Fixed Shortage Costs and the Classical Inventory Model

Many recent economic and inventory studies have included various types of fixed or lump-sum costs as important determinants of optimal behavior. In this paper, the classical inventory model is augmented to include fixed shortage costs. In general, the presence of fixed shortage costs can lead to complex optimal solutions. The purpose of this paper is to establish a set of sufficient conditions which guarantee the existence of an optimal ordering policy which is unique. The resulting optimal policy is described by a unique set of critical numbers which are bounded and decrease monotonically over the horizon for which the inventory system is to be operated.