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Cooperation and competition in inventory gamesMeca, A.; Garcia-Jurado, I.; Borm, Peter

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.

Supply chain management is related to the coordination of materials, products and information flows among suppliers, manufacturers, distributors, retailers and customers involved in producing and delivering a final product or service. In this setting the centralization of inventory management and coordination of actions, to further reduce costs and improve customer service level, is a relevant issue. In this paper, we provide a review of the applications of cooperative game theory in the management of centralized inventory systems. Besides, we introduce and study a new model of centralized inventory: a multi-client distribution network.

In this paper we deal with the cost allocation problem arising in an inventory transportation system with a single item and multiple agents that place joint orders using an EOQ policy. In our problem, the fixed order cost of each agent is the sum of a first component (common to all agents) plus a second component which depends on the distance from the agent to the supplier. We assume that agents are located on a line route, in the sense that if any subgroup of agents places a joint order, its fixed cost is the sum of the first component plus the second component of the agent in the group at maximal distance from the supplier. For these inventory transportation systems we introduce and characterize a rule which allows us to allocate the costs generated by the joint order. This rule has the same flavor as the Shapley value, but requires less computational effort. We show that our rule has good properties from the point of view of stability.