A simple approximation for a multistage capacitated production-inventory system

The authors develop a simple approximation for multistage production-inventory systems with limited production capacity and variable demands. Each production stage follows a base-stock policy for echelon inventory, constrained by production capacity and the availability of upstream inventory. The objective is to find base-stock levels that approximately minimize holding and backorder costs. The key step in the present procedure approximates the distribution of echelon inventory by a sum of exponentials; the parameters of the exponentials are chosen to match asymptotically exact expressions. The computational requirements of the method are minimal. In a test bed of 72 problems, each with five production stages, the average relative error for the present approximate optimization procedure is 1.9%.