The Newsboy Problem with Resalable Returns

We analyze a newsboy problem with resalable returns. A single order is placed before the selling season starts. Purchased products may be returned by the customer for a full refund within a certain time interval. Returned products are resalable, provided they arrive back before the end of the season and are undamaged. Products remaining at the end of the season are salvaged. All demands not met directly are lost. We derive a simple closed-form equation that determines the optimal order quantity given the demand distribution, the probability that a sold product is returned, and all relevant revenues and costs. We illustrate its use with real data from a large catalogue/internet mail order retailer.