Optimal dynamic return management of fixed inventories

While the primary effort of all retailers is to generate that initial sales, return management is generally identified as a secondary issue that does not necessarily need the same level of planning and proactive strategies. In this article, we position return management as a process that is at the interface of both inventory and revenue management by explicitly incorporating the return policy of the retailer in consumer's valuation. We consider a retailer that sells a fixed amount of inventory over a finite horizon. We assume that return policy is a decision variable that can be changed dynamically at every period. While flexible return policies generate more demand, it also induces more returns. We characterize the optimal dynamic return policies based on two costs of return scenarios. We show a conditional monotonicity result and discuss how these return policies change with respect to inventory and time. We then propose a heuristic and prove that it is asymptotically optimal. We also study the joint dynamic pricing and dynamic return management problem in the same setting and propose two more heuristics whose performance is tested numerically and found to be close to optimal for higher inventory levels. We extend our model to multiple competing retailers and characterize the resulting equilibrium return policy and prices.