Dynamic cost allocation for economic lot sizing games

Toriello, Alejandro; Uhan, Nelson A.

doi:10.1016/j.orl.2013.12.005

Cited by 14 publications

(4 citation statements)

References 11 publications

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“…Specifically, they prove that there exists an optimal dual solution that defines an allocation in the core and point out that it is not necessarily true that every optimal dual solution defines a core allocation. Toriello and Uhan (2014) also study ELS-games with general concave ordering costs and show how to compute a dynamic cost allocation in the strong sequential core of these games, i.e., an allocation over time that exactly distributes costs and is stable against coalitional defections at every period of the time horizon.…”

Section: Introductionmentioning

confidence: 99%

The effect of consolidated periods in heterogeneous lot-sizing games

Guardiola

Meca

Puerto

2021

TOP

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We consider a cooperative game defined by an economic lot-sizing problem with heterogeneous costs over a finite time horizon, in which each firm faces demand for a single product in each period and coalitions can pool orders. The model of cooperation works as follows: ordering channels and holding and backlogging technologies are shared among the members of the coalitions. This implies that each firm uses the best ordering channel and holding technology provided by the participants in the consortium. That is, they produce, hold inventory, pay backlogged demand and make orders at the minimum cost of the coalition members. Thus, firms aim at satisfying their demand over the planing horizon with minimal operation cost. Our contribution is to show that there exist fair allocations of the overall operation cost among the firms so that no group of agents profit from leaving the consortium. Then we propose a parametric family of cost allocations and provide sufficient conditions for this to be a stable family against coalitional defections of firms. Finally, we focus on those periods of the time horizon that are consolidated and we analyze their effect on the stability of cost allocations.

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Section: Introductionmentioning

confidence: 99%

The effect of consolidated periods in heterogeneous lot-sizing games

Guardiola

Meca

Puerto

2021

TOP

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“…The core as a solution to a cooperative game has the advantage that any imputation from it is undominated. This solution is quite popular in the literature on the application of dynamic game theory, not only because of the aforementioned property, but also because of its flexibility, allowing allocating the cooperative outcome in several ways, for instance, in lot sizing [3][4][5], pollution control [6][7][8], or non-renewable resource extraction [9]. In cooperative dynamic games, there is a known transformation of a characteristic function, which is a key component of any cooperative game measuring the claims of any group of players [10,11].…”

Section: Introductionmentioning

confidence: 99%

“…It holds that Proof. By the definition of the limiting characteristic function (5), we note that v t and vt are monotone. Taking into account their difference, it holds that v t − vt is monotone as well.…”

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confidence: 99%

The Relationship between the Core and the Modified Cores of a Dynamic Game

Sedakov

Sun

2020

Mathematics

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The core as a solution to a cooperative game has the advantage that any imputation from it is undominated. In cooperative dynamic games, there is a known transformation that demonstrates another advantage of the core—time consistency—keeping players adhering to it during the course of the game. Such a transformation may change the solution, so it is essential that the new core share common imputations with the original one. In this paper, we will establish the relationship between the original core of a dynamic game and the core after the transformation, and demonstrate that the latter can be a subset of the former.

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“…The topic of this study falls into a stream of recent research on applying cooperative game theory in the area of inventory management; see, for instance, Anily and Haviv (2007), Chen (2009), Chen and Zhang (2009), Dror and Hartman (2007), Müller et al (2002), and Zhang (2009) for detailed discussions on inventory games. After the first appearance of our study, Gopaladesikan et al (2012) and Toriello and Uhan (2014), building upon some structural properties established here, propose primal‐dual algorithms for computing a core allocation, and develop cost allocations in the strong sequential core for economic lot‐sizing games without backlogging, respectively.…”

Section: Introductionmentioning

confidence: 99%

Duality Approaches to Economic Lot‐Sizing Games

Chen

Zhang

2016

Production and Operations Management

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We consider the economic lot-sizing (ELS) game with general concave ordering cost.In this cooperative game, multiple retailers form a coalition by placing joint orders to a single supplier in order to reduce ordering cost. When both the inventory holding cost and backlogging cost are linear functions, it can be shown that the core of this game is non-empty. The main contribution of this paper is to show that a core allocation can be computed in polynomial time.Our approach is based on linear programming (LP) duality and is motivated by the work of Owen [19]. We suggest an integer programming formulation for the ELS problem and show that its LP relaxation admits zero integrality gap, which makes it possible to analyze the ELS game by using LP duality. We show that, there exists an optimal dual solution that defines an allocation in the core.An interesting feature of our approach is that it is not necessarily true that every optimal dual solution defines a core allocation. This is in contrast to the duality approach for other known cooperative games in the literature.

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Dynamic cost allocation for economic lot sizing games

Cited by 14 publications

References 11 publications

The effect of consolidated periods in heterogeneous lot-sizing games

The effect of consolidated periods in heterogeneous lot-sizing games

The Relationship between the Core and the Modified Cores of a Dynamic Game

Duality Approaches to Economic Lot‐Sizing Games

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