Inventory Allocation Under the Greedy Fulfillment Policy: The (Potential) Perils of the Hindsight Approach

We study the inventory allocation problem for an online retailer with multiple warehouses and geographically dispersed demand. The retailer fulfills customer orders using a greedy policy (i.e., ship from the cheapest available warehouse) and determines inventory allocation using the widely adopted hindsight or stochastic programming approach. Although this approach is popular in both academia and practice, its limitations remain poorly understood. We show that the hindsight solution coincides with the optimal allocation under the greedy policy, but for a mis-specified demand sequence that assumes an overly optimistic realization. This optimism can sometimes be harmless, but it can also lead to substantial inefficiencies. In particular, we identify three conditions under which the hindsight solution is asymptotically optimal as the lost-sales cost becomes large: (i) identical ordering costs across warehouses, (ii) unbounded warehouse capacities, and (iii) independence of demand across locations. Violating any of these may cause the hindsight solution to perform arbitrarily worse than the true optimum under the greedy policy. Surprisingly, we further show that even if the retailer were to pair the hindsight-based allocation with the best-possible fulfillment policy (not necessarily greedy), the resulting total cost can still be arbitrarily suboptimal. The significant suboptimality extends beyond the asymptotic limiting regime. These findings reveal fundamental limitations of the hindsight approach and highlight the need for more robust allocation strategies in practice.

Supplemental Material: All supplemental materials, including the code, data, and files required to reproduce the results, are available at https://doi.org/10.1287/opre.2024.0994.