A simple cost minimization procedure for the (Q, r) inventory system with a specified fixed cost per stockout occasion

For fast-moving A items, Silver et al. [E.A. Silver, D.F. Pyke, R. Peterson, Inventory Management and Production Planning and Scheduling, third ed., John Wiley & Sons, New York, NY, 1998] explore the (Q, r) inventory system with a specified cost per stockout occasion. However, a number of difficulties have impeded the implement of their solution procedure. That is, the total relevant cost function is not convex in general, so the convergence of the Silver et al.’s solution procedure to the optimal solution of the total relevant cost function is not necessarily true. An easier and more accurate solution procedure is proposed to overcome the shortcoming of the Silver et al.’s solution procedure.