An important issue in the management of supply chains and manufacturing systems is to control inventory costs at different locations throughout the system while satisfying an end-customer service-level requirement. The challenge involved is to solve a nonlinear constrained optimization problem that captures the key dynamics of a complex production-inventory system. In this paper, we first develop a multistage inventory-queue model and a job-queue decomposition approach that evaluates the performance of serial manufacturing and supply systems with inventory control at every stage. We then present an efficient procedure to minimize the overall inventory in the system while meeting the required service level. Our technique is relatively simple and delivers accurate performance estimates. Furthermore, numerical studies generate certain managerial insights into related design and control issues.
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