Input control for serial production lines consisting of processing and assembly operations with random yields

This paper deals with a serial production line where each of the stages can be either a processing or an assembly stage. A processing stage processes outputs from an upstream stage and transforms them into inputs for the downstream stage. Each processing stage is subject to yield losses. At an assembly stage, a batch of identical input components is processed and the nondefective components are then combined with the output from the upstream stage. The processing operation for the input component is imperfect. For such a system, we characterize the form of the optimal policy for input quality at each stage in the production line, when stochastically proportional yield is assumed at each stage, i.e., the distribution of the yield fraction is assumed to be independent of the lot size. The optimal policy exhibits same form of a critical number policy. For production lines consisting of assembly stages only, the critical numbers can be computed easily. When yields are of the ‘exponential’ type, the critical number policy is still optimal, although there are interesting differences in the policies for the different types of yield characterizations.