A generalized linear production model: A unifying model

Granot, Daniel

doi:10.1007/bf01580585

Cited by 109 publications

(52 citation statements)

References 14 publications

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“…For the linear production game, the relationship between the allocations defined by optimal dual solutions and the core is studied by Samet and Zemel [19]. Granot [7] extends Owen's approach to a more general linear production game.…”

Section: Our Results and Approachmentioning

confidence: 99%

Cost Allocation for Joint Replenishment Models

Zhang

2009

Operations Research

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We consider the one-warehouse multiple retailer inventory model with a submodular joint setup cost function. The objective of this model is to determine an inventory replenishment policy that minimizes the long-run average system cost over an infinite time horizon. Although the optimal policy for this problem is still unknown, a class of easy-to-implement power-of-two policies are 98% effective. This paper focuses on how the cost, under an optimal power-of-two policy, should be allocated to the retailers. This question generates an interesting cooperative game. We prove that this cooperative game has a non-empty core. The key to our result is a strong duality theorem for the one-warehouse multiple retailer problem under power-of-two policies.

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Section: Our Results and Approachmentioning

confidence: 99%

Cost Allocation for Joint Replenishment Models

Zhang

2009

Operations Research

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“…Non-emptiness of the core, however, can also be shown within a more general class of problems. This more general framework, termed generalized linear production model in [20], has a non-additive structure, and it encompasses for instance the cut-based LPformulation for Steiner Network problems [36]. It is a fascinating open problem to see if this framework can also be used to derive exact and approximate SE in strategic cost sharing games.…”

Section: Conclusion and Open Problemsmentioning

confidence: 99%

Strategic cooperation in cost sharing games

Hoefer

2011

Int J Game Theory

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In this paper we consider strategic cost sharing games with so-called arbitrary sharing based on various combinatorial optimization problems, such as vertex and set cover, facility location, and network design problems. We concentrate on the existence and computational complexity of strong equilibria, in which no coalition can improve the cost of each of its members.Our main result reveals a connection between strong equilibrium in strategic games and the core in traditional coalitional cost sharing games studied in economics. For set cover and facility location games this results in a tight characterization of the existence of strong equilibrium using the integrality gap of suitable linear programming formulations. Furthermore, it allows to derive all existing results for strong equilibria in network design cost sharing games with arbitrary sharing via a unified approach. In addition, we are able to show that in general the strong price of anarchy is always 1. This should be contrasted with the price of anarchy of Θ(n) for Nash equilibria. Finally, we indicate that the LP-approach can also be used to compute near-optimal and near-stable approximate strong equilibria.

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“…The study of cooperative combinatorial optimization games, which are defined through characteristic functions given as optimal values of combinatorial optimization problems, is a fruitful topic (see, for instance, Shapley and Shubik, 1972;Dubey and Shapley, 1984;Granot, 1986;Tamir, 1992;Deng et al, 1999Deng et al, , 2000Faigle and Kern, 2000). There are characterizations of the total balancedness of several classes of these games.…”

Section: Introductionmentioning

confidence: 99%

Production-inventory games: A new class of totally balanced combinatorial optimization games

Guardiola

Meca

Puerto

2009

Games and Economic Behavior

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In this paper we introduce a new class of cooperative games that arise from production-inventory problems. Several agents have to cover their demand over a finite time horizon and shortages are allowed. Each agent has its own unit production, inventory-holding and backlogging cost. Cooperation among agents is given by sharing production processes and warehouse facilities: agents in a coalition produce with the cheapest production cost and store with the cheapest inventory cost. We prove that the resulting cooperative game is totally balanced and the Owen set reduces to a singleton: the Owen point. Based on this type of allocation we find a population monotonic allocation scheme for this class of games. Finally, we point out the relationship of the Owen point with other well-known allocation rules such as the nucleolus and the Shapley value.

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A generalized linear production model: A unifying model

Cited by 109 publications

References 14 publications

Cost Allocation for Joint Replenishment Models

Cost Allocation for Joint Replenishment Models

Strategic cooperation in cost sharing games

Production-inventory games: A new class of totally balanced combinatorial optimization games

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