Scattered storage assignment: Mathematical model and valid inequalities to optimize the intra-order item distances

Abstract

In scattered storage, individual items are intentionally distributed across multiple positions in the picking area. Especially in e-commerce environments, where orders typically consist of a few items in small quantities, such a storage policy can reduce picking travel times by increasing the likelihood that items belonging to the same order can be found in nearby positions. In this paper, we propose a scattered storage policy that, when determining the position where each replenished item should be stored, tries to minimize the sum of pairwise distances (SPD) between all items belonging to the same order including a drop-off point. However, when solving the exact mathematical model using integer programming techniques (0–1), the combinatorial nature of the problem hinders performance. We show that the solutions of the MIP solver can be improved by relaxing some variables and adding valid inequalities based on graph properties and knapsack cover constraints. Finally, we prove that the SPD objective is 65% lower for our scattered storage policy than for a traditional volume based storage policy.