A Nonlinear Optimization Problem for Determining Safety Stocks in a Two-Stage Manufacturing System

Abstract

Safety stock is the inventory which is used to buffer against the uncertainties in business operations. Managers must decide how much safety stock of each raw material and each finished product should be maintained. Determining appropriate safety stock levels is an important decision. Too much safety stock would incur extra inventory carrying costs, whereas too less safety stock would increase the risk of having product stockouts and lost sales. In this paper, a nonlinear programming problem for determining safety stock levels in a two-stage manufacturing system, was presented. Instead of using the well-known search algorithms, simple decision rules for determining safety stock levels were derived from an analysis of the derivatives of cost functions, with respect to the delivery performances of suppliers and prior manufacturing process. Two algorithms based on those decision rules were proposed and tested on seventy-five problem instances. The results showed that the proposed algorithms provided, within 1 second, the solutions with less than 3% deviations, on average, from the known integer solutions or the best lower bounds. The algorithms also performed better than the pattern search algorithm, which was the method applied in the previous research.