Combining a Smart Pricing Policy with a Simple Replenishment Policy: Managing Uncertainties in the Presence of Stochastic Purchase Returns

This paper addresses operational challenges faced by retailers offering free return policies. We consider a general system with lost sales, positive lead time, periodic review, binomial demand, and an arbitrary restriction on price change frequency. We study the joint pricing and inventory decisions in the presence of stochastic returns. Specifically, when an item is purchased, it can be returned at a future random time and may be restocked for resale after passing an inspection. We assume a general stationary return time distribution. A key challenge in both policy design and analysis arises from the dynamic coupling introduced by returns being restocked over time. To address this, we propose a simple yet effective policy that combines a simple inventory policy with adaptive pricing based on observed sales and returns. Our results provide insights into how uncertainty in both demand and returns can be managed through adaptive pricing under various price change constraints. The analysis can be extended to more general settings, including (1) return fees and partial refunds, (2) nonstationary demand, and (3) service-level constraints. We also show numerically that misspecifying the return time distribution can lead to significant losses, even in a fully deterministic system without randomness. Funding: J. Uichanco was partially supported by the NSF [Grant 2208189]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/moor.2022.0172 .