The rack layout problem with stochastic demand and profit

In the last decade, methods applied to facility layout design in manufacturing have been applied to service industries. Facility layout design problems in service industries generally involve the partitioning of a building into departments and detailed design of each department. In this paper, we consider the problem of creating a detailed design for a department in a retail environment. In particular we study rack layout problems with stochastic demand and profit for a department, and we present an approach for determining the best merchandise arrangement. The model is formulated as a stochastic mixed-integer program with first-stage decision variables representing the investment of racks and shelves and second-stage decision variables representing the layout of the racks and shelves and arrangement of the merchandise. Our objective is to maximize the expected long-term profit of the department. A decomposition method is used to obtain the optimal solution. Computational results are reported for various cases.