An integrated model for space determination and site selection of distribution centers

In this paper we present an integrated distribution center site selection and space requirement problem on a two-stage network in which products are shipped from plants to distribution centers, where they are stored for an arbitrary period of time and then delivered to retailers. The objective of the problem is to minimize total inbound and outbound transportation costs and total distribution center construction cost – which includes fixed costs related to their locations and variable costs related to their space requirements for given service levels. Each distribution center is modeled as an M/G/c queueing system, in which each server represents a storage slot. We formulate this problem as a nonlinear mixed integer program with a probabilistic constraint. Two cases are considered. For the continuous unbounded size case, we find an approximate formula for the overflow probability and restructure this model into a connection location problem. For the discrete size option case, we reformulate the problem into a capacitated connection location problem with discrete size options. Computational results and a comparison of the two cases are provided.