Optimal dispatching in a periodic review cellular manufacturing system

We examine a periodically reviewed cellular manufacturing system where parts are dispatched from a central control station to n manufacturing cells. After being processed at a cell, parts are routed back to the control station for inspection. An inspection failure will result in a feedback job order. Optimal dispatching policies are pursued to minimize the expected in-process inventory costs over a finite horizon. A dynamic programming formulation is developed for optimal dispatching. We show that the dynamic recursive functions (i.e., cost-to-go functions) are convex and monotonic under the condition of low defect rates and relative low cost material handling. From the convex and monotonic properties, it is shown that optimal dispatching calls for a combination of zero-inventory and nonzero-inventory policies. The optimal input control is proved to be in the form of a pulling system.