Lot-sizing for inventory systems with product recovery

We study inventory systems with product recovery. Recovered items are as-good-as-new and satisfy the same demands as new items. The demand rate and return fraction are deterministic. The relevant costs are those for ordering recovery lots, for ordering production lots, for holding recoverable items in stock, and for holding new/recovered items in stock. We derive simple formulae that determine the optimal lot-sizes for the production/procurement of new items and for the recovery of returned items. These formulae are valid for finite and infinite production rates as well as finite and infinite recovery rates, and therefore more general than those in the literature. Moreover, the method of derivation is easy and insightful.