Supply Chain Collaboration

The core is a set-valued solution concept for cooperative games. In situations where the characteristic function is not monotone the classical definition may not be sufficient. Hence, we propose a subset of the core that is called subcoalition-perfect core. It will be proven that the subcoalition-perfect core coincides with the set of non-negative core allocations. Furthermore, an ellipsoid algorithm is provided which may be applied in many applications to compute an element in the subcoalition-perfect core. In addition, we discuss an application where the characteristic function is not monotone and perform a computational study.

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“…We refer to Meca and Timmer (2008) for a recent and very comprehensive survey on ordering/lot sizing models with multiple players.…”

Section: An Application: Cooperative Lot Sizing With Capacity Constramentioning

confidence: 99%

The subcoalition-perfect core of cooperative games

Drechsel

Kimms

2010

Ann Oper Res

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“…We refer to Meca and Timmer (2008) for a recent and very comprehensive survey on lot sizing/ordering optimisation models with multiple players. It should be noted that the use of the aforementioned models exclude costs for transshipments between the players makes answering Question 1 from above (how shall the optimisation problem be solved?)…”

Section: Game Properties and Research Questionsmentioning

confidence: 99%

Cooperative lot sizing with transshipments and scarce capacities: solutions and fair cost allocations

Drechsel¹,

Kimms²

2011

International Journal of Production Research

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In this article, we study the cooperative capacitated lot sizing problem where the available resources of the players may be used in common and payable transshipments may take place to transport items from one player to the other. Two research questions are attacked. On the one hand, there is the hard-to-solve optimisation problem of deciding which player shall produce what amount of items at what point of time, how many items shall be kept in stock when, and when transport of what quantities shall take place among which players. The objective is to minimise the total cost of the supply chain taking into account thorny side constraints due to capacity limits. On the other hand, there is the hard-to-solve problem of distributing cost shares among the players such that the cost allocation is stable and fair. Both questions are discussed in detail and answers are given by proposing mathematical programming approaches.

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“…Cachon and Netessine (2004), Leng and Parlar (2005), Meca and Timmer (2008), and give recent surveys about game theoretic approaches and applications in supply chain management. Thus, game theory seems to provide an adequate modeling basis for problems in supply chain management.…”

Section: Supply Chain Games In the Literaturementioning

confidence: 99%

Cooperative Lot Sizing Games in Supply Chains

Drechsel¹

2010

Lecture Notes in Economics and Mathematical Systems

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Supply Chain Collaboration

Cited by 10 publications

References 57 publications

The subcoalition-perfect core of cooperative games

The subcoalition-perfect core of cooperative games

Cooperative lot sizing with transshipments and scarce capacities: solutions and fair cost allocations

Cooperative Lot Sizing Games in Supply Chains

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