Non-cooperative consignment stock strategies for management in supply chain

This paper analyzes the coordination and competition issue in a two-level supply chain, having one vendor (or manufacturer) and one buyer (or retailer). A continuous deterministic model is presented. To satisfy the buyer's demands, the product is delivered in discrete batches from the vendor's stock to the buyer's stock and all shipments are realized instantaneously. We describe inventory patterns and the cost structure of production-distribution cycles (PDC) under generalized consignment stock (CS) policies. For the joint optimization case, the average total cost of production, shipment and stock-holding is minimized. Optimal solution techniques are presented and illustrated with numerical examples. In a competitive situation, the objective is to determine schedules, which minimize the individual average total costs in the PDC obtainable by individual decisions. This paper presents a non-cooperative two-person constrained game with agents (a vendor and a buyer) choosing the number and sizes of deliveries. Generalized CS-policies are considered as feasible individual strategies in the game. We consider the class of non-cooperative sub-games, indexed by two integer parameters connected with CS policies. It is proven that there exists a unique Nash equilibrium strategy in each of the considered sub-game. (C) 2012 Published by Elsevier B.V.