Managing physical inventory and return policies for omnichannel retailing

As the retail industry increasingly adopts an omnichannel strategy amidst the growth of e-commerce, this study explores the interplay between inventory and return policies in such a setting. Specifically, we focus on “return losses,” defined as the losses incurred by retailers due to customer product returns. We target how these return losses impact retailers’ profits and physical inventories. While previous research has mainly concentrated on cross-channel returns, little attention has been paid to how omnichannel return policies affect store inventory and profit. We posit that profit-maximizing retailers allow consumers to select their purchase channels based on utility but require returns to follow specific policies. In this paper, we model four return policies based on the channel of return: original purchasing channel return, offline return, online return, and cross-channel return. We use a newsvendor model to construct an optimal profit function that accounts for the additional profit from offline return, uncertainty demand, and inventory cost. Our analysis identifies the conditions under which certain return policies are beneficial or detrimental to omnichannel retailers. We discover that the retailer's product pricing, return losses, and consumer return hassle costs are the main factors influencing the best return policy and inventory policy decisions. Moreover, whether to increase or decrease store inventory and the relationship between physical inventory and return loss depend on the return policy, price, and return hassle cost. Numerical simulations support our findings, which offer practical guidance for omnichannel retailers aiming to optimize their inventory and return policies.