An integrated model for site selection and space determination of warehouses

In this paper we present an integrated model for site selection and space determination for warehouses in a two-stage network in which products are shipped from part suppliers to warehouses, where they are stored for an uncertain length of time and then delivered to assembly plants. The objective is to minimize the total inbound and outbound transportation costs and the total warehouse operation costs, which include the fixed costs related to their locations and the variable costs related to their space requirements for given service levels. Each warehouse is modeled as an M/G/c queueing system in which each storage slot acts as a server. 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 reformulate the problem into a set-covering problem. For the discrete size option case, we reformulate the problem into a capacitated connection location problem with discrete size options. Computational experiments are performed and the results show that the continuous model is appropriate for the small and median size problems and the discrete model is a good choice for the large size problems.