Should Only Popular Products Be Stocked? Warehouse Assortment Selection for E-Commerce Companies

Abstract

Problem definition: This paper studies the single-warehouse assortment selection problem that aims to minimize the order fulfillment cost under the cardinality constraint. We propose two fulfillment-related cost functions corresponding to spillover fulfillment and order-splitting, respectively. This problem includes the fill rate maximization problem as a special case. We show that although the objective function is submodular for a broad class of cost functions, the fill rate maximization problem with the largest order size being two is NP- hard.

Methodology: To make the problem tractable to solve, we formulate the general warehouse assortment problem under the two types of cost functions as mixed integer linear programs (MILPs). We also provide a dynamic programming algorithm to solve the problem in polynomial time if orders are non-overlapping. Furthermore, we propose a simple heuristic called the marginal choice indexing (MCI) policy that allows the warehouse to store the most popular products. This policy is easy to compute and hence is scalable to large-size problems. Although the performance of MCI can be arbitrarily bad in some extreme scenarios, we find a general condition under which it is optimal. This condition is satisfied by many multi-purchase choice models.

Managerial implications: Through extensive numerical experiments on a real-world dataset from RiRiShun Logistics, we find that the MCI policy is surprisingly near-optimal in all the settings we 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 MILP optimal solution in 14 out of 25 cases on the test data set, illustrating its robustness against demand fluctuations.

Keywords: warehouse assortment selection, demand choice models, submodular functions, marginal choice probability