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

Under a scattered storage policy, a single stock-keeping unit is stored in different locations throughout the warehouse. This policy aims to reduce travel times during order picking since it increases the probability of finding items belonging to the same order in nearby locations. Such type of storage policy is adequate for a typical e-commerce environment where a large variety of products are ordered in small quantities. The assignment of single items to different storage locations in the warehouse results in the scattered storage assignment problem. This paper proposes an exact algorithm for this problem that minimizes the sum of pairwise distances between the locations of the items belonging to the same order. We develop a mixed-integer model with different sets of valid inequalities (cuts) and test their performance on a set of data instances. Computational results show that the valid inequalities improve our model's objective function value by 32% compared to the initial formulation. Finally, we prove that the pairwise distance between items of the same order and the picker routing distances are better for our storage allocation policy than a more traditional storage allocation and random storage policy.