Incorporating the customer's perspective into the newsvendor problem

The newsvendor problem is a classic in management science partly because selecting an optimal inventory level in the face of uncertain demand is an important problem but also because the solution is so elegant and intuitive: the inventory should beselected so that the probability that the vendor stocks out should be set equal to the ratio of the item's unit cost to its unit price. A number of attempts have been made to enrich the factors treated in the analysis. For example, if price can be set by the vendor, this will influence demand. Extensions in which demand is related to the price charged lose the closed form, and elegance, of the original solution. Another assumption in the problem is that the demand, while uncertain, is not affected by the chosen inventory level. It might be supposed that a better-in-stock position will ultimately lead to higher demand. In this paper we examine the case in which expected demand is related to the expected value anticipated by the customer. We define this value as the consumer surplus(willingness to pay less price charged) times the likelihood that the customer finds the item in stock. With this refinement we show that the optimal inventory is such that the probability of stocking out is equal to the ratio of the item's unit cost to the customer's willingnessto pay. We apply the method to cases in which there are multiple products and find that the simple solution is preserved.