An accurate and reliable solution algorithm for the (Q, r) inventory system with a fixed shortage cost

For fast-moving class A items, the inventory policy is usually made by the (Q,r) inventory system with a normal lead-time demand distribution and a specified cost per stockout occasion. Silver et al. [E.A. Silver, D.F. Pyke, R. Peterson, Inventory Management and Production Planning and Scheduling, John Wiley & Sons, Inc, 1998] claim that the total relevant cost function is convex and that the convergence of their solution procedure to the optimal solution of the total relevant cost function is ensured. In this paper, we show that the total relevant cost function is not convex in general, and the convergence of the solution procedure to the optimal solution proposed by Silver et al. is not necessarily true. An alternative method to locate the optimal solution of the total relevant cost function is presented. Numerical examples are given to illustrate that the solution procedure presented by this article is superior to the one by Silver et al.