Distributionally Robust Multiperiod Inventory Model for Omnichannel Retailing Considering Buy-Online, Pickup-in-Store and Out-of-Stock, Home-Delivery Services

This article proposes the distributionally robust multiperiod inventory model incorporating the buy-online-pickup-in-store (BOPIS) and out-of-stock-home-delivery-service (OSHDS), which are the representative services of omnichannel retailing. Under this omnichannel system, the retailer operates both online and brick-and-mortar (B&M) stores simultaneously, which allow interactive flows of customer demands and desired products. The BOPIS allows customers who buy products through the online store to pick them up in the B&M store. Meanwhile, the OSHDS allows customers who find the product they want out of stock in a B&M store to receive it later, through express delivery from the online store. To capture the correlated uncertain demands of the BOPIS and OSHDS, we adopt a factor-based demand model that is affinely dependent on predefined uncertain factors. To handle a multistage decision process under uncertain demands, we utilize a rule-based approximation and distributionally robust bound to derive a tractable formulation. Computational results achieved in this article offer some insights that BOPIS and OSHDS play a role in providing retailer with flexibility, which could handle unsatisfied demands efficiently.