Inspection configuration and reprocessing decisions in serial production systems

In this paper we provide an integrated framework to consider manufacturing, inspection and reprocessing activities simultaneously in serial production systems. This model incorporates systematic treatment of time: time for processing and inspection, time for setups, time between consecutive production cycles, and in-process inventory holding times. The determination of optimal initial lot size, inspection configuration and reprocessing decisions is considered. Explicit analytical expressions for the component costs are developed, and the criterion is the minimization of the total cost. The total cost consists of component costs attributable to setup, WIP inventory, in-process inventory of rejects, inspection, manufacturing and reprocessing. Two distinct problems are considered. In the first problem, the number of production cycles and the initial lot size are fixed. In the second problem, the production target is fixed. A variant of the shortest path algorithm is developed to provide solutions. The algorithm is an extension of the traditional shortest path algorithm when the arc lengths are not known a priori but are determined as the algorithm progresses. The method is illustrated through numerical examples.