On 17 October, 2022, 2021 MSOM Data Driven Research Challenge announced the winners, and the paper by Associate Professor Liu Fang and his collaborators " Shall I Only Store Popular Products? Warehouse Assortment Selection for E-Companies" won the first prize. This is the first time that domestic scholars have won the first prize in the challenge.
This paper studies the single-warehouse assortment selection problem that aims to minimize the order fulfillment cost under the cardinality constraint. The paper proposes two types of fulfillment-related cost functions, which correspond to different preferences toward spillover fulfillment and order-splitting. This problem includes the fill rate maximization problem as a special case. First, the research shows that the objective function is submodular for a broad class of cost functions. Second, the research shows that even the fill rate maximization problem is N P-hard. Next, the research proposes a simple heuristic called the marginal choice indexing (MCI) policy, which stores the most popular products. The research finds a general condition under which the MCI policy is optimal, and this condition can be satisfied by all classic discrete choice models and several multi-purchase choice models. Furthermore, the paper proposes an enhanced mixed integer linear programming (MILP) formulation with the easy-to-implement benders decomposition scheme. Through the extensive numerical experiments on a real-world dataset from RiRiShun Logistics, the research finds that the MCI policy is surprisingly near-optimal in all the settings tested. Simply applying the MCI policy, the fill rate is estimated to improve by 9.18% on average compared to the current practice for the local transfer centers (LTCs) on the training data set. More surprisingly, the MCI policy outperforms the optimal policy in 14 out of 25 cases on the test data set. This demonstrates that the MCI policy is robust to the change of demand function since it only requires knowledge of the marginal choice probability.