Optimal Policies and Heuristics to Match Supply with Demand for Online Retailing

Abstract

Problem definition: We consider an online retailer selling multiple products to different zones over a finite horizon with multiple periods. At the start of the horizon, the retailer orders the products from a single supplier and stores them at multiple warehouses. The retailer determines the products’ order quantities and their storage quantities at each warehouse subject to its capacity constraint. At the end of each period, after random demands in the period are realized, the retailer chooses the retrieval quantities from each warehouse to fulfill the demands of each zone. The objective is to maximize the retailer’s expected profit over the finite horizon. Methodology/results: For the single-zone case, we show that the multiperiod problem is equivalent to a single-period problem and the optimal retrieval decisions follow a greedy policy that retrieves products from the lowest-cost warehouse. We design a nongreedy algorithm to find the optimal storage policy, which preserves a nested property: Among all nonempty warehouses, a smaller-index warehouse contains all the products stored in a larger-index warehouse. We also analytically characterize the optimal ordering policy. The multizone case is unfortunately intractable analytically, and we propose an efficient heuristic to solve it, which involves a nontrivial hybrid of three approximations. This hybrid heuristic outperforms two conventional benchmarks by up to 22.5% and 3.5% in our numerical experiments with various horizon lengths, fulfillment frequencies, warehouse capacities, demand variations, and demand correlations. Managerial implications: A case study based on data from a major fashion online retailer in Asia confirms the superiority of the hybrid heuristic. With delicate optimization, the heuristic improves the average profit by up to 16% compared with a dedicated policy adopted by the retailer. The hybrid heuristic continues to outperform the benchmarks for larger networks with various structures. Funding: X. Li is supported by the Singapore Ministry of Education [Tier 1 Grant 23-0619-P0001]. Y. F. Lim is grateful for the support from the Singapore Management University under the Maritime and Port Authority Research Fellowship and the Singapore Ministry of Education [Tier 1 Grant MSS23B001]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2021.0394 .