Omni-channel retailing: A data-driven distributionally robust approach for integrated fulfillment services under competition with traditional and online retailers

Abstract

Omni-channel (OC) retailing strategy provides consumers with seamless shopping experience by integrating different sales channels. In this study, we formulate a price and delivery lead time (DLT) dependent demand function for an omni-channel retailer (OCR) that provides integrated fulfillment services including buy-online-pick-up-in-store (BOPS) and order-in-store-deliver-to-home (OSDH) services. To investigate the extent of OC retailing success and its effects on the pre-existing retailing business models, we examine a dynamic competition between traditional, online, and OC retailing business models through a Nash-Stackelberg game. Our study also addresses the demand uncertainty as a multiplicative variable to the market potential of a product. To hedge against demand uncertainty, due to lack of perfect knowledge about the demand probability distribution, we construct a data-driven ambiguity set for candidate distributions based on the Wasserstein metric, which is utilized to quantify the distances between chosen distributions and the empirical distribution derived from the available data. In this case, part of the problem adopts a distributionally robust Nash equilibrium to find the optimal retailers’ decisions. The obtained results demonstrate the potential OC retailing functionality in terms of demand attraction and profitability. In addition, our results showed that utilizing the distributionally robust approach would lead to shorter DLT and higher sales prices compared to the deterministic demand environment. Interestingly, the pre-existing retailers’ sales prices under demand uncertainty can be higher than the situation under deterministic demand, while they are less than the sales prices before OCR entrance to the market. Therefore, there is no price inflation in the market in the presence of OCR.