Joint Product Framing and Order Fulfillment for E-Commerce Retailers

We consider a general joint product framing and order fulfillment problem with cardinality and capacity constraints faced by an online (e-commerce) retailer. There is a finite selling horizon and no replenishment opportunity. In each period, the retailer needs to decide how to ``frame" (e.g., display, rank, price, etc.) each product on her website as well as how to fulfill a new demand. Our proposed randomized heuristic policy is based on the solution of a deterministic approximation of the original stochastic control problem. The key challenge here is in constructing a randomization scheme that is easy to implement and satisfies some conditions that are sufficient to guarantee that the resulting policy is asymptotically optimal. We propose a novel two-step randomization scheme based on the idea of matrix decomposition and a re-scaling argument. We numerically test the performance of our heuristic policy and several benchmark policies using real-world data provided by a major US retailer. The results show that the proposed heuristic is very close to optimal, can be applied to large-scale problems in practice, and highlights the value of jointly optimizing product framing and order fulfillment decisions.