Single Period Combined Inventory and Pricing Models

Abstract

We consider a single product, single period inventory problem with stochastic price-dependent demand. The ordering and pricing decision has to be made at the beginning of the period before demand is realized. Unsatisfied demand is lost and excess inventory has to be salvaged. This problem is known in literature as the price-setting newsvendor model.

The standard approach is to assume stochastic demand to be composed of deterministic functions decreasing in price and a stochastic error term. After surveying these models we present our approach. Instead of using deterministic demand functions we directly specify the distribution functions of demand depending on price. The demand distribution function must be increasing in price implying a stochastic ordering of the random demand with respect to price. We provide analytical results concerning the optimality conditions and numerical examples for specific demand distributions and discuss the relation to the findings from the standard approach.

Contrary to classical economic theory, we show that the optimal inventory level is not a decreasing function over the whole price range but it is increasing for low selling prices and decreasing for higher prices which is plausible from a managerial point of view.