A model of a production-repair inventory system with time-varying demand and quality-dependent recovery channels

In this paper, we study an inventory system over an infinite planning horizon where a time-varying demand is satisfied by process cycles that consist of a production batch followed by a recovery batch. Our model considers three types of inventory-returned items, serviceable items, and raw material. Furthermore, our model considers two recovery channels-recovery into serviceable items and recovery into raw material. Serviceable items are thus sourced from two inputs-direct recovery and production from raw material. These raw materials can be salvaged from returned items, as well as bought from external sources whenever required. We propose an expression for the unit time total cost as well as a numerical method to find the optimal policy. The properties of the model are studied through numerical experiments, in particular, the feasible situations where hybrid policies are better than pure policies.