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This paper introduces a stochastic model of a distribution system where the stocking location is owned by a dealer (or retailer) and the product is supplied by a manufacturer. Inventory is managed by the dealer, and the manufacturer is responsible for delivery of the product through both regular replenishment and expedite shipment modes. The dealer and the manufacturer share the goal of providing a high level of customer service. Demand, moreover, is a function of the service level offered to the market by the dealer. We develop optimal stock control policies for the cases where each decision maker in turn is dominant and acts unilaterally while being constrained by the supply/demand linkages of the system. We also develop an optimum policy for the case where both levels are managed under centralized control (i.e., both levels cooperate). Results indicate that the expected profit for a dominant dealer (or dominant manufacturer) is higher under decentralized control than the optimal solution for either under centralized control. However, the centralized solution is a global‐optimal solution and therefore will guarantee longterm stability. Differences between the various solutions are analyzed explicitly to estimate the cost of coordination.
Ernst et al. (Tue,) studied this question.