On Base-Stock Level Inventory Control

Abstract

Mathematical models are used to discuss the following inventory situation customer demands on the warehouse stock of an item fluctuate independently and randomly during successive discrete time periods (e.g., weeks), demands that cannot be satisfied from stock on hand are “lost,” e.g., are satisfied elsewhere. There is a one-period lag in warehouse replenishments, and a base-stock-level policy determines the sizes of warehouse replenishment orders. Under these conditions available stock at the beginning of a period is a Markov chain, of Morse [Morse, P. M. 1959. Solutions of a class of discrete-time inventory problems. Opns Res. 7 67–78 (in particular pp. 76–78).]. This chain is discussed, and its probabilities are used to evaluate stock-out and inventory carrying costs associated with the end of a period. The above costs are also evaluated for the easily analyzed case in which disappointed demands backorder. A numerical example indicates that optimum base-stock-levels determined on the backordering assumption may be nearly identical with those determined assuming impatience.