Computing Optimal Stock Levels for Common Components in an Assembly System

Managing component inventories eeectively in assembly systems with several products that share many common components can lead to improved customer service. We consider a two-level, nite-horizon assembly problem with multiple end-products that have random demands and share several common components. The objective is to minimize the total cost which comprises of holding excess components and paying a penalty on backlogged demand of the end-products. We model this problem as a multi-period stochastic program. We show that it can be decomposed into a set of nested stochastic programs, each similar in structure to a one-period problem. We show that the problem is convex. We develop a simulation-based method for estimating the derivatives of costs with respect to component stock levels. These derivative estimates are then used in an optimization procedure to obtain optimal values. Our estimation algorithm takes advantage of special structure in the imbedded linear programs. Experiments suggest that our algorithm converges to good values on industrial size problems in reasonable time. Extensions to compute derivatives with respect to demand parameters, executing our algorithm in a rolling horizon, solving an innnite horizon stationary problem and taking advantage of special demand structures are also discussed.