A Benders decomposition approach to product location in carousel storage systems

In this paper we discuss the problem of locating items within carousel bins in order to minimize the average carousel rotational distance per retrieval. We consider two cases: (1) a single two-dimensional carousel and (2) a group of two one-dimensional carousels. The corresponding problems are formulated as mixed-integer programs. In the second problem we apply concepts from Markovian performance evaluation methods to write the objective functions in a simple linear form. We also define a set of uniqueness constraints that significantly reduces the size of the solution feasibility space. We then apply Benders decomposition algorithm to solve both problems. We develop a closed form solution for the dual subprobem and present numerical results to show the efficiency of the proposed solution methodology.