The goal of this paper is to describe, model, and optimize inventory in a reverse logistics system that supports the warranty returns and replacements for a consumer electronic device. The context and motivation for this work stem from a collaboration with an industrial partner, a Fortune 100 company that sells consumer electronics. The reverse logistics system is a closed-loop supply chain: failed devices are returned for repair and refurbishing; this inventory is then used to serve warranty claims or sold through a side sales channel. Managing inventory in this system is challenging because of the short life cycle of these devices and the rapidly declining value for the inventory. We examine an inventory model that captures these dynamics. We characterize the structure of the optimal policy for this problem for stochastic demand and introduce an algorithm to calculate optimal sell-down levels. We also provide a closed-form policy for the deterministic version of the problem, and we use this policy as a certainty-equivalent approximation to the stochastic optimal policy. Finally, using numerical experiments, we analyze the sensitivity of this system to changes in various parameters, and we also evaluate the performance of the certainty-equivalent approximation using data from our industrial partner. The online appendix is available at https://doi.org/10.1287/msom.2017.0622 .

Online purchases constitute about one-tenth of U.S. retail sales. The supply chains that support online retailing are fundamentally different from those that support traditional brick-and-mortar stores. Traditional solutions are not always appropriate to solve online retailing’s operations problems; thus, there is an opportunity to understand and improve these novel supply chains. One key characteristic of the inventory systems for online retailing is demand spillover, whereby a stockout at a fulfillment center (FC) results in demand spilling over to another FC. For this context we examine how to allocate inventory to the FCs under a periodic-review joint-replenishment policy, with an objective to minimize outbound shipping costs for a fixed amount of inventory. We first show how traditional decentralized allocation policies may perform suboptimally and induce dynamics (whiplash) that result in costly spillover. We find that this phenomenon increases with the prevalence of local stockouts and with the level of inventory imbalance. We then describe that inventory imbalance occurs in online retailing because of operational realities and provide evidence based on real data. Finally, we propose a heuristic to allocate inventory accounting for possible spillover during the lead time. We test the heuristic by a simulation and show that it performs better than the status quo policy, is robust to operational realities, and captures over 90% of the possible improvement as compared to a pseudo-optimal policy. The online appendix is available at https://doi.org/10.1287/msom.2016.0614 .