Implementation of the Newsvendor Model with Clearance Pricing: How to (and How Not to) Estimate a Salvage Value

The newsvendor model is designed to decide how much of a product to order when the product is to be sold over a short selling season with stochastic demand and there are no additional opportunities to replenish inventory. There are many practical situations that reasonably conform to those assumptions, but the traditional newsvendor model also assumes a fixed salvage value: all inventory left over at the end of the season is sold off at a fixed per-unit price. The fixed salvage value assumption is questionable when a clearance price is rationally chosen in response to the events observed during the selling season: a deep discount should be taken if there is plenty of inventory remaining at the end of the season, whereas a shallow discount is appropriate for a product with higher than expected demand. This paper solves for the optimal order quantity in the newsvendor model, assuming rational clearance pricing. We then study the performance of the traditional newsvendor model. The key to effective implementation of the traditional newsvendor model is choosing an appropriate fixed salvage value. (We show that an optimal order quantity cannot be generally achieved by merely enhancing the traditional newsvendor model to include a nonlinear salvage value function.) We demonstrate that several intuitive methods for estimating the salvage value can lead to an excessively large order quantity and a substantial profit loss. Even though the traditional model can result in poor performance, the model seems as if it is working correctly: the order quantity chosen is optimal given the salvage value inputted to the model, and the observed salvage value given the chosen order quantity equals the inputted one. We discuss how to estimate a salvage value that leads the traditional newsvendor model to the optimal or near-optimal order quantity. Our results highlight the importance of understanding how a model can interact with its own inputs: when inputs to a model are influenced by the decisions of the model, care is needed to appreciate how that interaction influences the decisions recommended by the model and how the model's inputs should be estimated.