Cargodriven eng cdit working paper intermodal hinterland network design

Intermodal hinterland network design with multiple actors Yann Bouchery, Jan Fransoo Beta Working Paper series 449

BETA publicatie ISBN ISSN NUR Eindhoven

WP 449 (working paper)

804 March 2014

Intermodal hinterland network design with multiple actors Yann BOUCHERY*, Jan FRANSOO Eindhoven University of Technology, School of Industrial Engineering P.O. Box 513, 5600 MB Eindhoven, the Netherlands

March 14, 2014

Abstract: Hinterland transportation has become increasingly critical for efficient global container supply chain performance. This paper analyzes the implications of the common presence of multiple actors in intermodal hinterland supply chains. We propose several models to analyze the objectives of the different actors and develop structural properties of the actors’ behavior. Our results show that, in general, the objectives of the different actors involved in the design of intermodal hinterland networks are not aligned. We also show that the actors’ behavior should be taken into consideration in the design phase of intermodal hinterland networks and that the impact of being overly optimistic when estimating these actors’ behavior may be substantial. The proposed results provide a better understanding of the dynamics of intermodal hinterland networks and can help achieve better coordination across the container supply chain.

Keywords: hinterland supply chain, intermodal transportation, hub-and-spoke network design, multiple actors

* Corresponding author: Yann Bouchery, y.bouchery@tue.nl, Tel: +31 4 02 47 43 88

1. Introduction Containerization has been the main technological revolution of the maritime industry in the past 30 years.

This innovation has shaped current global supply chains by substantially reducing transportation costs.

For example, the freight rate on a port-to-port basis between Shanghai and Rotterdam for a 40-foot container is €0.21 per km (OECD/ITF, 2009). This freight rate implies that the maritime transportation cost for 32-inch television screens from Asia to Europe is less than €3 per screen. As a result, global container traffic has been growing at almost three times world gross domestic product growth since the early 1990s (UN-ESCAP, 2005). This paper analyzes the efficiency of container transportation systems in the hinterland supply chain. Although the distance covered by the container in the hinterland is typically small, inland transportation costs are often substantial. For example, the freight rate for inland transportation by truck from the port of Rotterdam typically ranges from €1.50 per km to €4 per km, depending on the distance and weight (OECD/ITF, 2009); this is 7–19 times higher than the maritime transportation freight rate. Hinterland activities also include container handling operations. Summing up all the costs related to hinterland operations, Notteboom and Rodrigue (2005) estimate that the proportion of inland costs relative to the total transportation costs of container shipping ranges from 40% to 80%.

Thus, improving the efficiency of the hinterland supply chain could provide substantial benefits from a global supply chain perspective.

Hinterland operations provide a critical contribution to the global performance of the container supply chain. As a result, all the actors involved in the global container supply chain have increased their presence in hinterland operations. For example, APM Terminals, a subsidiary of Maersk line (the world’s largest container liner company), operates 74 container terminals and 166 inland services worldwide.

Terminal operating companies are also becoming increasingly involved in hinterland operations (see, e.g., Veenstra et al., 2012). In addition, hinterland access is a key determinant of port competitiveness (Van den Berg and De Langen, 2011). Containerization has indeed increased the competition between ports by enlarging the proportion of contestable hinterland—that is, the hinterland region that can be efficiently accessed from more than one port (Notteboom, 2010). The trend toward bigger ships also puts more pressure on the hinterland networks. Thus, congestion is becoming a key issue for most port authorities worldwide (OECD/ITF, 2013). Acknowledging this, port authorities are becoming increasingly active in the hinterland. For example, the port of Barcelona has actively contributed to the development of the inland terminal of Zaragoza to reduce pressure on the road transportation network. As a result, the share of rail volume between Barcelona and Zaragoza has increased from 9% in 2007 to 52% in 2009. Van den Berg and De Langen (2011) provide a detailed case study of the Zaragoza inland terminal, and Rodrigue et al. (2010) offer examples of the actors involved in inland terminals.

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This paper analyzes the implications of the presence of multiple actors in most hinterland supply chains. Indeed, no single actor usually fulfills the role of supply chain leader in such hinterland supply chains (Bontekoning et al., 2004), and thus the performance of the hinterland network depends on the behavior of the different actors involved (De Langen and Chouly, 2004). This issue has been frequently emphasized and discussed in the maritime economics literature (Notteboom, 2008; Roso et al., 2009; Van Der Horst and De Langen, 2008). For example, Song and Panayides (2008) empirically show a positive correlation between port integration in the hinterland supply chain and port competitiveness. However, model-based research on hinterland network design with multiple actors is scarce. Fransoo and Lee (2013) recently argued that research from the operations management community is lacking on container transportation systems despite its critical role in current global supply chains. They identify key industry problems and other worthwhile areas for further research. Among the proposed problems, the coordination of container shipments across the container supply chain can be particularly challenging.

This issue is clearly related to the multiple-actors feature of such supply chains.

We propose several models to account for the objectives and behaviors of the different actors involved in hinterland networks. Our main contributions are twofold. First, we analyze and characterize the structural properties of the different settings considered. These properties enable us to propose efficient algorithms to solve the problem in these different settings. Second, we apply the results to an example based on the features of the hinterland network in the Netherlands and provide related insights.

We prove that, in general, the objectives of the different actors involved in the design of hinterland networks are not aligned. Our results also show that the actors’ behavior should be taken into account in the design phase of hinterland networks and that the impact of being too optimistic when estimating these actors’ behavior can be substantial. The results serve as a basis for appropriately taking multiple actors into account in hinterland network design problems.

We organized the rest of the paper as follows: Section 2 analyzes the existing literature. Section 3 focuses on the description of the model and on the mathematical formulation of the different settings considered. Section 4 analyzes the structural properties of the different problem settings considered.

Section 5 details the most important insights of our research by focusing on an example based on the features of the hinterland supply chain in the Netherlands. Finally, section 6 offers conclusions.

2. Literature review When focusing on hinterland networks, the major impact of containerization is the increasing role of intermodal transportation. Intermodal transportation involves the transportation of the load from origin to destination in the same transportation unit without handling of the goods themselves when changing modes (Crainic and Kim, 2007). The shipping container is the most common transportation unit used in

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intermodal hinterland networks, and most of these networks are organized in hub-and-spoke setting (Crainic and Kim, 2007). The first articles focusing on hub-and-spoke network design problems can be traced back to 1986 (O’Kelly, 1986a, 1986b). The literature on hub location has since expanded rapidly.

Alumur and Kara (2008), Campbell and O’Kelly (2012), and Farahani et al. (2013) all provide reviews.

Several classical formulations of the hub location problem appear in the literature (e.g., hub median, hub center, hub covering), but the most commonly used model for hinterland transportation network design is the p-hub median problem. This problem consists of locating a definite number of hubs and deciding how to allocate a set of origin/destination nodes to these hubs to minimize the total transportation costs of the system. The cost of transporting one unit of flow per unit distance is discounted on interhub arcs to represent the economies of scale achieved by such consolidation systems. This feature creates an incentive to route origin/destination flow through more than one hub because, though this increases the total distance travelled, it may lead to an overall cost reduction. The basic p-hub median model (and many of its extensions) assumes that economies of scale are somehow exogenous to the decisions made about hub location and origin/destination allocation. A fixed discount factor is typically applied to account for economies of scale on interhub arcs. This limitation was first addressed by O’Kelly and Bryan (1998), who account for flow-dependent economies of scale on interhub arcs by considering strictly increasing concave transportation cost functions. They prove that the optimal hub locations may differ greatly from the results obtained without taking flow-dependent economies of scale into account. The p-hub median problem is known to be NP-hard. However, a great amount of research has strived to find efficient ways of solving the problem (either optimally or by using heuristic approaches), and large-scale problems can now be solved efficiently. The p-hub median problem can be considered an extension of the p-median problem for facility location (Hakimi, 1964, 1965), which takes interdependency between facilities into account. As for the facility location research, many extensions of the basic model settings have been proposed.

Bontekoning et al. (2004) present a review of the early research on intermodal transportation for hinterland supply chains. Following the same trend as global container traffic, the literature on intermodal hub-and-spoke network design has quickly expanded in the past decade (Alumur, Kara and Karasan, 2012; Alumur, Yaman and Kara, 2012; Arnold et al., 2004; Groothedde et al., 2005; Ishfaq and Sox, 2010, 2011, 2012; Jeong et al., 2007; Limbourg and Jourquin, 2009; Meng and Wang, 2011; Racunica and Wynter, 2005; Sörensen and Vanovermeire, 2013; Zhang et al., 2013). These articles primarily extend the classical p-hub median problem by taking classical features of intermodal container transportation into account. The most commonly considered aspects are flow-dependent economies of scale for transportation and transshipment activities, travel time, service constraints, and congestion in the system. These studies usually propose a new model that incorporates some features proved to be of

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practical importance. Then, they develop new solution techniques to solve the proposed problem and focus on assessing the efficiency of the considered solution technique.

To our knowledge, only two recently published articles consider multiple actors in intermodal huband-spoke network design problems. Meng and Wang (2011) formulate user equilibrium constraints to take the behavior of intermodal operators into account. User equilibrium constraints are commonly used in the multicommodity network design literature (see, e.g., Yamada et al., 2009). Sörensen and Vanovermeire (2013) argue that, in general, the location and transportations costs typically included in intermodal hub location problems are not paid by the same actors. Thus, they consider these two types of costs separately and develop a bi-objective optimization model to identify the existing trade-offs between both types of costs. These two articles are particularly noteworthy here because they attempt to contribute to what is often acknowledged as the most challenging aspect of container supply chains. However, the authors primarily focus on identifying effective procedures to solve their proposed model. Thus, the impact of having multiple actors involved in such supply chains cannot be assessed from the proposed results. In the current paper, we attempt to better understand the consequences of having multiple actors involved in hinterland supply chains. By focusing on multiple model formulations, we highlight the implications of considering several objectives for the location and allocation decisions addressed in huband-spoke network design problems.

3. Model description 3.1 Context The model we propose describes some real settings of many contemporary hinterland supply chains. For the sake of clarity, we present the model in terms of import flows from a single port to various destinations. The problem could be reversed by considering export flows from various origins to a single port. Our results hold in that case as well. We assume that the flows under consideration are containerized. Because the dimensions of containers have been standardized (Agarwal and Ergun, 2008), the proposed model takes only one type of container into account. We consider that the containers must be delivered to a fixed set of destinations with deterministic demand as this is usually the case in the hub location literature. When arriving at their destination, the containers are unloaded. We do not explicitly take into account empty container management but consider this a parameter of the model. Two options are available for delivering a container from origin to destination: direct shipment by truck and intermodal transportation. In the latter case, we assume that the containers are loaded on a train from the port to an inland terminal. When directly connected with a sea port, the inland terminal can be referred to as an “extended gate” (Veenstra et al., 2012), a “dry port” (Roso et al., 2009), or an “inland port” (Rodrigue et

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al., 2010). We focus on train transportation because this is the most developed intermodal transportation solution worldwide. However, the model is also valid for road-barge and road-short sea intermodal transportation systems. After arriving at the terminal, the containers are transshipped to trucks to reach their final destination.

The objective of the model is to analyze how to locate these inland terminals while acknowledging that several actors are involved in such a decision. Table 1 provides a list of the potential actors involved in inland terminal location decisions along with some examples of their respective objectives. We focus on three objective functions, or location rules, in the proposed model. First, as we mentioned previously, the port authorities involved in such inland terminal projects are mainly interested in maximizing the volume transported by rail from the port to the inland terminal, to reduce road traffic congestion in the port surroundings and thus increase their competitiveness. This objective may also be followed by the train operator company. We note that this objective is equivalent to maximizing terminal utilization in the proposed model. Maximizing terminal utilization is of interest to the inland terminal operator. Local authorities may also view this objective as essential because efficient terminal utilization would positively affect the local economy; thus, the first location rule is terminal utilization, or TU. Second, from a public authority perspective, the main objective may be to minimize the total number of kilometers traveled by truck because intermodal transportation is often considered less polluting. This objective is equivalent to maximizing modal shift; thus, the second location rule is modal shift, or MS. Third, the total cost minimization objective traditionally used in the hub location literature is of critical importance for making intermodal transportation a viable option because cost is one of the major criteria for shippers and freight forwarders; thus, the third location rule is total cost, or TC. The objectives followed by the different actors as well as their individual bargaining power may strongly differ from one specific inland terminal situation to another. Each practical situation has its own set of characteristics based on past behaviors, political issues, trust, and willingness to collaborate of each actor.

Actors

Example of objective

Proposed location rule

Terminal operators

Maximize terminal utilization

TU

Port authorities

Reduce road traffic congestion in the port surrounding

TU

Public authorities

Minimize the distance traveled by truck

MS

Local authorities

Maximize terminal utilization

TU

Rail operators

Maximize train service utilization

TU

Shippers

Minimize transportation costs

TC

Freight forwarders

Minimize transportation costs

TC

Table 1: Actors involved in inland terminal location decisions

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Compared with the classical p-hub median problem we described in section 2, we consider a single origin and a single inland terminal to locate. This problem setting enables us to evaluate the dynamics of inland terminal locations with multiple actors and is in line with Campbell and O’Kelly (2012), who argue that “new single hub model formulations continue to provide intriguing formulation issues” (p.

163).

Our model takes into account flow-dependent economies of scale for train transportation and transshipment operations at the inland terminal. We model the train transportation cost per container and the transshipment cost per container as general concave nondecreasing functions of the total number of operated containers. This feature creates a cost interdependency among the allocation decisions made for each destination. The destinations are considered individual companies, such as retailers, requesting a transportation service in the model. In addition to the inland terminal location problem, the allocation problem consists of deciding, for each destination, which share of the total flow should be allocated to the inland terminal (i.e., shipped by intermodal transportation). Three allocation rules are considered. When focusing on costs, flow-dependent economies of scale and a multiple-actors setting lead to some noteworthy allocation issues. In the classical single-actor vision of hub location problems, O’Kelly and Bryan (1998) point out that “some origin-destination pairs may be routed via a path that is not their leastcost path because doing so will minimize total network travel cost” (p. 608). This statement may not hold in a multiple-actor setting. The situation is similar to a classical problem in the traffic assignment literature. Because of congestion, the solution that minimizes the total traveling time in the system is not equivalent to the solution that minimizes the travel times of the individual users. This leads to two extreme behaviors that Wardrop (1952) describes as user equilibrium (each user minimizes its own travel time) versus system optimum (the total travel time of the system is minimized). This paper examines both user equilibrium (UE) and system optimum (SO). For the UE allocation rule, we consider that each destination allocates the demand flow between direct and intermodal shipment to minimize its own transportation costs. For the SO allocation rule, the destinations take the total costs in the system into account in making their allocation decisions. The third allocation rule considered is to maximize the modal shift (MS). A destination may indeed be willing to reduce its environmental impact by favoring intermodal transportation. This objective of maximizing the modal shift is equivalent to minimizing the distance travelled by road. In real-life situations, we acknowledge that a mix of these strategies would be encountered. Each destination may have its own positioning with respect to MS, UE, and SO rules.

Moreover, the freight forwarders and truck operators often deal with several destinations; thus, some pooling effects are encountered. However, we focus on the three extreme scenarios—all UE, all SO, and all MS—in our analysis to examine the impact of allocation decisions on the overall performance of the hinterland supply chain.

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The strong interrelationship between the location and the allocation subproblem is the key feature of any hub location problem. In the setting considered herein, we can obtain the optimal hub location through enumeration; thus, the most complex part is the allocation subproblem. In what follows, we combine the three allocation and three location rules to assess the effect of the interactions among different actors on optimal decisions. By mixing the considered allocation and location rules, we propose and analyze nine formulations.

3.2 Model formulations The hinterland supply chain under study consists of a single port (considered as the origin) with N ∈ ℵ* destinations. A deterministic constant flow ni must be shipped from origin to destination j ∈ {1;...; N }.

Here, n j is expressed in number of containers, and only one type of container is available (40-foot containers); thus, we assume that n j ∈ ℵ* for all j ∈ {1;...; N }. At most, one inland terminal must be located among M ∈ ℵ* candidate locations. Each potential terminal location is referred to as location

i ∈ {1;...; M } . In addition, we refer to the origin (i.e., the port) as location i = 0 .

The truck transportation cost function considered is linear in the distance and in the number of containers shipped. The truck transportation cost per container.km may be destination dependent to account for the different rates proposed by different truck operators as well as for the different empty container management practices developed by each destination.

Thus, we can express the cost of transporting one container from location i ∈ {0;...; M } to destination

j ∈ {1;...; N } as follows:

Z i1, j = δ i , j Z truck , j ,

(1)

where

δ i, j = the distance from location i to destination j (expressed in km) and Z truck , j = the truck transportation cost per container.km for destination j (expressed in €/container.km).

While delivery takes place through intermodal transportation, train transportation is used from the origin to the inland terminal. We define the cost of shipping one container by train from the origin to the inland terminal i ∈ {1;...; M } as follows:

Z 02,i ( K ) = δ 0,i Z train ( K ) , where

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(2)

δ 0,i

= the distance from the origin to inland terminal j (expressed in km),

Z train (K ) = the flow-dependent train transportation cost per container.km (in €/container.km), and

K ∈ ℜ *+ = the total number of containers shipped by train.

The train transportation cost function is linear in distance. However, flow-dependent economies of scale are taken into account; thus, the train transportation cost per container depends on the total amount of containers shipped by train K . We further assume that K .Z train ( K ) is a concave nondecreasing function. Thus, the train transportation cost per container is nonincreasing in the total number of containers shipped by train, and the marginal cost of shipping an additional container is nonnegative and nonincreasing in the amount shipped.

In addition to train and truck transportation costs, intermodal transportation implies additional container handling operations at the inland terminal. We define the cost of transshipping one container at terminal i ∈ {1;...; M } is follows:

Z i1, 2 ( K ) = γ i ( K ) ,

(3)

where

γ i (K ) = the flow-dependent transshipment cost per container at terminal i (in €/container) and K ∈ ℜ *+ = the total number of containers transshipped at terminal i .

Note that the total number of containers transshipped at terminal i is equal to the total number of containers shipped by train. The transshipment cost depends on the location considered to account for the difference in land and labor costs as well as for the difference in terminal layout, equipment, and size.

This cost also accounts for the difference in cost from transshipping to a truck or to a train at the origin, if any. In addition, we define γ 0 ( K ) = 0 , for all K ∈ ℜ *+ . The transshipment cost per container depends on the total amount of containers transshipped at terminal i . We further assume that K .γ i ( K ) is a concave nondecreasing function. Thus, the transshipment cost per container is nonincreasing in the total number of containers transshipped, and the marginal cost of transshipping an additional container is nonnegative and nonincreasing in the amount transshipped.

The total cost of shipping one container from the origin to destination j ∈ {1;...; N } by intermodal transportation through inland terminal i ∈ {1;...; M } is equal to Z 0, i ( K ) + Z i ( K ) + Z i , j . To simplify 2

1, 2

1

the notation, we define the following:

Z 03,i ( K ) = Z 02,i ( K ) + Z i1, 2 ( K ) .

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(4)

Note that Z 0, 0 ( K ) = 0 for all K ∈ ℜ + . As is usually the case in the hub location literature, we further 3

define 0 ≤ X i , j ≤ 1 as the proportion of flow from origin to destination j being routed through terminal

i . Here, X 0, j = 1 indicates that the entire flow from origin to destination j is delivered by direct shipment, while X i , j = 1 , where i ∈ {1;...; M }, indicates that the entire flow from origin to destination j is delivered by intermodal transportation using inland terminal i .

We define the following three following objective functions, depending on the location rule under consideration: M

N

(

)

MIN ∑∑ n j Z i1, j + Z 03,i ( K ) X i , j ,

(5)

i = 0 j =1

M

N

MIN ∑∑ n j Z i1, j X i , j , and

(6)

MAX K .

(7)

i = 0 j =1

Objective 5 corresponds to minimizing the total cost (TC location rule). Objective 6 corresponds to minimizing the total truck transportation costs—that is, maximizing the modal shift (MS location rule).

Finally, objective 7 aims to maximize the number of containers shipped by train—that is, maximizing terminal utilization (TU location rule).

For any of the three location rules, the following set of constraints must be considered: M

∑y i =1

i

≤1,

(8)

yi ∈ {0;1}, ∀i ∈ {1;...; M } ,

(9)

X i , j ≤ yi , ∀j ∈ {1;...; N }, ∀i ∈ {1;...; M },

(10)

M

∑X i =0

i, j

= 1, ∀j ∈ {1;...; N },

X i , j ≥ 0, ∀i ∈ {0;...; M }, ∀j ∈ {1;...; N } , and M

(11)

(12)

N

K = ∑∑ n j X i , j . i =1 j =1

10

(13)

As constraints 9 show,

yi

are binary variables equal to 1 if inland terminal i is open and 0 otherwise.

Constraints 8 ensure that, at most, one inland terminal can be opened. Constraints 10 imply that flow can be routed only through an open terminal. Constraints 11 ensure that the total amount of flow is shipped from origin to destinations. Constraints 12 ensure that the proportions of flow routed are nonnegative.

Finally, constraint 13 is used to account for the number of containers routed by intermodal transportation.

When the location and the allocation rules under consideration are different, some additional constraints must be considered. We formulate these additional constraints in section 4.1. Note that objective function 5 under constraints 8–13 corresponds to the TC/SO problem—that is, the classical hub location formulation with the objective of minimizing the total transportation costs in the network. The MS/MS problem is represented by objective function 6 under constraints 8–13.

4. The allocation subproblem 4.1 Constraints formulation In the allocation subproblem, we assume that the inland terminal i ∈ {1;...; M } is open. For the MS allocation rule, the objective of maximizing modal shift is equivalent to the objective of minimizing the traveled distance by road. Thus, for each destination, the decision is made by comparing the distance from the inland terminal and the distance from the port. If the destination j is located closer to the inland terminal, the entire demand flow n j will be shipped by intermodal transportation. Otherwise, the entire demand flow will be shipped directly by truck. This single routing condition enables simplification of the analysis. Theorem 1 shows that this condition also holds for the UE and SO allocation rules.

Theorem 1: The single routing condition holds for each destination for the UE, SO, and MS allocation rules.

Proofs appear in appendix A. As we explained in section 3.2, the chosen allocation rule may result in the addition of some constraints to the general problem (as soon as the location and allocation rules are different). For the MS allocation rule, the following sets of constraints need to be taken into consideration: M

∑yX i =1

i

i, j

( Z 01, j − Z i1, j ) ≥ 0, ∀j ∈ {1;...; N } , and

(14)

( Z i1, j − Z 01, j ) ≥ 0, ∀j ∈ {1;...; N }.

(15)

M

∑y X i =1

i

0, j

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Constraints 14 imply that X i , j = 0 if δ i , j > δ 0, j . Constraints 15 imply that X 0, j = 0 if δ 0, j > δ i , j .

Objective 5 under constraints 8–15 corresponds to the TC/MS problem, while objective 7 under constraints 8–15 corresponds to the TU/MS problem.

The UE allocation rule results in the following sets of constraints: M

∑yX i

i =1

i, j

( Z 01, j − Z i1, j − Z 03,i ( K + (1 − X i , j )n j )) ≥ 0, ∀j ∈ {1;...; N } , and

(16)

( Z i1, j + Z 03,i ( K + (1 − X i , j )n j ) − Z 01, j ) ≥ 0, ∀j ∈ {1;...; N } .

(17)

M

∑yX i =1

i

0, j

Constraints 16 imply that X i , j = 0 if it is cheaper for destination j to be shipped directly. Constraints 17 imply that X 0, j = 0 if it is cheaper for destination j to be shipped through terminal i . The TC/UE, MS/UE, and TU/UE problems consist of objectives 5, 6, and 7, respectively, under constraints 8–13 as well as constraints 16–17.

Finally the SO allocation rule implies the following sets of constraints:

 1 K 3 1 3  y X Z 0,i ( K ) − Z 03,i ( K + (1 − X i , j )n j ∑ i i , j  Z 0 , j − Z i , j − Z 0 ,i ( K + (1 − X i , j ) n j ) + n i =1 j 

(

M

and M

∑y X i =1

i



) ≥ 0, ∀j ∈ {1;...; N }, 

(18)

 1 K 3 1 3  Z 0,i ( K ) − Z 03,i ( K + (1 − X i , j )n j 0 , j  Z i , j − Z 0 , j + Z 0 ,i ( K + (1 − X i , j ) n j ) − nj 

(



) ≥ 0, ∀j ∈ {1;...; N }. 

(19)

Compared with constraints 16, constraints 18 also take into account the train transportation cost reduction incurred by the other destinations. These constraints imply that X i , j = 0 if it is globally cheaper to ship the demand flow from destination j directly. The same line of reasoning is applied to formulate constraints 19. These imply that X 0, j = 0 if it is globally cheaper to ship the demand flow from destination j through terminal i .

As explained previously, examination of the problems under the MS allocation rule is simple because the allocation decisions may be taken independently for each destination and because we restrict our attention to the case in which, at most, one inland terminal can be used. The next two sections are devoted to the UE and SO allocations rules. The allocation subproblem is complex for these two allocation rules because the decisions made for each destination are interdependent.

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4.2 User equilibrium allocation As Fisk (1984) points out, Wardrop’s first principle of user equilibrium is equivalent to the Nash equilibrium principle in noncooperative game theory. This concept is characterized by the property that neither player can unilaterally reduce transportation costs by changing its decision. In this section, we show that several Nash equilibria may exist in some settings of the UE allocation rule. Then, we propose an algorithm to identify all the existing Nash equilibria for a given problem, based on some structural properties of the proposed model.

We refer to the N players noncooperative game corresponding to the UE allocation rule as the UE allocation game. In this game, each destination is considered a player of the game. Each destination aims to maximize its relative profit compared with direct shipment costs. Using theorem 1, we can assert that each destination j ∈ {1;...; N } has two options X i , j ∈ {0;1} and tries to maximize its relative profit Pj ,

{

which depends not only on player j ’s action X i , j but also on the others players’ actions X i , − j = X i , k

k ∈ {1;...; N }, k ≠ j}. Then, X i , j = 0 corresponds to the case in which destination j chooses direct shipment. By definition, Pj (0, X i , − j ) = 0 , independent of the decisions made by the other players. When

X i , j = 1 , this corresponds to the case in which destination j decides on delivery using terminal i . Then, Pj (1, X i , − j ) may be either negative or positive, depending on the other players’ decisions, due to flowdependent economies of scale for train transportation and transshipment operations. We consider that

K .Z 03,i ( K ) is divided among the actors by following the proportional allocation rule—namely, a player 3

transporting n j out of K containers by intermodal transportation would be charged n j .Z 0, i ( K ) . We obtain the following:

(

)

N

Pj (1, X i , − j ) = n j Z 01, j − Z i1, j − Z 03,i ( K ) K =∑ X i ,k nk .

(20)

k =1

Note that in the special case in which Pj (1, X i , − j ) = 0 , we assume that player j would choose direct shipment. This decision may indeed be viewed as less risky because it is not affected by the other players’ decisions. Nash equilibrium is obtained when neither player can individually increase its profit by changing the decision.

{

We define X i* = X i*,1 ;...; X i*, N

}

as a Nash equilibrium if the following properties hold for all

j ∈ {1;...; N } and for all X i , j ∈ {0;1} : Pj ( X i*, j , X i*, − j ) ≥ Pj ( X i , j , X i*, − j ) .

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(21)

X i*, j = 1 <=> Pj (1, X i*, − j ) > Pj (0, X i*, − j ) .

(22)

Nash (1950) proves that there is at least one Nash equilibrium under general assumptions by applying the fixed point theorem. However, this equilibrium may be obtained by requiring at least one player to choose a probability distribution over the set of potential actions to protect against other players’ reactions. This type of strategy is a mixed strategy, as opposed to a pure strategy. A pure strategies Nash equilibrium (PSNE) is such that each player chooses an action for sure. This type of equilibrium may not always exist (e.g., the matching pennies game). Theorem 2 proves that at least one PSNE exists for the UE allocation game. This is because Pj (0, X i , − j ) = 0 , independent of the other players’ decisions. Thus, each player can be protected against all the other players’ actions while following a pure strategy.

Theorem 2: The UE allocation game leads to at least one PSNE.

In N players noncooperative games, several PSNEs may exist. Theorem 3 states that this is also the case for the UE allocation game.

Theorem 3: The UE allocation game may lead to several PSNEs. As we show in the proof (see appendix A), this result holds even when considering only two players. In this case, the situation is encountered when neither of the players has enough volume to make intermodal transportation profitable in a stand-alone setting and when the combination of both players’ volumes makes intermodal transportation profitable for each. This example can be viewed as a stag hunt game in which two PSNEs exist. The first one, when the two players choose direct shipment, is called risk dominant. The second, when both players choose intermodal transportation, is called payoff dominant.

Several Nash equilibria may exist, which is of critical importance. To our knowledge, the only article considering UE constraints in an intermodal hub location problem is that of Meng and Wang (2011).

However, the authors minimize the total cost under these UE constraints without acknowledging that the proposed solution may not lead to a unique Nash equilibrium. Thus, in a situation with several PSNEs, only the payoff-dominant Nash equilibrium is considered. We examine the impacts of this assumption further in section 5.

The structural properties of the UE allocation game enable us to simplify the analysis and design an algorithm to identify all the existing PSNEs, as we show in proposition 1 (resulting from theorem 4 and corollary 1).

14

Theorem 4: Assume that there are L ≥ 2 PSNEs in a given setting of the UE allocation game. For all

l ∈ {1;...; L} , let U i ,l be the set of all players choosing intermodal transportation under equilibrium l ( U i ,l may be empty). Then, it is possible to order the L ≥ 2 PSNEs such that U i ,l +1 ⊂ U i ,l , ∀l ∈ {1;...; L − 1}.

Corollary 1: Assume that there are L PSNEs in a given setting of the UE allocation game. Then,

N  L ≤   +1. 2 In the two-player setting with two PSNEs considered previously, we find that U i , 2 = ∅ corresponds to the risk-dominant equilibrium and that U i ,1 = {1;2} correspond to the payoff-dominant equilibrium. We observe that theorem 4 holds for this example, as U i , 2 ⊂ U i ,1 . Moreover, we have all the PSNEs for this game by using corollary 1.

Algorithm UE Step 1: For all j ∈ {1;...; N } , compute Λ i , j = Z 0, j − Z i , j .

1

1

Step 2: Rank all destination j ∈ {1;...; N } from the largest to the smallest value of Λ i, j .

Step 3: Set τ = 0 , N τ = N .

    q 3   Step 4: Solve qτ = max 0; max Λ i , q > Z 0,i  ∑ n j    .   q∈{1;...; Nτ }  j =1      *

{

}

Step 5: U i ,1+τ = j ∈ {1;...; N } j ≤ qτ* .



  q∈{1;...; qτ }  

    n ∑ j  .  j =1    

Step 6: Solve pτ = max 0; max*  Λ i , q ≤ Z 0, i  *

3

q

Step 7: If pτ* = 0 , then stop. Otherwise, go to Step 8.

{

}

Step 8: Set τ = τ + 1 , set N τ = 0;...; pτ*−1 , and go to Step 4.

Proposition 1: Algorithm UE enables the identification of all the PSNEs of the UE allocation game.

15

We use algorithm UE in section 5 in an example in which several PSNEs exist. We further analyze the impacts of having more than one Nash equilibrium and derive several insights.

4.3 System optimum allocation In the SO allocation rule, the destinations take the total cost of the system into account in making their allocation decision. Compared with the UE allocation rule, some destinations may decide to use the inland terminal even if this choice increases their individual cost, as soon as the volume added for train transportation and transshipment operations provides a stronger cost reduction for the other players using intermodal transportation. Because the number of destinations is bounded, we can ensure that there is an allocation minimizing the total cost in the system. However, this allocation may not be unique. We define the SO allocation as the allocation minimizing the total cost of the system with the minimum number of 3

destinations using intermodal transportation. For the SO allocation rule, K .Z 0, i ( K ) should be considered globally. This cost must be compared with the sum of individual savings in truck transportation cost when the containers are shipped through terminal i instead of being shipped directly.

The following algorithm (algorithm SO) can determine the system optimum allocation—that is, the set S i of the destinations being shipped to using intermodal transportation.

Algorithm SO Step 1: For all j ∈ {1;...; N } , compute Λ i , j = Z 0, j − Z i , j .

1

1

Step 2: Rank all destination j ∈ {1;...; N } from the largest to the smallest value of Λ i, j . q   q   q 3   Step 3: Solve q = min arg max ∑ n j Λ i , j − ∑ n j Z 0,i  ∑ n j    .   q∈{1;...; N }  j =1 j =1  j =1      *

q  Step 4: If ∑ n j Λ i , j − ∑ n j Z  ∑ n j  > 0 , then S i = j ∈ {1;...; N } j ≤ q * . Otherwise, S i = ∅ .  j =1  j =1 j =1   q*

q*

{

*

3 0 ,i

}

Proposition 2: Algorithm SO enables the identification of S i .

q  q  3   Λ − n n Z ∑ ∑ j 0 , i  ∑ n j  may not always be a monotonic function of q ; thus, local j i, j = j =1 j =1 j 1   q

Note that

optima may exist. A remaining issue is to verify that the SO allocation is stable in the sense of

16

cooperative game theory when S i ≠ ∅ . Indeed, the SO allocation would be of interest only if there is an

 q  3   n Z ∑ j 0 , i  ∑ n j  such that no group of destinations has the incentive to act independently j =1  j =1  q

allocation of

by setting up another service. This problem involves proving the nonemptiness of the core for the cooperative game (S i ≠ ∅; v ) with the following characteristic function:

  v(S ⊆ Si ) − > ∑ n j Λ i , j − ∑ n j Z 03, i  ∑ n j  and v(∅ ) = 0 . j ∈S j ∈S  j ∈S 

(23)

Theorem 5: The cooperative game (S i ; v ) is convex and thus has a nonempty core.

Note that determining the set of allocations in the core of the game is outside the scope of this paper.

4.4 Performance comparisons of the allocation rules The results we presented in the previous sections may also help in comparing the performance of the allocation rules with respect to the different location objectives considered. Theorem 6 shows that for any potential terminal location, the allocation rule inducing the highest terminal utilization is MS, followed by SO and finally the payoff-dominant PSNE. In addition to theorem 4, theorem 6 allows for a direct ranking of the different allocation rules in terms of terminal utilization for a given terminal location.

Theorem 6: Let M i be the set of destinations using terminal i for the modal shift allocation rule; then, for all i ∈ {1;...; M },

U i ,1 ⊆ S i ⊆ M i .

Theorem 6 also implies that the SO allocation rule performs better than the UE allocation rule in terms of modal shift. In terms of total cost, the situation is not as clear. Indeed, in most of the cases, the MS allocation rule would perform better than the UE allocation because the marginal train transportation and transshipment costs per container added are relatively low in most practical situations. However, an exception is when the UE and SO allocation rules lead to not using the terminal. In this case, the MS allocation rule leads to an increase in total cost when the distance from at least one destination to the terminal is lower than the distance to the port.

17

5. Example and insights This section is based on an example representing features of the hinterland network in the Netherlands.

The main objective here is to explore the implications of having multiple actors involved in such a supply chain. We apply the modeling developed in section 3, and the theoretical results of section 4 enable us to quickly solve the problem. In this example, N = 25 and M = 10 . The locations of the destinations and potential terminal locations appear in figure 1. The crosses represent the destinations, the dots represent the potential terminal locations, and the square represents the location of the port. The terminal location numbers also appear in figure 1. In this example, we calculate the distances by considering the Euclidean norm.

6 9 7

2

10

4 1 8 5 3

Figure 1: The hinterland supply chin considered For each of the 10 potential inland terminal locations, we determine all the PSNEs, the SO allocation, and the MS allocation. In each case, we estimate the total cost, the modal shift, and the terminal utilization.

We calculate terminal utilization by dividing the actual number of containers transshipped at the terminal N

by the total amount of potential containers (i.e., K /

â&#x2C6;&#x2018;n j =1

j

). We also consider the situation in which no

terminal has been opened. We calculate modal shift by comparing the total distance traveled by truck in any situation with this latter case. Note that we assume that the containers are loaded with 20 tons of cargo; thus, the number of ton.kilometers shifted from the road can be estimated. The results appear in table 2.

18

Total Cost (â&#x201A;Ź) DS

Modal Shift

Terminal

(ton.km)

Utilization (%)

Total Cost (â&#x201A;Ź)

Modal Shift

Terminal

(ton.km)

Utilization (%)

S5

10 130.62

64 840

54%

46%

M5

10 150.42

65 980

61%

30%

U6,1

11 749.89

-

0%

0%

S6

11 749.89

-

0%

57%

M6

12 168.69

48 360

52%

11 749.89

-

0%

U1,1

9 891.01

65 300

U1,2

10 886.05

44 160

U1,3

11 749.89

-

S1

9 597.84

72 720

M1

9 614.09

74 440

65%

U7,1

11 749.89

-

0%

U2,1

10 129.35

56 860

46%

S7

11 524.04

20 900

57%

U2,2

11 749.89

-

0%

M7

11 585.01

21 480

70%

S2

9 556.69

68 740

67%

U8,1

9 701.18

56 260

52%

M2

9 562.98

69 460

72%

U8,2

11 749.89

-

0%

U3,1

11 749.89

-

0%

S8

9 463.53

62 080

67%

S3

11 446.99

60 000

43%

M8

9 489.35

62 240

72%

M3

11 448.94

60 300

46%

U9,1

11 749.89

-

0%

U4,1

10 618.40

29 660

76%

S9

10 478.83

49 580

74%

U4,2

11 749.89

-

0%

M9

10 492.97

49 820

78%

S4

10 590.89

30 540

80%

U10,1

11 749.89

-

0%

M4

10 609.24

30 740

85%

S10

10 715.00

66 320

59%

U5,1

10 817.76

49 440

28%

M10

10 715.00

66 320

59%

U5,2

11 749.89

-

0%

Table 2: Overall results We can derive several insights from these results. We first focus on analyzing the impact of considering several objectives for the location decision. We perform this analysis by focusing on the SO allocation rule because this is the most commonly used rule in the literature. (Note that the same type of analysis can be performed with the other allocation rules we consider.) When considering the TC location rule, the best solution is terminal 8. For the MS location rule, the best solution is terminal 1. Finally, for the TU location rule, the best solution is terminal 4. This demonstrates that the objectives of the different actors involved in the design of intermodal hinterland networks are not aligned.

Insight 1: In general, the objectives of the different actors involved in the design of intermodal hinterland networks are not aligned.

From a practical point of view, insight 1 means that the result obtained using a terminal utilization maximization objective or a modal shift maximization objective may not be viable in practice if it ends up in a solution that is too costly. This implies that port authorities, public authorities, and local authorities may be required to subsidize such train services and terminal operations to make intermodal

19

transportation viable from a cost perspective. This feature is in line with the results presented in the maritime economics literature (Van den Berg and De Langen, 2011). In addition, the location obtained using a cost minimization objective, as is usually the case in the literature, may not accurately represent the location decision made in practice, as other objectives may play a role.

Continuing with such an analysis, we note that some solutions that are not optimal for any of the location rules considered represent interesting trade-offs. For example, terminal 2 is the second-best solution in terms of total cost, the second-best solution in terms of modal shift, and the third-best solution in terms of terminal utilization. We can conclude that identifying such trade-offs may be of significant interest in helping align the objectives of the different actors involved. One way to obtain such a solution is to consider multiobjective optimization techniques.

Insight 2: Multiobjective optimization may yield solutions that align the interests of the different actors involved in the design of intermodal hinterland networks.

To our knowledge, Sรถrensen and Vanovermeire's (2013) study is the only one that considers multiobjective optimization techniques to take into account the multiple-actors feature of intermodal hinterland networks. However, their first attempt to model the multiple-actors feature of intermodal supply chains using multiobjective optimization focuses mainly on proposing and assessing a solution procedure for the problem. Additional research is required to generate insights into and solutions for practical decision making.

Comparing the best locations for the three location objectives considered, we note that the optimal TU location is close to the port, the optimal TC location is at a midrange distance, and the optimal MS solution is farther inland. We could explain such a result as follows: The optimal MS location is farther inland than the optimal TC location because the train transportation and transshipment costs are not included when optimizing modal shift. Thus, locating the terminal farther inland may increase the distance traveled by train. From a cost perspective, reducing the distance traveled by train while slightly increasing the distance traveled by truck is a better option. Although the inland terminal is closer to the port, the number of destinations that are closer from the terminal than from the port is increasing, and thus the train transportation cost decreases (as the distance decreases and the volume increases). As a result, terminal utilization increases.

Insight 3: Inland terminals close to the port are better in terms of utilization, midrange terminals are better from a total cost perspective, and distant inland terminals perform better for modal shift.

20

Insight 3 can be used to understand the dynamics of inland terminal location in a hinterland network. As Roso et al. (2009) point out, all types of terminals may be encountered in practice. The comparative advantages and drawbacks of such terminal locations can be assessed in terms of total cost, terminal utilization, and modal shift. Nevertheless, insight 3 needs to be taken with caution because the interaction and competition among several terminals are not taken into account in the proposed model and may play a role.

We derive the second set of insights from analyzing the impacts of taking several allocation rules into account. First, the optimal location may depend on the considered allocation rule. This situation could be encountered for the TC location rule by excluding terminal 8 from the analysis (by considering that this terminal may not be available). In this case, terminal 1 is the best location if the UE allocation rule is considered. Conversely, terminal 2 is the best option for the SO and the MS allocation rules. We can conclude that the behaviors of the actors should be taken into account in the design phase of intermodal hinterland networks.

Insight 4: The optimal location depends on the considered allocation rule. Thus, the behavior of the actors should be taken into account in the design phase of intermodal hinterland networks.

In practice, actorsâ&#x20AC;&#x2122; behaviors are often difficult to determine accurately when the system is running; thus, determining these behaviors in the design phase may be challenging. Additional research is required to address such difficulties. In accordance with theorem 6, we also note in this example that the SO allocation rule used in most of the hub location literature results in an overly optimistic view of real situations.

Insight 5: The system optimum allocation rule leads to overly optimistic results in terms of total cost, modal shift, and terminal utilization.

The impacts of being overly optimistic can be substantial. In some situations, the system optimum allocation may lead to a solution that seems appealing, while the only existing PSNE has no destinations using the terminal. This situation is encountered for terminals 3, 7, 9, and 10. To assess what might occur in such a situation, we exclude terminals 8, 2, 1, and 5 from the analysis. The total cost optimal location for the SO allocation rule in such a scenario is terminal 9, leading to a total daily cost of â&#x201A;Ź10 478.83 and 74% terminal utilization. Assume now that the network is designed according to this solution and that the allocation rule followed by the actors is UE instead of SO. Then, no destinations would use the terminal.

Conversely, choosing terminal 4 with an expected cost of â&#x201A;Ź10 590.89 and an expected terminal utilization

21

of 80% for the SO allocation rule would have been a much better choice because, in this case, the payoffdominant user equilibrium leads to a total cost of €10 618.40 and terminal utilization of 76%.

Insight 6: The impacts of being overly optimistic when estimating actors’ behavior in the design phase can be substantial.

Insight 6 can help explain why some intermodal transportation projects are predicted to be effective in theory while being very difficult to turn into profitable projects in practice. This insight is in accordance with Rodrigue et al. (2010), who report that “both public and private actors have a tendency to overestimate the benefits and traffic potential and underestimate the costs and externalities of inland port projects” (p. 528). The proposed model can be used to help the different actors involved in inland terminal projects to better assess the traffic potential and related benefits of such projects.

Finally, we discuss some insights derived from having several PSNEs. First, we note that the riskdominant Nash equilibrium involves having no destination shipped to from the inland terminal for all the potential terminal considered.

Insight 7: In most of the cases, the risk-dominant Nash equilibrium involves not using the inland terminal.

Indeed, no actor is powerful enough to make intermodal transportation profitable by acting individually because economies of scale are of key importance for efficient intermodal transportation. This issue is not taken into account in the hub location literature. It follows that the actors, even if they are competitors, need to develop mutual trust to make intermodal transportation viable.

Insight 8: Mutual trust among the actors is a prerequisite for efficient intermodal hinterland transportation.

The question of how to promote such mutual trust in practice is of great interest. For example, several destinations may agree on guaranteed minimum volumes shipped by intermodal transportation before the implementation of the inland terminal. Such practice is currently employed in the Netherlands, where port authorities and governmental agencies act as a platform for such mutual trust agreements. Indeed, 11 traders in the region of Westland have signed an agreement to transport 10 000–15 000 containers per year by barge from the port of Rotterdam to the container terminal of Hook of Holland (project Fresh

22

Corridor 7). We refer to the maritime economics literature focusing on hinterland supply chains for related discussions (see, e.g., Van Der Horst and De Langen, 2008).

Finally, the example we have presented shows that more than two PSNEs may exist, as in the case of terminal 1. Understanding the dynamic behind the users’ behavior to forecast which equilibrium is more likely to occur in practice is of great importance. For example, formulating user equilibrium constraints while considering a total cost minimization objective, as proposed by Meng and Wang (2011), may not accurately represent the current situation and may be viewed as being overly optimistic in the performance of the intermodal hinterland transportation system if the cost-dominant Nash equilibrium is not chosen by the actors in the networks. Additional research is required to understand actors’ behavior in such intermodal hinterland networks.

6. Conclusion In this paper, we analyzed the implications of having multiple actors involved in intermodal hinterland supply chains. Our main research contribution is to compare the solutions obtained while considering the different objectives and behaviors of the actors involved. This process enables us to assess the impact of not accurately estimating actors’ behavior when designing an intermodal hinterland network. We found new theoretical results pertaining to some structural properties of the actors’ behavior. These results make it possible to design algorithms to solve the allocation subproblems optimally. Our results also show that the literature modeling the multiple-actors feature of current intermodal hinterland supply chains provides only a partial representation of the existing actors’ equilibria. In addition, we derive new insights from an example representing features of the hinterland network in the Netherlands. We prove that, in general, the objectives of the different actors involved in the design of intermodal hinterland networks are not aligned.

Our results also show that the actors’ behavior should be taken into account in the design phase of intermodal hinterland networks and that the impact of being overly optimistic when estimating these actors’ behavior can be substantial. Finally, we show that multiobjective optimization can yield solutions that balance the conflicting objectives of the different actors in the network design phase and that such a technique can help coordinate the container shipments across the container supply chain.

This research underscores the importance of taking into account the multiple-actors setting of intermodal hinterland networks. The results may also generalize to the entire container supply chain, but further research is necessary for this end. Several techniques can be adequately used to take this multipleactors setting into account. Among others, we show that multiobjective optimization and game theory are of primary relevance. We hope that our results help pave the way for further research from the operations management community on container transportation systems.

23

Acknowledgments The research was partly funded by Dinalog, the Dutch Institute for Advanced Logistics.

Appendix A Proof of Theorem 1 We need to prove that X i , j ∈ {0;1} for all j ∈ {1;...; N }, for the three considered allocation rules.

MS allocation rule For all j ∈ {1;...; N },

if

Z i1, j < Z 01, j ,

then

δ i , j < δ 0, j => X i , j = 1 .

Otherwise,

Z i1, j > Z 01, j => δ i , j > δ 0, j => X i , j = 0 .

UE allocation rule By contradiction, assume that 1 > X i , j > 0

for a given

j ∈ {1;...; N }. This implies that

X i , j n j ( Z i1, j + Z 03,i ( K )) < X i , j n j Z 01, j => n j ( Z i1, j + Z 03,i ( K )) < n j Z 01, j . Because Z 03,i is nonincreasing in K , we obtain n j ( Z i1, j + Z 03,i ( K + (1 − X i , j )n j )) < n j Z 01, j , implying that X i , j = 1 .

SO allocation rule By contradiction, assume that 1 > X i , j 1 > 0 for a given j1 ∈ {1;...; N } . Using the results of the UE allocation rule, we can conclude that choosing X i , j 1 = 1 will reduce the transportation cost for destination j1 without increasing the costs for the other destinations (the costs could even be reduced because the number of containers shipped through the inland terminal is increasing). We can conclude that X i , j 1 = 1 at optimality.

Proof of Theorem 2 We can construct a PSNE as follows: We begin by setting X i , j = 0 ∀j ∈ {1;...; N } . If none of the players can increase their profit by individually using intermodal transportation, then considering direct shipment for all the players is a PSNE. Otherwise, there is a destination k ∈ {1;...; N } such that

Pk (1, X i , − j = 0) ≥ Pj (0, X i , − j = 0) . Let X i ,k = 1 . If none of the remaining players can increase their profit by individually using intermodal transportation, then considering direct shipment for all the players except for player k is a PSNE. Otherwise, the same procedure can be repeated, and any player included in the set of players using intermodal transportation will never have any incentive to change its decision

24

to direct shipment (because Z 0,i ( K ) K is nonincreasing in K). Because {1;...; N } is a finite set, the 3

proposed procedure necessarily converges; thus, a PSNE always exists for the UE allocation game.

Proof of Theorem 3 Consider the special case in which the UE allocation game is restricted to only two players. The payoff matrix above can be used to model this game. Player 1 can decide to choose either top or bottom, while player 2 can decide to choose either left or right. The payoffs received by each player appear in each of the four cells representing possible outcomes of the game; the first value is received by player 1, and the second is received by player 2. Because of the special feature of the game, the payoff associated with direct shipment is equal to 0. In addition, A ≥ B and a ≥ b as a result of economies of scale. Consider the case in which A > 0 > B and a > 0 > b . In this case, the corresponding UE allocation game is similar to a stag hunt game in which two PSNEs exist.

Proof of Theorem 4 Theorem 4 derives from the notion that any player included in the set of players using intermodal transportation in any given PSNE will never have an incentive to change its decision to direct shipment, while increasing the number of players using intermodal transportation due to flow-dependent economies of scale.

Proof of Corollary 1 Assume that there are L PSNEs in a given setting of the UE allocation game. Using theorem 4, we can deduce that Card (U i ,l +1 ) ≤ Card (U i ,l ), ∀l ∈ {1;...; L − 1} . Because S l +1 and S l are two distinct Nash equilibria, we also find that Card (U i ,l +1 ) < Card (U i ,l ), ∀l ∈ {1;...; L − 1} .

By contradiction, assume that there are l ∈ {1;...; L − 1} , such that Card (U i ,l +1 ) + 1 = Card (U i ,l ) .

Then, only one player is added to the set of players using intermodal transportation. This player’s profit is strictly greater than zero in the case of intermodal transportation given the other players’ decisions; thus,

25

U l +1 is not a Nash equilibrium. This proves that ∀l ∈ {1;...; L − 1}, Card (U l ) ≥ Card (U l +1 ) + 2 ; thus,

N  L ≤   + 1. 2 Proof of Proposition 1 Let τ = 0 . Assume that qτ = N ; then, Λ i , N *

 N    N 3   > Z  ∑ n j  and ∀q ∈ {1;...; N }, Λ i ,q > Z 0,i  ∑ n j  .  j =1   j =1  3 0 ,i

It follows that ∀q ∈ {1;...; N }, Pq (1, X i , −q = 1) > 0 , and thus U i ,1 = { j ∈ {1;...; N }} is the payoffdominant PSNE. If qτ* < N , then player N will choose direct shipment even when all the players are



using the terminal because Λ i , N ≤ Z 0,i  3



N

∑n j =1

j

  => PN (1, X i , − N = 1) ≤ 0 ; thus, X i*, N = 0 for all the  

existing PSNEs. By induction, it follows with the same argument that X i*, j = 0 for all q > qτ* . Using the

{

}

argumentation developed in the case in which qτ* = N , we prove that U i ,1 = j ∈ {1;...; N } j ≤ qτ* is the payoff-dominant PSNE.



Assume that pτ* = 0 ; then, ∀q ≤ qτ* , Λ i ,q > Z 0,i  3





destinations are shipped to directly, Λ i ,1 ≤ Z 0,i  3



1

∑n j =1

  . Considering first that all the  

N

∑n j =1

j

  j  => P1 (1, X i , − N = 0) > 0 ; thus, player 1 can 

individually decide to use the inland terminal. By induction, it follows that all the destinations q ≤ qτ* can iteratively decide to use the inland terminal while being profitable. Thus, U 1 is the only PSNE of the

 qτ  > Z  ∑ n j  . Using the same  j =1    *

given UE allocation game. Otherwise, qτ > pτ > 0 because Λ i ,q* *

*

τ

3 0 ,i

argument as in the case of pτ* = 0 , we can show that all the destinations q , such that pτ* < q ≤ qτ* , can iteratively decide to use the inland terminal while being profitable, and we conclude that

{

}

U i , 2 ⊂ j ∈ {1;...; N } j ≤ pτ* . The procedure may then be iterated to find U i , 2 if this exists. Using corollary 1, algorithm UE necessarily stops, and all the PSNEs can be identified.

26

Proof of Proposition 2 Proving proposition 2 implies showing that ranking all destinations j ∈ {1;...; N } from the largest to the smallest value of Λ i, j enables the identification of S i . By contradiction, assume that the destinations are



q  q  q    3    n Λ − n Z n ∑ j i, j j 0 ,i  ∑ j   .  q∈{1;...; N }  ∑ j =1  j =1     j =1 

not ranked according to their Λ i, j value, and let q * = min arg max

p > q*

If q*

∑n Λ j =1

j

Λ i , p > Λ i ,q* ,

that

then

q  q q  q  − ∑ n j Z  ∑ n j  < ∑ n j Λ i , j + n p Λ i , p −  ∑ n j + n p  Z 03,i  ∑ n j + n p  j =1  j =1  j =1  j =1   j =1  q*

i, j

such *

*

*

*

3 0 ,i

because

K .Z 03,i ( K ) is concave in K . Thus, an optimum is reached at q * when Λ i ,q ≥ Λ i ,q for all q ≤ q * and *

when Λ i ,q < Λ i ,q* for all q > q * , and ranking all destinations j ∈ {1;...; N } from the largest to the smallest value of Λ i, j enables the identification of S i .

Proof of Theorem 5 A cooperative

(S i

≠ ∅; v ) game is convex when v is supermodular; that is, ∀T , V ⊆ S i ,

v(T ∪ V ) + v(T ∩ V ) ≥ v(T ) + v(V ) .

This

property

is

equivalent

to

v(T ∪ { j}) − v(T ) ≤ v(V ∪ { j}) − v(V ) , ∀T ⊆ V ⊆ S i \ { j}, ∀j ∈ S i .

∀T ⊆ V ⊆ S i \ { j}, ∀j ∈ S i : v(V ∪ { j}) − v(V ) − v(T ∪ { j}) + v(T ) =

∑{n} Z

k∈T ∪ j

k

3 0 ,i

         ∑ nk  − ∑ nk Z 03,i  ∑ nk  − ∑ nk Z 03,i  ∑ nk  + ∑ nk Z 03,i  ∑ nk  ≥ 0      k∈V   k∈V  k∈V ∪{ j }  k∈V ∪{ j }  k∈V  k∈T ∪{ j }  k∈V 3

because K .Z 0,i ( K ) is nondecreasing concave in K . Proposition 8 follows from the fact that any convex game has a nonempty core.

Proof of Theorem 6

{

}

We first prove that ∀i ∈ {1; M }, S i ⊆ M i . Note that M i = j ∈ {1;...; N } Λ i , j ≤ 0

because

Λ i , j = Z 01, j − Z i1, j = (δ 0, j − δ i , j ).Ztruck j . If S i = ∅ , the result holds. Assume that S i ≠ ∅ , and let

27

a ∈ Si .

Then, Λ i ,a ≥ Λ i ,q* , where q * is defined as in algorithm SO. Moreover, because

q   q  q  q * = min arg max ∑ n j Λ i , j − ∑ n j Z 03,i  ∑ n j    , Λ i ,q* > 0 ; thus, Λ i ,a ≥ 0 and a ∈ M i .   q∈{1;...; N }  j =1 j =1  j =1     

To prove that U i ,1 ⊆ S i , we argue that any destination that is individually better when using the inland terminal contributes to global cost minimization because this decision has no negative effect on the other destinations. By transitivity of the inclusion, we can conclude that U i ,1 ⊆ S i ⊆ M i .

References Agarwal, R., Ergun, Ö. 2008. Ship scheduling and network design for cargo routing in liner shipping.

Transportation Science 42, 175–196.

Alumur, S., Kara, B.Y. 2008. Network hub location problems: The state of the art. European Journal of Operational Research 190, 1–21.

Alumur, S.A., Kara, B.Y., Karasan, O.E. 2012. Multimodal hub location and hub network design. Omega 40, 927–939.

Alumur, S.A., Yaman, H., Kara, B.Y. 2012. Hierarchical multimodal hub location problem with timedefinite deliveries. Transportation Research. Part E: Logistics and Transportation Review 48, 1107–1120.

Arnold, P., Peeters, D., Thomas, I. 2004. Modelling a rail/road intermodal transportation system.

Transportation Research. Part E: Logistics and Transportation Review 40, 255–270.

Bontekoning, Y.., Macharis, C., Trip, J. 2004. Is a new applied transportation research field emerging? A review of intermodal rail–truck freight transport literature. Transportation Research. Part A: Policy and Practice 38, 1–34.

Campbell, J.F., O’Kelly, M.E. 2012. Twenty-five years of hub location research. Transportation Science 46, 153–169.

Crainic, T.G., Kim, K.H. 2007. Intermodal transportation, in: Handbooks in Operations Research and Management Science. Volume 14: Transportation (pp. 467–537). Amsterdam: Elsevier.

De Langen, P.W., Chouly, A. 2004. Hinterland access regimes in seaports. European Journal of Transport and Infrastructure Research 4, 361–380.

Farahani, R.Z., Hekmatfar, M., Arabani, A.B., Nikbakhsh, E. 2013. Hub location problems: A review of models, classification, solution techniques, and applications. Computers & Industrial Engineering 64, 1096–1109.

Fisk, C.S. 1984. Game theory and transportation systems modelling. Transportation Research. Part B: Methodological 18, 301–313.

28

Fransoo, J.C., Lee, C.-Y. 2013. The critical role of ocean container transport in global supply chain performance. Production and Operations Management 22, 253–268.

Groothedde, B., Ruijgrok, C., Tavasszy, L. 2005. Towards collaborative, intermodal hub networks: A case study in the fast moving consumer goods market. Transportation Research. Part E: Logistics and Transportation Review 41, 567–583.

Hakimi, S.L. 1964. Optimum locations of switching centers and the absolute centers and medians of a graph. Operations Research 12, 450–459.

Hakimi, S.L. 1965. Optimum distribution of switching centers in a communication network and some related graph theoretic problems. Operations Research 13, 462–475.

Ishfaq, R., Sox, C.R. 2010. Intermodal logistics: The interplay of financial, operational and service issues.

Transportation Research. Part E: Logistics and Transportation Review 46, 926–949.

Ishfaq, R., Sox, C.R. 2011. Hub location–allocation in intermodal logistic networks. European Journal of Operational Research 210, 213–230.

Ishfaq, R., Sox, C.R. 2012. Design of intermodal logistics networks with hub delays. European Journal of Operational Research 220, 629–641.

Jeong, S.-J., Lee, C.-G., Bookbinder, J.H. 2007. The European freight railway system as a hub-and-spoke network. Transportation Research. Part A: Policy and Practice 41, 523–536.

Limbourg, S., Jourquin, B. 2009. Optimal rail-road container terminal locations on the European network.

Transportation Research. Part E: Logistics and Transportation Review 45, 551–563.

Meng, Q., Wang, X. 2011. Intermodal hub-and-spoke network design: Incorporating multiple stakeholders and multi-type containers. Transportation Research. Part B: Methodological 45, 724–742.

Nash, J.F. 1950. Equilibrium points in n-person games. PNAS 36, 48–49.

Notteboom, T.E. 2008. The relationship between seaports and the intermodal hinterland in light of global supply chains: European challenges (No. 2008-10). OECD International Transport Forum.

Notteboom, T.E. 2010. Concentration and the formation of multi-port gateway regions in the European container port system: An update. Journal of Transport Geography 18, 567–583.

Notteboom, T.E., Rodrigue, J.-P. 2005. Port regionalization: Towards a new phase in port development.

Maritime Policy & Management 32, 297–313.

OECD/ITF. 2009. Port competition and hinterland connections. Round Table 143, OECD Publishing.

OECD/ITF. 2013. Efficient hinterland transport infrastructure and services for large container ports.

Discussion paper 2013-19, OECD Publishing.

O’Kelly, M.E. 1986a. Activity levels at hub facilities in interacting networks. Geographical Analysis 18, 343–356.

O’Kelly, M.E. 1986b. The location of interacting hub facilities. Transportation Science 20, 92–106.

29

O’Kelly, M., Bryan, D. 1998. Hub location with flow economies of scale. Transportation Research. Part B: Methodological 32, 605–616.

Racunica, I., Wynter, L. 2005. Optimal location of intermodal freight hubs. Transportation Research. Part B: Methodological 39, 453–477.

Rodrigue, J.-P., Debrie, J., Fremont, A., Gouvernal, E. 2010. Functions and actors of inland ports: European and North American dynamics. Journal of Transport Geography 18, 519–529.

Roso, V., Woxenius, J., Lumsden, K. 2009. The dry port concept: connecting container seaports with the hinterland. Journal of Transport Geography 17, 338–345.

Song, D.-W., Panayides, P.M. 2008. Global supply chain and port/terminal: Integration and competitiveness. Maritime Policy & Management 35, 73–87.

Sörensen, K., Vanovermeire, C. 2013. Bi-objective optimization of the intermodal terminal location problem as a policy-support tool. Computers in Industry 64, 128–135.

UN-ESCAP (United Nations Economic and Social Comission for Asia and Pacific). 2005. Regional shipping and port development strategies (container traffic forecast) (No. Report ST/ESCAP/2398). New York: United Nations.

Van den Berg, R., De Langen, P.W. 2011. Hinterland strategies of port authorities: A case study of the port of Barcelona. Research in Transportation Economics 33, 6–14.

Van Der Horst, M.R., De Langen, P.W. 2008. Coordination in hinterland transport chains: A major challenge for the seaport community. Maritime Economics & Logistics 10, 108–129.

Veenstra, A., Zuidwijk, R., van Asperen, E. 2012. The extended gate concept for container terminals: Expanding the notion of dry ports. Maritime Economics & Logistics 14, 14–32.

Wardrop, J.G. 1952. Road paper: Some theoretical aspects of road traffic research. ICE Proceedings: Engineering Divisions 1, 325–362.

Yamada, T., Russ, B.F., Castro, J., Taniguchi, E. 2009. Designing multimodal freight transport networks: A heuristic approach and applications. Transportation Science 43, 129–143.

Zhang, M., Wiegmans, B., Tavasszy, L. 2013. Optimization of multimodal networks including environmental costs: A model and findings for transport policy. Computers in Industry 64, 136– 145.

30

Working Papers Beta 2009 - 2014

nr. Year Title

Author(s)

449 2014 Intermodal hinterland network design with multiple Yann Bouchery, Jan Fransoo actors 448 2014 The Share-a-Ride Problem: People and Parcels Sharing Taxis 447 2014 Stochastic inventory models for a single item at a single location 446 2014 Optimal and heuristic repairable stocking and expediting in a fluctuating demand environment 445 2014 Connecting inventory control and repair shop control: a differentiated control structure for

Baoxiang Li, Dmitry Krushinsky, Hajo A. Reijers, Tom Van Woensel K.H. van Donselaar, R.A.C.M. Broekmeulen Joachim Arts, Rob Basten, Geert-Jan van Houtum M.A. Driessen, W.D. Rustenburg, G.J. van Houtum, V.C.S. Wiers

repairable spare parts 444 2014 A survey on design and usage of Software

Samuil Angelov, Jos Trienekens,

Reference Architectures

Rob Kusters

Extending and Adapting the Architecture Tradeoff

Samuil Angelov, Jos J.M. Trienekens,

443 2014 Analysis Method for the Evaluation of Software

Paul Grefen

Reference Architectures A multimodal network flow problem with product 442 2014 Quality preservation, transshipment, and asset

Maryam SteadieSeifi, Nico Dellaert, Tom Van Woensel

management 441 2013 Integrating passenger and freight transportation: Model formulation and insights 440 2013 The Price of Payment Delay

Veaceslav Ghilas, Emrah Demir, Tom Van Woensel K. van der Vliet, M.J. Reindorp, J.C. Fransoo

439 2013 On Characterization of the Core of Lane Covering Games via Dual Solutions

Behzad Hezarkhani, Marco Slikker, Tom van Woensel

438 2013 Destocking, the Bullwhip Effect, and the Credit Crisis: Empirical Modeling of Supply Chain

Maximiliano Udenio, Jan C. Fransoo,

Dynamics

Robert Peels

437 2013 Methodological support for business process Redesign in healthcare: a systematic literature review

Rob J.B. Vanwersch, Khurram Shahzad, Irene Vanderfeesten, Kris Vanhaecht, Paul Grefen, Liliane Pintelon, Jan Mendling, Geofridus G. Van Merode, Hajo A. Reijers

436 2013 Dynamics and equilibria under incremental Horizontal differentiation on the Salop circle

435 2013 Analyzing Conformance to Clinical Protocols Involving Advanced Synchronizations

434 2013 Models for Ambulance Planning on the Strategic and the Tactical Level

B. Vermeulen, J.A. La PoutrĂŠ, A.G. de Kok

Hui Yan, Pieter Van Gorp, Uzay Kaymak, Xudong Lu, Richard Vdovjak, Hendriks H.M. Korsten, Huilong Duan J. Theresia van Essen, Johann L. Hurink, Stefan Nickel, Melanie Reuter Stefano Fazi, Tom Van Woensel,

433 2013 Mode Allocation and Scheduling of Inland Container Transportation: A Case-Study in the Netherlands Socially responsible transportation and lot sizing:

Jan C. Fransoo

Yann Bouchery, Asma Ghaffari,

432 2013 Insights from multiobjective optimization

Zied Jemai, Jan Fransoo

431 2013 Inventory routing for dynamic waste collection

Martijn Mes, Marco Schutten, Arturo PĂŠrez Rivera

430 2013 Simulation and Logistics Optimization of an Integrated Emergency Post

429 2013 Last Time Buy and Repair Decisions for Spare Parts

428 2013 A Review of Recent Research on Green Road Freight Transportation

427 2013 Typology of Repair Shops for Maintenance Spare Parts

N.J. Borgman, M.R.K. Mes, I.M.H. Vliegen, E.W. Hans

S. Behfard, M.C. van der Heijden, A. Al Hanbali, W.H.M. Zijm

Emrah Demir, Tolga Bektas, Gilbert Laporte

M.A. Driessen, V.C.S. Wiers, G.J. van Houtum, W.D. Rustenburg

426 2013 A value network development model and Implications for innovation and production network B. Vermeulen, A.G. de Kok management 425 2013 Single Vehicle Routing with Stochastic Demands: Approximate Dynamic Programming

424 2013 Influence of Spillback Effect on Dynamic Shortest Path Problems with Travel-Time-Dependent Network Disruptions

C. Zhang, N.P. Dellaert, L. Zhao, T. Van Woensel, D. Sever

Derya Sever, Nico Dellaert, Tom Van Woensel, Ton de Kok

423 2013 Dynamic Shortest Path Problem with Travel-Time- Derya Sever, Lei Zhao, Nico Dellaert, Dependent Stochastic Disruptions: Hybrid Tom Van Woensel, Ton de Kok Approximate Dynamic Programming Algorithms with a Clustering Approach 422 2013 System-oriented inventory models for spare

R.J.I. Basten, G.J. van Houtum

parts

421 2013 Lost Sales Inventory Models with Batch Ordering And Handling Costs 420 2013 Response speed and the bullwhip

T. Van Woensel, N. Erkip, A. Curseu, J.C. Fransoo Maximiliano Udenio, Jan C. Fransoo, Eleni Vatamidou, Nico Dellaert

419 2013 Anticipatory Routing of Police Helicopters

Rick van Urk, Martijn R.K. Mes, Erwin W. Hans

418 2013 Supply Chain Finance: research challenges ahead

Kasper van der Vliet, Matthew J. Reindorp, Jan C. Fransoo

Improving the Performance of Sorter Systems

S.W.A. Haneyah, J.M.J. Schutten,

417 2013 By Scheduling Inbound Containers Regional logistics land allocation policies: 416 2013 Stimulating spatial concentration of logistics

K. Fikse Frank P. van den Heuvel, Peter W. de Langen, Karel H. van Donselaar,

firms

Jan C. Fransoo

The development of measures of process

Heidi L. Romero, Remco M. Dijkman,

415 2013 harmonization

Paul W.P.J. Grefen, Arjan van Weele

BASE/X. Business Agility through Cross-

Paul Grefen, Egon LĂźftenegger,

414 2013 Organizational Service Engineering

Eric van der Linden, Caren Weisleder

The Time-Dependent Vehicle Routing Problem 413 2013 with Soft Time Windows and Stochastic Travel Times

Duygu Tas, Nico Dellaert, Tom van

Clearing the Sky - Understanding SLA 412 2013 Elements in Cloud Computing Approximations for the waiting time distribution 411 2013 In an M/G/c priority queue

410 2013

409 2013

408 2013

407 2013

406 2013

405 2013 404 2013

Woensel, Ton de Kok

Marco Comuzzi, Guus Jacobs, Paul Grefen A. Al Hanbali, E.M. Alvarez, M.C. van der van der Heijden

To co-locate or not? Location decisions and logistics concentration areas

Frank P. van den Heuvel, Karel H. van Donselaar, Rob A.C.M. Broekmeulen, Jan C. Fransoo, Peter W. de Langen

The Time-Dependent Pollution-Routing Problem

Anna Franceschetti, DorothĂŠe Honhon,Tom van Woensel, Tolga Bektas, GilbertLaporte.

Scheduling the scheduling task: A time Management perspective on scheduling

Clustering Clinical Departments for Wards to Achieve a Prespecified Blocking Probability

MyPHRMachines: Personal Health Desktops in the Cloud

J.A. Larco, V. Wiers, J. Fransoo

J. Theresia van Essen, Mark van Houdenhoven, Johann L. Hurink

Pieter Van Gorp, Marco Comuzzi

Maximising the Value of Supply Chain Finance

Kasper van der Vliet, Matthew J. Reindorp, Jan C. Fransoo

Reaching 50 million nanostores: retail

Edgar E. Blanco, Jan C. Fransoo

distribution in emerging megacities

A Vehicle Routing Problem with Flexible Time 403 2013 Windows

Duygu Tas, Ola Jabali, Tom van Woensel

402 2012 The Service Dominant Business Model: A Service Focused Conceptualization

401 2012 Relationship between freight accessibility and Logistics employment in US counties

Egon L端ftenegger, Marco Comuzzi, Paul Grefen, Caren Weisleder

Frank P. van den Heuvel, Liliana Rivera,Karel H. van Donselaar, Ad de Jong,Yossi Sheffi, Peter W. de Langen, Jan C.Fransoo Qiushi Zhu, Hao Peng, Geert-Jan van

400 2012 A Condition-Based Maintenance Policy for MultiComponent Systems with a High Maintenance

Houtum

Setup Cost 399 2012 A flexible iterative improvement heuristic to Support creation of feasible shift rosters in

E. van der Veen, J.L. Hurink, J.M.J. Schutten, S.T. Uijland

Self-rostering Scheduled Service Network Design with

K. Sharypova, T.G. Crainic, T. van 398 2012 Synchronization and Transshipment Constraints Woensel, J.C. Fransoo For Intermodal Container Transportation Networks 397 2012 Destocking, the bullwhip effect, and the credit Crisis: empirical modeling of supply chain

Maximiliano Udenio, Jan C. Fransoo, Robert Peels

Dynamics 396 2012 Vehicle routing with restricted loading capacities

395 2012 Service differentiation through selective lateral transshipments

J. Gromicho, J.J. van Hoorn, A.L. Kok J.M.J. Schutten

E.M. Alvarez, M.C. van der Heijden, I.M.H. Vliegen, W.H.M. Zijm

394 2012 A Generalized Simulation Model of an Integrated Emergency Post

Martijn Mes, Manon Bruens

393 2012 Business Process Technology and the Cloud: Defining a Business Process Cloud Platform

Vasil Stoitsev, Paul Grefen

392 2012 Vehicle Routing with Soft Time Windows and Stochastic Travel Times: A Column Generation

D. Tas, M. Gendreau, N. Dellaert,

And Branch-and-Price Solution Approach

T. van Woensel, A.G. de Kok

391 2012 Improve OR-Schedule to Reduce Number of Required Beds 390 2012 How does development lead time affect

J.T. v. Essen, J.M. Bosch, E.W. Hans, M. v. Houdenhoven, J.L. Hurink Andres Pufall, Jan C. Fransoo, Ad de

performance over the ramp-up lifecycle?

Jong

Evidence from the consumer electronics

Andreas Pufall, Jan C. Fransoo, Ad de

389 2012 industry

The Impact of Product Complexity on Ramp388 2012 Up Performance

Jong, Ton de Kok

Frank P.v.d. Heuvel, Peter W.de Langen, Karel H. v. Donselaar, Jan C. Fransoo

Co-location synergies: specialized versus diverse 387 2012 logistics concentration areas

Proximity matters: Synergies through co-location 386 2012 of logistics establishments

Spatial concentration and location dynamics in 385 2012 logistics:the case of a Dutch province

384 2012 FNet: An Index for Advanced Business Process Querying

383 2012

382 2012

381 2012

Defining Various Pathway Terms

Frank P.v.d. Heuvel, Peter W.de Langen, Karel H. v.Donselaar, Jan C. Fransoo

Frank P. v.d.Heuvel, Peter W.de Langen, Karel H.v. Donselaar, Jan C. Fransoo

Zhiqiang Yan, Remco Dijkman, Paul Grefen W.R. Dalinghaus, P.M.E. Van Gorp

Egon L端ftenegger, Paul Grefen, Caren Weisleder

The Service Dominant Strategy Canvas: Defining and Visualizing a Service Dominant

Stefano Fazi, Tom van Woensel,

Strategy through the Traditional Strategic Lens

Jan C. Fransoo

A Stochastic Variable Size Bin Packing Problem

K. Sharypova, T. van Woensel,

With Time Constraints

J.C. Fransoo Frank P. van den Heuvel, Peter W. de

380 2012 Coordination and Analysis of Barge Container Hinterland Networks

Langen, Karel H. van Donselaar, Jan C. Fransoo

379 2012 Proximity matters: Synergies through co-location of logistics establishments

Heidi Romero, Remco Dijkman,

378 2012 A literature review in process harmonization: a conceptual framework

S.W.A. Haneya, J.M.J. Schutten,

377 2012

Paul Grefen, Arjan van Weele

P.C. Schuur, W.H.M. Zijm

A Generic Material Flow Control Model for

H.G.H. Tiemessen, M. Fleischmann,

Two Different Industries

G.J. van Houtum, J.A.E.E. van Nunen, E. Pratsini

Improving the performance of sorter systems by 375 2012 scheduling inbound containers

Albert Douma, Martijn Mes

Strategies for dynamic appointment making by 374 2012 container terminals

Pieter van Gorp, Marco Comuzzi

MyPHRMachines: Lifelong Personal Health 373 2012 Records in the Cloud

E.M. Alvarez, M.C. van der Heijden,

372 2012 Service differentiation in spare parts supply through dedicated stocks

Frank Karsten, Rob Basten

371 2012

370 2012

W.H.M. Zijm

Spare parts inventory pooling: how to share

X.Lin, R.J.I. Basten, A.A. Kranenburg,

the benefits

G.J. van Houtum

Condition based spare parts supply

Martijn Mes

Using Simulation to Assess the Opportunities of 369 2011 Dynamic Waste Collection

J. Arts, S.D. Flapper, K. Vernooij

J.T. van Essen, J.L. Hurink, W. Aggregate overhaul and supply chain planning for Hartholt, 368 2011 rotables B.J. van den Akker

367 2011 Operating Room Rescheduling

Kristel M.R. Hoen, Tarkan Tan, Jan C. Fransoo, Geert-Jan van Houtum

366 2011 Switching Transport Modes to Meet Voluntary Carbon Emission Targets

Elisa Alvarez, Matthieu van der Heijden

365 2011 On two-echelon inventory systems with Poisson demand and lost sales

J.T. van Essen, E.W. Hans, J.L. Hurink,

364 2011

Duygu Tas, Nico Dellaert, Tom van Woensel, Ton de Kok

Minimizing the Waiting Time for Emergency Surgery

Vehicle Routing Problem with Stochastic Travel 363 2011 Times Including Soft Time Windows and Service Costs 362 2011 A New Approximate Evaluation Method for TwoEchelon Inventory Systems with Emergency Shipments 361 2011 Approximating Multi-Objective Time-Dependent Optimization Problems

A. Oversberg

Erhun Özkan, Geert-Jan van Houtum, Yasemin Serin

Said Dabia, El-Ghazali Talbi, Tom Van Woensel, Ton de Kok Said Dabia, Stefan Röpke, Tom Van Woensel, Ton de Kok

A.G. Karaarslan, G.P. Kiesmüller, A.G. 360 2011 Branch and Cut and Price for the Time Dependent de Kok Vehicle Routing Problem with Time Window 359 2011 Analysis of an Assemble-to-Order System with Different Review Periods

Ahmad Al Hanbali, Matthieu van der Heijden

Interval Availability Analysis of a Two-Echelon, 358 2011 Multi-Item System

Felipe Caro, Charles J. Corbett, Tarkan Tan, Rob Zuidwijk

Carbon-Optimal and Carbon-Neutral Supply 357 2011 Chains

Sameh Haneyah, Henk Zijm, Marco Schutten, Peter Schuur

Generic Planning and Control of Automated 356 2011 Material Handling Systems: Practical Requirements Versus Existing Theory

M. van der Heijden, B. Iskandar

Last time buy decisions for products sold under 355 2011 warranty

Frank P. van den Heuvel, Peter W. de Langen, Karel H. van Donselaar, Jan C. Fransoo

354 2011 Spatial concentration and location dynamics in logistics: the case of a Dutch provence

Frank P. van den Heuvel, Peter W. de Langen, Karel H. van Donselaar, Jan C. Fransoo

353 2011 Identification of Employment Concentration Areas

Pieter van Gorp, Remco Dijkman

352 2011 BOMN 2.0 Execution Semantics Formalized as Graph Rewrite Rules: extended version

Frank Karsten, Marco Slikker, GeertJan van Houtum

351 2011 Resource pooling and cost allocation among independent service providers

E. Lüftenegger, S. Angelov, P. Grefen

350 2011

A Framework for Business Innovation Directions

The Road to a Business Process Architecture: An 349 2011 Overview of Approaches and their Use

Remco Dijkman, Irene Vanderfeesten, Hajo A. Reijers K.M.R. Hoen, T. Tan, J.C. Fransoo G.J. van Houtum

Effect of carbon emission regulations on transport Murat Firat, Cor Hurkens 348 2011 mode selection under stochastic demand An improved MIP-based combinatorial approach 347 2011 for a multi-skill workforce scheduling problem

346 2011

An approximate approach for the joint problem of level of repair analysis and spare parts stocking

R.J.I. Basten, M.C. van der Heijden, J.M.J. Schutten R.J.I. Basten, M.C. van der Heijden, J.M.J. Schutten

Joint optimization of level of repair analysis and 345 2011 spare parts stocks

Ton G. de Kok

Inventory control with manufacturing lead time 344 2011 flexibility

Frank Karsten, Marco Slikker, GeertJan van Houtum

Analysis of resource pooling games via a new 343 2011 extenstion of the Erlang loss function

Murat Firat, C.A.J. Hurkens, Gerhard J. Woeginger

342 2010 Vehicle refueling with limited resources

Bilge Atasoy, Refik Güllü, TarkanTan

341 2010 Optimal Inventory Policies with Non-stationary Supply Disruptions and Advance Supply Information

Kurtulus Baris Öner, Alan Scheller-Wolf Geert-Jan van Houtum

Redundancy Optimization for Critical Components Joachim Arts, Gudrun Kiesmüller 339 2010 in High-Availability Capital Goods

338 2010 Analysis of a two-echelon inventory system with two supply modes

Murat Firat, Gerhard J. Woeginger

335 2010 Analysis of the dial-a-ride problem of Hunsaker and Savelsbergh

Murat Firat, Cor Hurkens

334 2010 Attaining stability in multi-skill workforce scheduling A.J.M.M. Weijters, J.T.S. Ribeiro

333 2010 Flexible Heuristics Miner (FHM)

P.T. Vanberkel, R.J. Boucherie, E.W. Hans, J.L. Hurink, W.A.M. van Lent, W.H. van Harten

Peter T. Vanberkel, Richard J. 332 2010 An exact approach for relating recovering surgical Boucherie, Erwin W. Hans, Johann L. patient workload to the master surgical schedule Hurink, Nelly Litvak Efficiency evaluation for pooling resources in 331 2010 health care

M.M. Jansen, A.G. de Kok, I.J.B.F. Adan

The Effect of Workload Constraints in 330 2010 Mathematical Programming Models for Production Christian Howard, Ingrid Reijnen, Johan Marklund, Tarkan Tan Planning 329 2010 Using pipeline information in a multi-echelon spare parts inventory system H.G.H. Tiemessen, G.J. van Houtum Reducing costs of repairable spare parts supply 328 2010 systems via dynamic scheduling

F.P. van den Heuvel, P.W. de Langen, K.H. van Donselaar, J.C. Fransoo

Identification of Employment Concentration and 327 2010 Specialization Areas: Theory and Application

Murat Firat, Cor Hurkens

A combinatorial approach to multi-skill workforce 326 2010 scheduling

Murat Firat, Cor Hurkens, Alexandre Laugier

325 2010 Stability in multi-skill workforce scheduling

M.A. Driessen, J.J. Arts, G.J. v.

Houtum, W.D. Rustenburg, B. Huisman

324 2010 Maintenance spare parts planning and control: A framework for control and agenda for future research Near-optimal heuristics to set base stock levels in 323 2010 a two-echelon distribution network

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Working Papers published before 2009 see: http://beta.ieis.tue.nl