MODELING AND SENSITIVITY ANALYSIS OF VENDOR MANAGED INVENTORY SYSTEM BASED UPON STACKELBERG GAME THEORY, ASSUMING THAT THE PRODUCER IS THE LEADER

In this paper, we consider a supply chain consisting of one producer and multiple retailers, where the producer 165 applies a vendor managed inventory in the supply chain. Production of a single product is assumed and the demand for this item in the retail market is a decreasing function, with respect to price. Although similar problems have been studied and analyzed by several researchers in the past, this work diers from others in several ways. The most important contributions of this article are: (1) Modeling centralized and decentralized states of the considered supply chain as non-linear programming. (2) Considering two situations for the decentralized supply chain: (a) producer sells the product at the same unit price to all retailers; (b) producer sells the product at dierent prices to retailers; (c) producing random data for parameters of the models and comparing centralized and decentralized state performances with each other; and (d) providing a sensitivity analysis for model parameters and vendor managed inventory systems. It is worthwhile to note that the decentralized state formulation is performed based on the Stackelberg game theory, and under the assumption that the producer is the leader of the game. The results of our analysis indicate that; (i) dierences in selling prices for retailers does not have much eect on the member pro ts of the supply chain, but can have a signi cant eect on prices; (2) sensitivity analysis of the model parameters indicates that the in uence of each parameter on system performance signi cantly depends on whether the overall demand of the system is less than the production rate or is equal to the production rate; (3) considering system performance in the centralized state as a benchmark, system pro t in a decentralized state is, on average, 0.94 centralized system pro t. Also, for cases in which the overall demand of the system is less than the production rate, the dierence between centralized and decentralized states is greater than that of the case whose production rate is equal to overall demand.