Dynamic and static item allocation for the in-store front warehouses

In response to furious competition from emerging online retailers, traditional supermarkets begin leveraging their brick-and-mortar store chains by setting up small in-store front warehouses to facilitate order picking processes for online orders. In this article, we investigate how to select products and allocate space for the in-store front warehouse under dynamic and static strategies to minimize the total order-picking workload. For the dynamic allocation problem, we formulate it as a mixed-integer programming (MIP) model, which can be decomposed into a master multichoice knapsack problem (MCKP) and an order picking problem (OPP) as subproblems. An exact algorithm and a heuristic that is 1/2-bounded under certain routing policies are proposed. For the static allocation problem, we construct a stochastic gradient estimator of the expected travel distance by infinitesimal perturbation analysis (IPA) and introduce a discrete Frank-Wolfe algorithm to solve it. Numerical results reveal that the logic of dynamic allocation for the in-store front warehouse is different from that for regular warehouses, and the storage location assignment for the shelf area in supermarkets greatly impact the performance of these allocation strategies. The experimental results using data from a real retailer validate the effectiveness of proposed algorithms.