Decentralized Online Order Fulfillment in Omni-Channel Retailers

We consider an order fulfillment problem of an omni-channel retailer that ships online orders from its distribution center (DC) and brick-and-mortar stores. Stores use their local information, not observed by the retailer, that can lead them to accept or reject fulfillment requests of items in an online order. We investigate the problem of sequencing requests to stores and inventory rationing decisions at the DC to minimize expected costs under uncertain store acceptance behavior and when items are indistinguishable in terms of shipping. First, under the scenario that stores are used only when the DC has insufficient inventory, we propose a Markov Decision Process formulation and analyze the performance of myopic policies that are preferable because of their interpretability. We show that the performance rate of a myopic approach that orders stores by cost only depends on the number of items in an order, which is small in practice. We also determine conditions for the range of acceptance probabilities for the myopic policy to be optimal for small-sized orders. Using optimality conditions for a special case of the problem, we develop an adaptive variant of the myopic policy, and propose a new degree-based strategy that balances shipping costs and acceptance probabilities. Numerical testing suggests that the best-performing sequencing policy is within 1% of optimality on average. Moreover, using two years of data from a large omni-channel retailer in North America, we observe that adaptive policies, albeit more complex, are beneficial in reducing costs and split deliveries if acceptance rates can be estimated accurately. Second, we determine when the retailer should ship from stores or ration the inventory at the DC. We show that for single-item orders, the optimal policy has a threshold structure, where, remarkably, the highest priority region is also subject to rationing. We then consider the novel multi-unit-single-item rationing problem, and leverage the structure of the single-unit model to develop a heuristic. We numerically establish the efficacy of rationing models and our heuristic.