Optimal fulfillment and transshipment strategies in omnichannel retailing with cross-channel returns

The popularity of online shopping has been steadily increasing among consumers, especially after the COVID-19 pandemic. To meet growing customer demand and remain competitive, retailers are increasingly focusing on leveraging online sales growth, particularly adopting cross-channel strategies. However, operating online and offline channels seamlessly and efficiently presents significant challenges. To address these challenges, we develop a dynamic programming model that determines optimal fulfillment and transshipment strategies for omnichannel retailing with cross-channel returns. We consider a retailer operating both online and offline channels, each carrying its own inventory. We allow omnichannel fulfillment (i.e., online orders can be fulfilled from any channel) and cross-channel returns (i.e., online orders can be returned online or to any store, while store purchases can only be returned to any store location). Our study provides insights into a retailer’s initial inventory allocation and dynamic fulfillment and transshipment decisions that maximize total profit under uncertainty given customer returns. We determine the optimal initial inventory allocation across channels, jointly with fulfillment and transshipment decisions. Specifically, we address three key decisions simultaneously: (i) how to allocate initial inventory (ii) where to fulfill an online order over time, and (iii) when and where to transship items to balance inventory over time. To support practical implementation, we develop two computationally efficient heuristics that approximate optimal decisions in complex omnichannel settings.