We study the problem of a retailer that maximizes profit through joint replenishment, pricing and removal decisions. This problem is motivated by the observation that retailers usually retain rights to remove inventory from their network either by returning it to the suppliers or through liquidation in the face of random demand and capacity constraints. We develop a tractable dynamic program by leveraging the concept of $L^\natural$-concavity that allows us to partially characterize the structure of optimal policies. Different modes of return rights are considered, and we explore extensions that consider lead-time, perishability and temporal demand dependency under capacity constraints. We additionally present illustrative numerical results.
Inventory, Planning and Control (IPC), Amazon.com, Seattle, WA 98109. August 2017