A Study For Network Design In Multi-commodity Supply Chains

A good supply chain design can not only save costs,but also improve the service level,increases customer satisfaction,and thus enhance the competitiveness of an enterprise.Therefore,the design of a good supply chain network is becoming more and more important in the context of economic globalization.In this paper,we study a model which consists of one external supplier,a set of potential distribution centers,and a set of retailers,each of which is faced with uncertain demands.The demand of each retailer is fulfilled by a single distribution center for all commodities.In order to minimize the cost,we introduce the submodular function and the cutting plane algorithm.This algorithm can effectively solve the nonlinear programming problem at this time.Then,on the basis of this model,we consider the process that the distribution centers spend some money to buy the same amount of commodities from the external supplier in the n period.We obtain a function of the difference between the purchase,inventory and transportation costs and expected benefit,and we prove that the function is also a submodular function.Next,we consider the commodities are not the same number,we prove that it is a submodular function.Lastly,we consider the number is a random variable,and we also prove that it is a submodular function.So we can use the cutting plane algorithm to solve them.Computational results show that the cutting plane algorithm can solve problem instances efficiently.