Non-cooperative strategies for production and shipments lot sizing in the vendor-buyer system

This paper considers a decentralized dynamic production-distribution control. A discrete deterministic model in which a vendor produces a product and supplies it to the buyer is considered. Several papers on vendor-buyer integrated production inventory management assume that policies are set by a central decision maker to optimize total system performance. Although vendor and buyer may agree to minimize the total cost, at least one of them has a private incentive to deviate from the agreement. In the competitive situation, the objective is to determine schedules which minimize the individual average total cost of production, shipment and stockholding. We assume that the division of shipment costs is centrally coordinated or negotiated initially. It leads to a class of non-cooperative constrained games, indexed by two parameters connected with partitions of shipment costs. Non-cooperative strategies are considered as feasible strategies in a restricted non-cooperative game. Some properties of equilibrium strategies are investigated as acceptable equilibrium strategies of subgames in the game.