Omnichannel retailing with different order fulfillment and return options

The omnichannel strategies buy-online-and-return-in-store (BORS) and buy-online-and-pick-up-in-store (BOPS) have attracted attention from both industry and academia. In practice, major retailers adopt BORS and BOPS both individually and jointly, which motivates us to explore when it is profitable for a retailer to adopt BORS or/and BOPS strategy. We formulate a stylised model that captures (1) consumers' uncertainty about product match, (2) the offline search cost for consumers, and (3) the cross-selling effect of the consumers' store visit. We find that the cross-selling benefit and the offline search cost have a significant impact on the retailer's optimal omnichannel strategy. When the cross-selling benefit is sufficiently low, adopting BORS alone is optimal for the retailer. When the cross-selling benefit is moderate and the offline search cost is high, adopting both strategies has a complementary effect, and it is optimal for the retailer to adopt both omnichannel strategies jointly. However, when the cross-selling benefit is sufficiently high, adopting both strategies could be less profitable to the retailer than adopting the BOPS strategy alone. Moreover, consumer surplus may decrease in this case, suggesting that adopting both omnichannel strategies could result in a lose-lose situation for both the retailer and the consumers.