Discounted Cost Models with Lost Sales

Abstract

In the literature of stochastic inventory models, there are two different assumptions about the excess demand unfilled from existing inventories: the backlog assumption and the lost sales assumption. The former is more popular in the literature, partly because historically the inventory studies started with spare parts inventory management problems in military applications, where the backlog assumption is realistic. However, in many other business situations, it is quite often that demand that cannot be satisfied on time is lost. This is particularly true in a competitive business environment. For example, in many retail establishments such as a supermarket or a department store, a customer chooses a competitive brand and goes to another store if his/her preferred brand is out of stock.