Optimal Policies and Heuristics To Match Supply With Demand For Online Retailing
We consider an online retailer selling multiple products to multiple zones over a single period. The retailer orders the products from a single supplier and stores them at multiple warehouses. At the start of the selling period, the retailer determines the order quantities of the products and their storage quantities at each warehouse subject to its capacity constraint. At the end of the period, after knowing the demands, the retailer determines the retrieval quantities from each warehouse to fulfill the demands. The retailer’s objective is to maximize her expected profit. For the single-zone case, we solve the problem optimally. The optimal retrieval policy is a greedy policy. We design a polynomial-time algorithm to determine the optimal storage policy, which preserves a nested property: Among all non-empty warehouses, a smaller-index warehouse contains all the products stored in a larger-index warehouse. The optimal ordering policy is a newsvendor-type policy. The problem becomes intractable analytically if there are multiple zones and we propose an efficient heuristic to solve it. This heuristic involves a non-trivial hybrid approximation of the second-stage expected profit. The heuristic is data driven, which uses demand samples as inputs to solve the problem without knowing the true demand distributions. Our numerical experiments suggest that this heuristic achieves a larger profit in a much shorter time compared to state-of-the-art approaches. The advantage of our heuristic becomes more obvious as the tail of the demand distribution becomes fatter or as the problem size becomes larger, clearly showing the heuristic’s efficiency. A case study based on data from a major fashion online retailer in Asia further confirms the superiority of the heuristic. With flexible fulfillment, our heuristic improves the efficiency by 28% on average compared to a dedicated policy adopted by the retailer.