 12811918 5355764 5712947 6445366 8763797 8769726 17537426

1560406 3182791 12846118 5377051 5735803 6472536 8794036 8799287 17582400

1.3 2.3 3.3 4.3 5.3 6.3 7.3 8.3 9.3

1548482 1652295 1464872 3170358 3298889 3052089 12841206 13067711 12651357 5361210 5486294 5222082 5732061 5884708 5566182 6472010 6593432 6323872 8777557 8992923 8472823 8769865 8981149 8616569

1267962856 2185512648 8640998842 3529179137 4310723579 3600716492 6139295311 4979736273

1541452 3161129 12822855 5349482 5719099 6460164 8762088 8755934

17571346 18019555 17331979 10533776686

17551084

87

Base stocks

(4 ,5, 3, 4, 2, 3) (5, 7, 4, 6, 3, 5) (12,18,10,15,8,12) (2, 3, 3, 5, 10, 15) (2, 3, 3, 5, 10, 15) (2, 3, 3, 5, 10, 15) (3 ,2, 2, 5, 4, 3, 12, 10, 8) (5, 3, 2, 7, 5, 4, 19, 16, 14) (3,4,2,3,2,2,5,7,4, 5,3,4,12,18,10,16,9,13) (4 ,5, 3, 4, 2, 3) (5, 7, 4, 6, 3, 5) (12,18,10,15,8,12) (2, 3, 3, 5, 10, 15) (2, 3, 3, 5, 10, 15) (2, 3, 3, 5, 10, 15) (3 ,2, 2, 5, 4, 3, 12, 10, 8) (5, 3, 2, 7, 5, 4, 19, 16, 14) (3,4,2,3,2,2,5,7,4, 5,3,4,12,18,10,16,9,13) (4 ,5, 3, 4, 2, 3) (5, 7, 4, 6, 3, 5) (12,18,10,15,8,12) (2, 3, 3, 5, 10, 15) (2, 3, 3, 5, 10, 15) (2, 3, 3, 5, 10, 15) (3 ,2, 2, 5, 4, 3, 12, 10, 8) (5, 3, 2, 7, 5, 4, 19, 16, 14) (3,4,2,3,2,2,5,7,4, 5,3,4,12,18,10,16,9,13)

Table 19: Outcome of the numerical experiments for the non-ADI policy

Experiment: Non-ADI

Average

Max

1.1 2.1 3.1 4.1 5.1 6.1 7.1 8.1 9.1

1505977 1622495 1375714 3036093 3238407 2885399 12563478 12966803 12140470 5384185 5552033 5158741 5568787 5771614 5368454 6414099 6867007 6194327 8398326 8719219 8030447 8624590 8932119 8304493 17081877 17528203 16680823

1496225 3021978 12531922 5367504 5550426 6392436 8372916 8599810 17046563

95% confidence interval: upper bound 1515730 3050207 12595033 5400867 5587149 6435761 8423735 8649369 17117192

1.2 2.2 3.2 4.2 5.2 6.2 7.2 8.2 9.2

1108993 1192835 1007620 2252508 2354434 2108291 9799961 10120929 9530251 3708505 3882900 3567240 4246075 4465754 4052071 5306734 5492586 5141756 6333872 6498825 6120136 6705915 6943641 6475278 13083318 13349211 12815190

1102283 2242962 9778380 3695123 4230036 5289935 6319431 6686622 13060365

1115704 2262054 9821542 3721888 4262115 5323532 6348314 6725207 13106272

1.3 2.3 3.3 4.3 5.3 6.3 7.3 8.3 9.3

1184825 2382116 9790690 3547420 4229865 5826301 6584719 6703407

1207833416 3019948900 13499317507 4855226663 4723353236 5131871569 8319509593 9211459669

1177964 2371267 9767753 3533664 4216297 5812158 6566712 6684460

13355458 13645294 13074245 15160721194

13331150

1257145 2513500 10049415 3711015 4389409 6012686 6815360 6993084

Min

95% confidence interval: lower bound

1100066 2241961 9480208 3342767 4050945 5641398 6264579 6489408

88

Base stocks

(4 ,5, 3, 4, 2, 3) (5, 7, 4, 6, 3, 5) (12, 18, 10, 15, 8, 12) (2, 3, 3, 5, 10, 15) (2, 3, 3, 5, 10, 15) (2, 3, 3, 5, 10, 15) (3, 2, 2, 5, 4, 3, 12, 10, 8) (5, 3, 2, 7, 5, 4, 19, 16, 14) (3,4,2,3,2,2,5,7,4, 5,3,4,12,18,10,16,9,13) (4 ,5, 3, 4, 2, 3) (5, 7, 4, 6, 3, 5) (12,18,10,15,8,12) (2, 3, 3, 5, 10, 15) (2, 3, 3, 5, 10, 15) (2, 3, 3, 5, 10, 15) (3 ,2, 2, 5, 4, 3, 12, 10, 8) (5, 3, 2, 7, 5, 4, 19, 16, 14) (3,4,2,3,2,2,5,7,4, 5,3,4,12,18,10,16,9,13) (4 ,5, 3, 4, 2, 3) (5, 7, 4, 6, 3, 5) (12,18,10,15,8,12) (2, 3, 3, 5, 10, 15) (2, 3, 3, 5, 10, 15) (2, 3, 3, 5, 10, 15) (3 ,2, 2, 5, 4, 3, 12, 10, 8) (5, 3, 2, 7, 5, 4, 19, 16, 14) (3,4,2,3,2,2,5,7,4, 5,3,4,12,18,10,16,9,13)

Table 20: Outcome of the numerical experiments for the PMAO policy

Experiment: PMAO

Average

Max

1.1 2.1 3.1 4.1 5.1 6.1 7.1 8.1 9.1

1479832 1629548 1355744 2977409 3145662 2817790 11998294 12380753 11715754 4723850 4919195 4504922 5351454 5642516 5097446 6358514 6535053 6135414 8166326 8400334 7796804 8236214 8507998 7962917 16399947 16730692 16022666

1470225 2963640 11968244 4708706 5333362 6339948 8143563 8214424 16369794

95% confidence interval: upper bound 1489439 2991178 12028344 4738994 5369547 6377080 8189090 8258005 16430101

1.2 2.2 3.2 4.2 5.2 6.2 7.2 8.2 9.2

1070103 1154971 1009255 2160268 2277123 2031776 8943979 9189658 8714972 3184831 3327131 3029046 3863634 4063430 3722977 5137449 5308167 4977853 5958170 6182032 5760088 6205818 6463803 5981496 12186866 12474214 11945382

1064148 2150899 8925505 3173398 3851642 5124446 5943577 6188399 12163475

1076057 2169636 8962452 3196263 3875627 5150452 5972763 6223237 12210256

1.3 2.3 3.3 4.3 5.3 6.3 7.3 8.3 9.3

1157236 2350822 9533652 3131953 4108792 5812167 6473921 6576547

1168739720 3060657169 10128096938 2635794804 4566578966 5864082012 6648944298 7227473171

1150487 2339901 9513785 3121817 4095451 5797049 6457824 6559764

13075446 13415262 12756334 15572021076

13050811

1222206 2495525 9784559 3271757 4278540 5982160 6678774 6743993

Min

95% confidence interval: lower bound

1078409 2228142 9327911 3027268 3947139 5612231 6304086 6396952

89

Base stocks

(3, 4, 3, 4, 2, 3) (4, 6, 4, 5, 3, 5) (9, 13, 8, 12, 8, 11) (2, 2, 3, 4, 7, 11) (2, 3, 3, 4, 8, 12) (2, 3, 4, 5, 9, 14) (3, 2, 2, 4, 3, 3, 9, 8, 8) (4, 3, 2, 6, 5, 4, 14, 13, 13) (3,4,2,3,2,2,4,5,3, 4,3,4,9,13,8,13,8,12) (2, 3, 2, 3, 2, 2) (3, 4, 3, 3, 3, 3) (5, 7, 5, 7, 5, 7) (1, 2, 2, 3, 4, 6) (1, 2, 2, 3, 5, 8) (2, 2, 2, 3, 6, 8) (2,2,1,3,2,2,5,6,5) (2,2,2,4,3,3,7,8,7) (2,2,2,2,1,2,3,4, 2,3,2,3,5,7,6,8,5,7) (3, 4, 3, 4, 2, 3) (4, 6, 4, 5, 3, 5) (9, 13, 8, 12, 8, 11) (2, 2, 3, 4, 7, 11) (2, 3, 3, 4, 8, 12) (2, 3, 4, 5, 9, 14) (3, 2, 2, 4, 3, 3, 9, 8, 8) (4, 3, 2, 6, 5, 4, 14, 13, 13) (3,4,2,3,2,2,4,5,3, 4,3,4,9,13,8,13,8,12)

Table 21: Outcome of the numerical experiments for the PMAO-extension policy

Experiment: PMAOextension

Average

Max

1.1 2.1 3.1 4.1 5.1 6.1 7.1 8.1 9.1

1472356 1590460 1334548 2972454 3126840 2806861 11856766 12176956 11539171 4655666 4866061 4466727 5324995 5524975 5117382 6334684 6639016 6039360 8142630 8435550 7823064 8142691 8416638 7837820 16302104 16820847 15947184

1462256 2957486 11829324 4638711 5307862 6314283 8120221 8120030 16272609

95% confidence interval: upper bound 1482456 2987422 11884208 4672620 5342127 6355086 8165039 8165353 16331599

1.2 2.2 3.2 4.2 5.2 6.2 7.2 8.2 9.2

1067410 1154474 986619 2152896 2266440 2033606 8839787 9054213 8643653 3176176 3304228 3057091 3808564 3964131 3663942 5117334 5267318 4979590 5951700 6099054 5770589 6103243 6260287 5926418 12051297 12388731 11724810

1061192 2143449 8822201 3164636 3795379 5104126 5937992 6088052 12029173

1073627 2162342 8857373 3187716 3821750 5130542 5965407 6118434 12073420

1.3 2.3 3.3 4.3 5.3 6.3 7.3 8.3 9.3

1161360 2346632 9441476 3050577 4111570 5806840 6469106 6477381

867798162 2148665322 10557130668 2460311152 4392751066 6770452430 7147857390 6849370774

1155544 2337481 9421191 3040785 4098486 5790596 6452415 6461043

12955882 13311558 12542463 18794226492

12928818

1220179 2473422 9679659 3174807 4275043 5993054 6695815 6679317

Min

95% confidence interval: lower bound

1085571 2236766 9218274 2898121 3946804 5585054 6242154 6208227

90

Base stocks

(3, 4, 3, 4, 2, 3) (4, 6, 4, 5, 3, 5) (9, 13, 8, 12, 8, 11) (2, 2, 3, 4, 7, 11) (2, 3, 3, 4, 8, 12) (2, 3, 4, 5, 9, 14) (3, 2, 2, 4, 3, 3, 9, 8, 8) (4, 3, 2, 6, 5, 4, 14, 13, 13) (3,4,2,3,2,2,4,5,3, 4,3,4,9,13,8,13,8,12) (2, 3, 2, 3, 2, 2) (3, 4, 3, 3, 3, 3) (5, 7, 5, 7, 5, 7) (1, 2, 2, 3, 4, 6) (1, 2, 2, 3, 5, 8) (2, 2, 2, 3, 6, 8) (2,2,1,3,2,2,5,6,5) (2,2,2,4,3,3,7,8,7) (2,2,2,2,1,2,3,4,2, 3,2,3,5,7,6,8,5,7) (3, 4, 3, 4, 2, 3) (4, 6, 4, 5, 3, 5) (9, 13, 8, 12, 8, 11) (2, 2, 3, 4, 7, 11) (2, 3, 3, 4, 8, 12) (2, 3, 4, 5, 9, 14) (3, 2, 2, 4, 3, 3, 9, 8, 8) (4, 3, 2, 6, 5, 4, 14, 13, 13) (3,4,2,3,2,2,4,5,3, 4,3,4,9,13,8,13,8,12)

Table 22: Outcome of the numerical experiments for the PMAO-CM-priority policy

Experiment: PMAO-CMpriority

Average

Max

1.1 2.1 3.1 4.1 5.1 6.1 7.1 8.1 9.1

1472711 1589959 1344543 2964099 3085315 2792642 11897326 12223860 11486522 4705643 4928165 4510359 5313671 5558990 5045535 6345734 6590627 6112711 8132533 8424818 7912266 8191384 8433658 7946151 16370065 16738815 16047639

1463769 2949889 11866057 4689358 5296216 6326088 8111211 8171379 16340197

95% confidence interval: upper bound 1481652 2978309 11928595 4721928 5331127 6365379 8153855 8211389 16399932

1.2 2.2 3.2 4.2 5.2 6.2 7.2 8.2 9.2

1066840 1147599 994953 2151093 2265625 2022966 8895307 9145130 8679317 3160416 3279783 3036242 3851697 3976952 3730018 5114106 5282936 4954431 5945145 6174532 5745672 6173021 6364847 5959779 12136882 12418582 11883703

1060320 2141992 8875619 3149746 3841705 5100902 5930580 6157835 12114017

1073360 2160194 8914995 3171086 3861688 5127310 5959711 6188207 12159746

1.3 2.3 3.3 4.3 5.3 6.3 7.3 8.3 9.3

1158662 2349450 9528541 3120840 4123251 5797978 6469190 6563342

1474393411 2672155102 12652548865 2960377585 4644315262 5676627877 6801066570 7198639253

1151082 2339246 9506335 3110099 4109797 5783104 6452909 6546593

13049313 13370239 12760985 14319004008

13025690

1248896 2463249 9883405 3269673 4281409 5976981 6697332 6783318

Min

95% confidence interval: lower bound

1055533 2202368 9286576 2972109 3963087 5604101 6312228 6368681

91

Base stocks

(3, 4, 3, 4, 2, 3) (4, 6, 4, 5, 3, 5) (9, 13, 8, 12, 8, 11) (2, 2, 3, 4, 7, 11) (2, 3, 3, 4, 8, 12) (2, 3, 4, 5, 9, 14) (3, 2, 2, 4, 3, 3, 9, 8, 8) (4, 3, 2, 6, 5, 4, 14, 13, 13) (3,4,2,3,2,2,4,5,3, 4,3,4,9,13,8,13,8,12) (2, 3, 2, 3, 2, 2) (3, 4, 3, 3, 3, 3) (5, 7, 5, 7, 5, 7) (1, 2, 2, 3, 4, 6) (1, 2, 2, 3, 5, 8) (2, 2, 2, 3, 6, 8) (2,2,1,3,2,2,5,6,5) (2,2,2,4,3,3,7,8,7) (2,2,2,2,1,2,3,4,2, 3,2,3,5,7,6,8,5,7) (3, 4, 3, 4, 2, 3) (4, 6, 4, 5, 3, 5) (9, 13, 8, 12, 8, 11) (2, 2, 3, 4, 7, 11) (2, 3, 3, 4, 8, 12) (2, 3, 4, 5, 9, 14) (3, 2, 2, 4, 3, 3, 9, 8, 8) (4, 3, 2, 6, 5, 4, 14, 13, 13) (3,4,2,3,2,2,4,5,3, 4,3,4,9,13,8,13,8,12)