A Nonlinear Programming Methodology for the Design of Product-Service System Contracts ˜ a , Gabriel Santelicesa , Milton Rom´anb Rodrigo Pascuala , Mat´ıas Sina a
´ ˜ Mackenna Mining Engineering Department, Pontificia Universidad Catolica de Chile, Vicuna 4860, Santiago, Chile b
˜ Mackenna 4860, Santiago, Chile DICTUC Tire, Vicuna Abstract
This paper proposes an original methodology for the optimal design of use-oriented ProductService System (PSS) contracts. In a PSS instead of paying for the product, the client pays a fee for its performance. The contribution of this work to the existing literature is to provide a quantitative tool for the development of a use-oriented PSS contract based on non-repairable component reliability and risk sharing. It can be extended to other performance metrics such as availability and reliability. A well designed PSS achieves a mutual growth agreement for the client and the supplier if it aligns their interests through channel coordination. This is achieved by balancing the improvement in the expected cost and profit for the client and the supplier respectively. The improvement is measured with respect to a baseline scenario where no PSS contract exists. The methodology is tested using a case study that analyses mining haul-truck tires. The results show a significant overall improvement in the main key performance indicators and environmental impact of the value chain. Keywords: Product-Service Systems, physical asset management, service contracts, channel coordination.
1
Introduction
A Product-Service System (PSS) is an agreement between a client and a supplier in which a traditional product-oriented business strategy shifts to a service-oriented one [1]. This means that the client pays for the performance of the product instead of paying for the product itself. A PSS usually adds value to the value chain, provides an optimal answer to the customers needs and increase the sustainability of the business models of both the client and the supplier [2]. A PSS contract can be: i) product-oriented, ii) use-oriented or iii) result-oriented. In a product-oriented PSS the clients buys the product as usual but it also includes an additional service such as maintenance, spare-parts provisioning and/or training. In a use-oriented PSS the client pays for the use or availability of the product. Finally, in a result-oriented PSS the client pays for the performance or capability of the product. The decision of which kind of PSS to adopt depends on the specific characteristics of the business chain [3]. The PSS concept was developed in response to the increasingly complex business environment. It is a way in which suppliers can enhance their competitiveness and reduce risks associated to market volatility [4]. PSS can align the interests of the client and the supplier to create an overall improvement in the business value chain. Moreover, PSS can create value to the client through a better response to the needs that are related to the use of the product. It eliminates the responsibilities of owning the product so that the client can focus on its core business. For the supplier the PSS creates value as it increases its profits through the sale of additional services [2] and gives a competitive advantage that is difficult to imitate by the competition. PSS can also create value for the environment since a PSS leads to a more responsible relationship within the value chain [3]. To effectively establish a PSS relationship there are several barriers that must be overcome by the client and the product supplier. Some of them are: i) the need of reciprocal trust between the client and the supplier, ii) the lack of enthusiasm of clients about an unowned consumption and iii) the suppliers concern with the 1
risk of a new pricing policy[5]. Therefore, firms must undergo a transition in their organizational structure to effectively overcome this barriers. The transition is difficult and requires collaboration between the client and the supplier to be successfully done [6]. In this context, channel coordination arises as an attractive solution to align interests in the value chain as it can provides flexibility, creates new value and generates extra profit [7]. While an interesting body of knowledge has been published on the PSS as a concept [2], no work has been published to optimize the design of a PSS contract subjected to non-repairable components reliability to the authors’ knowledge. In the following sections it is shown that components’ reliability may have a strong impact on the contract performance. Therefore, a structured methodology is proposed for the design of a use-oriented PSS contract based on this concept and risk sharing. It that can be implemented easily to different operational conditions which results in optimal solutions for the client’s requirements. In this contract the supplier has the ownership of the component and is responsible for its performance. On the other hand, the client pays a fee for its use and usually has individual and unlimited access to it. This paper is structured as follows. Section 2 presents a general literature review of PSS and channel coordination to provide a context for the problem formulation. Section 3 develops the formulation of the proposed methodology for the design of the PSS contract based in component reliability and channel coordination. Section 4 presents the case study of mining haul truck tires, the results and a sensitivity analysis. Finally, section 5 presents the conclusions and future lines of work.
2
Literature review
PSS studies have increased in the last years due to the potential benefits that they can create to the value chain. Casadesus and Ricart establish that a PSS is conformed by 3 main components: i) a strategy, ii) a business model and iii) tactics [8]. These components may be organized in a hierarchical relationship in which the strategy leads to a business model while the selected business model creates tactics for its optimal implementation. Maussang et al. propose that for many suppliers their strategy is to achieve a competitive advantage with respect to other companies in order to increase their market share [9]. Nonetheless, Cavalieri and Pezzotta suggest that the existing literature lacks of quantitative tools for the design of PSS that aligns the strategy of a firm with its business model and tactics [10]. There are some works on the design of maintenance outsourcing contracts using analytical models that can be extended to PSS contracts, but no one addresses these contracts directly. Tarakci et al. present several incentive policies to achieve channel coordination in maintenance outsourcing contracts [11]. They extend their work by studying the effect that backup machines have in the risk mitigation of machine failure [12]. Wang presents different contract designs based on the level that the maintenance activities are outsourced [13]. Pascual et al. consider imperfect maintenance and contracts with a finite time horizon [14]. They also consider in a more recent work a mechanism to reach channel coordination over a finite time period [7]. Channel coordination is a concept that can be used for the development of a PSS as it can align interests. Several works have addressed the problem of developing contracts with channel coordination. Kanda et al. develop a detailed review of channel coordination in the supply chain which includes different coordination mechanism and gaps in the literature [15]. Arshinder et al. link coordination mechanism with the supply chain performance [16]. Hill and Omar establish that the supply chain can reach coordination when the members effectively minimize the global cost and share the profits obtained [17]. Barrat consider the implementation issues that arises the development of coordination and the mechanism to overcome them [18].
2
3
Model formulation
The contract developed is a use-oriented PSS for a non-repairable component. The client must pay the supplier a fee that depends on the time that the component is effectively used until it needs to be replaced. The improvement that the contract creates for the client and the supplier is measured with respect to a base case scenario, where the component is sold at a fixed price per unit. The objective is to maximize and equally share the improvement between the client and the supplier under the PSS contract.
3.1
Base case
In the base case the client buys a non-repairable component to a supplier for a unit price of C0 (mu, monetary units) while the supplier has a unit cost of CF (mu). In this initial scenario the product is expected to last t e (tu, time units) until it has to be replaced. Therefore, the expected cost for the client (cb ) (mu/tu) and profit for the supplier (πb ) (mu/tu) can be written as, C0 te
(1)
C0 − CF te
(2)
cb =
πb =
3.2
PSS contract
The PSS contract is use-oriented so the client pays a fee for the effective time that the components is used. Equation 1 and Figure 1 show the fee structure, depending on the component’s duration. C0 t t + C 1 − if t ≤ t e 0 te te C(t) = (1 − α) C0 t if t > t e t
(3)
e
C0 (1−α)/te
C(t)
1
1
C0/te
Use Prorate Total
t (tu)
Figure 1: Fee structure of the PSS.
3
The fee includes a pro-rata cost and a usage cost that decreases as the component life increases. In the case of the usage cost there is an extended life sharing factor α once the component passes t e . Similarly, the pro-rata cost decreases linearly until t e . The objective is to create an incentive for the client to improve its operational conditions so that the component lasts longer. This fee guarantees that the supplier will not reduce its profit in the case that the expected life of the component decreases. Therefore, it is more probable that the supplier will be willing to develop a PSS agreement. Moreover, the client can extend the expected life of the component by increasing an indirect maintenance cost (cm ). The reliability function of the component depends on the operational conditions and the time that the component is used, as it is shown in Figure 2. 1 cm = ∞ cm *
0.8
cm = 0 R(t)
0.6 0.4 0.2 0 0
5
10 t (tu)
15
20
Figure 2: Reliability function of the component under different operational conditions.
The expected improvement that the PSS contract creates for the client (γc ) and the supplier (γs ) are calculated with respect to the base case. The improvement is measured as a percentage rather than in absolute terms, so that both business relative sizes are considered. γc =
cb − cP SS cb
(4)
γs =
πP SS − πb πb
(5)
The expected cost for the client (cP SS ) and the profit for the supplier (πP SS ) per time units under the PSS contract are functions of the indirect maintenance cost and the extended-life sharing factor. For the optimal configuration of the PSS contract the improvement for the client and the supplier must satisfy the following, max γc (cm , α) + γs (cm , α) cm ,α
s.t.
γc (cm , α) = γs (cm , α)
(6)
cP SS ≤ cb πP SS ≥ πb This work presents two different models for the design of the PSS. In the first model the component fails only by the use that the client gives to it. In the second one, it can also present manufacture failures on early stages of its life. If the component fails due to manufacture failures the client does not have to pay the pro-rata cost.
4
3.3
Model 1
The reliability function for the component in this model is a Weibull distribution of two parameters, where βc is the shape parameter and ηc (cm ) is the characteristic life of the component. R (t, cm ) = e
−
βc t ηc (cm )
(7)
Using equations 1 and 7 the expected cost (C) that the clients pays until de component is replaced may be written as, ∞
Z
C(t)f (t, cm ) dt
C= 0
Z C = C0
te 0
C f (t, cm ) dt + (1 − α) 0 te
Z
(8)
∞
te
tf (t, cm ) dt
(9)
where f (t, cm ) is the density function of failure. By adding the maintenance cost to equation 9, the expected cost of the client (C c ) is obtained. Similarly, the expected profit of the supplier (πs ) may be obtained by adding its unit cost to equation 9.
Z C c = C0
te 0
Z π s = C0
te 0
∞
Z
C f (t, cm ) dt + (1 − α) 0 te
te
Z tf (t, cm ) dt + cm
C f (t, cm ) dt + (1 − α) 0 te
Z
∞
0
tf (t, cm ) dt
(10)
∞
te
tf (t, cm ) dt − CF
(11)
The expected cost of the client and expected profit of the supplier may be written as closed form equations using the following expressions,
Z F t e , cm =
te
0
f (t, cm ) dt = 1 − R t e , cm
Z T F (cm ) =
∞
R (t, cm ) dt
0
Z T I t e , cm =
(13)
te
0
Z
(12)
R (t, cm ) dt
(14)
Z tf (t, cm ) dt =
R (t, cm ) dt − tR (t, cm )
(15)
where F t e , cm is the failure cumulative density function, T F (cm ) is the expected life of the compo nent and T I t e , cm is the expected time to intervene. Then, the expected cost of the client and the expected profit of the supplier are,
5
h i i C0 h (1 − α)T F + α T I − t e R(t e ) + t e − T I + cm T F te
Cc =
πs = C c − cm T F − CF
(16)
(17)
Equations 16 and 17 may be divided by the expected life of the component (T F ) in order to obtain the expected cost and profit per time units.
cP SS1
" # i te − T I C0 α h = (1 − α) + T I − t e R(t e ) + + cm te TF TF
πP SS1 = cP SS − cm −
3.4
CF
(18)
(19)
TF
Model 2
The reliability function for the component in this model is a Mixed Weibull distribution represented by equations 20 and 21. This is a linear combination of the reliability function of the client and the supplier, where the relative weight of the client and the supplier are pc and ps respectively. The main difference between both models is that the reliability function of the supplier depends only on the time that the component is effectively used. The objective of this model is to include the manufacture failures that the component may present on early stages of its life. R (t, cm ) = pc e
−
βc t ηc (cm )
+ ps e
βs − ηts
(20)
= pc Rc (t, cm ) + ps Rs (t) pc + ps = 1
(21)
The client must pay the pro-rata cost only if the component fails before te and its not due to manufacture problems. Therefore, it is necessary to calculate both costs separately. The expected usage cost (C use ) that the client pays to the supplier under this model may be written as,
C C use = 0 te
Z
te
0
C t [pc fc (t, cm ) + ps fs (t)] dt + (1 − α) 0 te
Z
∞ te
t [pc fc (t, cm ) + ps fs (t)] dt
(22)
Similarly, the expected pro-rata cost (C pro ) that the client pays under this model is, Z C pro = C0
te
0
! t 1− pc fc (t, cm ) dt te
(23)
Analogously to Model 1, the expected cost of the client (cP SS ) and the expected profit of the supplier (πP SS ) may be written as closed form equations.
cP SS2
i t e − T Ic C0 α h + cm = T I − t e R(t e ) + pc (1 − α) + te TF TF
6
(24)
πP SS2 = cP SS − cm −
CF TF
(25)
where,
4
T F (cm ) = pc T Fc (cm ) + ps T Fs
(26)
T I t e , cm = pc T Ic t e , cm + ps T Is (t e )
(27)
R t e , cm = pc Rc t e , cm + ps Rs (t e )
(28)
Case study
In an open pit mine, haul-truck tires are a considerable fraction of the operational expenses. They also represent a problem for the mines as the practice to stockpile the used tires affects the environment and requires considerable amount of space inside the mine. To solve this issue some mining companies have developed programs to recycle them. For example, there are companies that have used tires as a derived fuel or insulating material for the construction industry. Nevertheless, due to the remote locations where these companies operate there are still no alternatives to deal effectively with this problem. Therefore, the development of a PSS contract that extends the expected life of the tires arises as a solution that could lead to economical and environmental benefits for the business chain. Figure 3 shows a size reference for the mining haul-truck tires.
Figure 3: Mining haul truck tires size reference.
Mining haul-truck tires are usually bought by the mining companies through a contract with a specific supplier that establishes a list price per unit. Under this policy, companies try to increase the expected life of the tires by increasing the maintenance costs of the trucks’ roads [19]. Mining haultruck tires receive minimal maintenance policies and their expected life can change drastically depending on the mine’s characteristics. For the case study, the characteristic life of the reliability function of the tires is modelled as follows,
7
βc m cm − η cm ηc (cm ) = η10 1 + κ 1 − e
(29)
The parameters used for each model and the base case are presented in Table 1. Table 1: Parameters of the case study.
4.1
Parameter
Value
Units
C0 CF te η10 ηcm ηs βc βcm βs Pc Ps κ
50 35 3 3.5 2 20 2.5 0.7 0.7 0.95 0.05 1.5
mu mu tu tu tu tu -
Results
The problem presented in equation 6 can be solved graphically by analysing the curve formed by the intersection of the surfaces created by equations 4 and 5. Figure 4 illustrates this analysis for model 1.
1.5 1
Client
0.5
γ
0 −0.5 −1
Supplier
−1.5 −2 3
2
1
0
0
0.5
1
α
cm (mu/tu)
Figure 4: Improvement of the client and the supplier with PSS under model 1.
The intersection curve of both surfaces is presented in Figure 5 for model 1 and in Figure 6 for model 2. The resulting curves show that there is a unique optimal configuration in the contract that maximizes the improvement for the client and the supplier.
8
0.187
γ
γ
0.187
γ
0.14 0
1.31
0.14 0.25
3
cm (mu/tu)
(a) cm axis view
0.306
α
0.35
(b) α axis view
Figure 5: Intersection curve for model 1.
0.234
γ
γ
0.234
0.22 0.3
0.91
0.22 0.34
2
c (mu/tu)
0.356
m
(a) cm axis view
α
0.38
(b) α axis view
Figure 6: Intersection curve for model 2.
4.2
Sensitivity analysis
The results show that the proposed methodology creates a considerable improvement in the value chain under both models. Nevertheless, it is important to study how changes in the list price of the tires affect the improvement as the market price of many components is subject to uncertainty. Figures 7 and 8 illustrate the optimal PSS configuration for both models when the list price of the tires (C0 ) increases and decreases by 20 %.
9
0.27
C0 = 40
0.27
γ
γ
C0 = 40
0.187
C0 = 50
0.187 C0 = 50
0.143
0.143
C0 = 60
C0 = 60
0.1 0
1.31
0.1 0.2
3
c (mu/tu)
0.245
0.306
m
(a) cm axis view
α
0.415
0.5
(b) α axis view
Figure 7: Sensitivity analysis for model 1.
C0 = 40
C0 = 40
0.338
C0 = 50
0.234
γ
γ
0.338
C0 = 60
0.179
0.179
0.1 0
0.91
0.1 0.22
2
cm (mu/tu)
(a) cm axis view
C0 = 50
0.234 C0 = 60
0.288
0.356
α
0.481
0.55
(b) α axis view
Figure 8: Sensitivity analysis for model 2. Figures 7 and 8 show that only the extended-life sharing factor changes while the maintenance costs remain constant for both models. However, it is important to study the difference between the improvement under the first PSS contract configuration (C0 = 50) and the proposed variations. According to the results of model 1, the client obtains an improvement of 17% and the supplier of 101% over the base case when the price decreases 20%. On the contrary, when the price increases 20%, the client obtains an improvement of 20% and the supplier of 1% over the base case. The results are analogous for model 2. The client obtains an improvement of 22% and the supplier of 128% over the base case when the price decreases 20%. When the price increases 20%, the client obtains an improvement of 24% and the supplier of 2% over the base case.
4.3
Discussion
The results obtained for the case study show that the proposed PSS methodology creates a significant improvement in the expected cost of the client and profit of the supplier. This is achieved by developing an effective channel coordination within the business chain so that the client and the supplier align their interests. Another important improvement that the PSS contract creates is that it increases the expected life of the tires in both models as the maintenance cost increases. This demonstrates 10
that a PSS can reduce the environmental impact of the business chain. The sensitivity analysis shows that for both models the improvement that the PSS contract creates for the client and the supplier is sensitive to changes in the list price of the tires. However, only the discount over the usage fee changes while the maintenance cost remains constant for each optimal configuration. This result arises the question of how much value does the flexibility in the design of the PSS contract creates when there is uncertainty over the market price of the component. Based on the results it is recommended to create a mechanism to adjust the extended-life sharing factor at specific periods of time during the contract depending of the market price of the tires.
5
Conclusions
This paper develops a quantitative methodology for the design of use-oriented PSS contracts. It is based on non-repairable components reliability and risk sharing. The objective is that the client and the supplier follow a simple and straightforward formulation to reach an optimal configuration for the contract, based on the extended-life sharing factor and the indirect maintenance cost that the client pays. In order to align both interests, channel coordination is achieved by improving equally the client cost and the supplier profit with respect to a base line scenario without the PSS contract. The contribution of this work to the existing PSS literature is to provide a quantitative tool for the design of contracts and show its results in a case study. The methodology can be applied to many kind of components due to the flexibility of the Mixed Weibull distribution to model the components’ reliability. Moreover, the proposed approach helps to deal with information asymmetry, a common difficulty in contracts’ design, by encouraging mutual trust. Mutual trust is needed as the proposed methodology requires that the supplier reveals its unit cost per component to estimate his improvement. Accordingly, the PSS contract is designed to overcome this difficulties. Given the results, there are possible future lines of work: i) the current work can be extended to the case of repairable components subjected to perfect and imperfect maintenance services. A possible approach to achieve this is to modify the fee structure so that the maintenance cost is paid by the supplier. ii) Study the effects of uncertainty over the list price of the components to enhance the design of the PSS contract and adapt it to different market scenarios. iii) Study the effects of investments and the contract duration over the optimal fee through a net present value analysis. iv) Consider information asymmetry in certain variables to study the optimal contract configuration with a game theory approach.
11
References [1] Vasantha, G.V.A.; [et al]. (2011). A review of product-service systems design methodologies, Journal of Engineering Design, Vol. 23, no. 9, pp. 635-659. [2] Baines, T. ;[et al]. (2007). State-of-the-art in product-service systems. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, Vol. 221, no. 10 , pp. 1543–1552. [3] Tukker, A. (2004). Eight types of product-service system: Eight ways to sustainability? Experiences from SusProNet. Business Strategy and the Environment, Vol. 13, no. 4, pp. 246-260. [4] Marquez, P.; [et al.]. (2013). A methodology for product-service systems development. Procedia CIRP, Vol. 7, pp.371-376. [5] Cook, M.; [et al.]. (2006). The transfer and application of Product Service Systems:from academia to UK manufacturing firms. Journal of cleaner Production, Vol. 14, no. 17, pp.1455-1465. [6] Oliva, R; Kallenberg, R. (2003). Managing the transition from products to services. International Journal of Service Industry Management, Vol. 14, no. 2, pp. 160-172. [7] Pascual, R.; [et al.]. (2016). Channel Coordination on Fixed Term Maintenance Outsourcing Contracts. IIE Transactions, Vol. 29, no. 5, pp.564-577. [8] Casadesus, R; Ricart, J. (2010). From Strategy to Business Models and onto Tactics. Long Range Planning, Vol. 43, no. 2-3, pp. 195-215. [9] Maussang, N.; [et al]. (2009). Product-service system design methodology: from the PSS architecture design to the products specifications. Journal of Engineering Design, Vol. 20, no 4, pp. 349-366. [10] Cavalieri, S.; Pezzotta, G. (2012). Product-Service Systems Engineering: State of the art and research challenges. Computers in Industry, Vol. 63, no. 4, pp. 278-288. [11] Tarakci, H.; [et al.]. (2006). Incentive Maintenance Outsourcing Contracts for Channel Coordination and Improvement. IIE Transactions, Vol. 38, no. 8, pp.671-684. [12] Tarakci, H.; [et al.]. (2014). Maintenance-Outsourcing Contracts for a System with Backup Machines. International Journal of Production Research, Vol. 52, no. 11, pp.3259-3272. [13] Wang, W. (2010). A Model for Maintenance Service Contract Design, Negotiation and Optimization. European Journal of Operational Research, Vol. 201, no. 1, pp.239-246. [14] Pascual, R.; [et al.]. (2013). Optimizing Maintenance Service Contracts under Imperfect Maintenance and a Finite Time Horizon. Applied Stochastic Models in Business and Industry, Vol. 29, no. 5, pp.564-577. [15] Kanda, A.; Deshmukh, SG. (2008). Supply Chain Coordination: Perspectives, Empirical Studies and Research Directions. Journal of Production Economics, Vol. 115, no. 2, pp.316-335. [16] Arshinder, K.;[et al.]. (2004). Development of a decision support tool for supply chain coordination using contracts. Journal of Advances in Management Research, Vol. 5, no. 2, pp.20-41. [17] Hill, RM.; Omar, M. (2006). Another look at the single-vendor single-buyer integrated production inventory problem. International Journal of Production Research, Vol. 44, no. 4, pp.791-800. [18] Barrat, M. (2004). Understanding the meaning of collaboration in the supply chain. Supply Chain Management: An International Journal, Vol. 9, no. 1, pp.30-42. [19] Caterpillar Global Mining. (2007). The last mile from every tire: how haul road maintenance can extend tire life. Viewpoint, Vol 1, pp. 2-5.
12