The Newsvendor Problem with a General Price Dependent Demand Distribution

Abstract

We consider a single product, single period inventory problem with stochastic price-dependent demand. The ordering and pricing decisions have to be made at the beginning of the period before demand is realized. Unsatisfied demand is lost and excess inventory has to be salvaged. The standard approach is to assume stochastic demand to be composed of deterministic functions decreasing in price and a stochastic error term. Instead of using deterministic demand functions we directly specify the distribution functions of demand depending on price. We provide analytical results concerning the optimality conditions and numerical examples based on specific demand distributions and discuss the relation of the findings to the standard approach. We show that the optimal inventory level is not a decreasing function over the whole price range, but it increases for low selling prices and decreases for higher prices, which is plausible from a managerial point of view.