A Bender's Decomposition Method to Solve Stochastic Distribution Network Design Problem with Two Echelons and Inter-Depot Transportation

In many practical distribution networks, managers face significant uncertainties in demand, local price of building facilities, transportation cost, and macro and microeconomic parameters. This paper addresses design of distribution networks in a supply chain system which optimizes the performance of distribution networks subject to required service level. This service level, which is considered for each arbitrary request arriving at a distribution center (facility), has a (pre-specified) small probability of being lost. In this mathematical model, customer’s demand is stochastic that follows uniform distribution. In this model, inter-depot transportation (transportation between distributions centers (DCs)), capacities of facilities, and coverage radius restrictions are considered. For this restriction, each DC cannot service all customers. The aim of this model is to select and optimize location of plants and DCs. Also, the best flow of products between DCs and from plants to DCs and from DCs to customers will be determined. The paper presents a mixed integer programming model and proposed an exact solution procedure in regard to Benders’ decomposition method.