Sequential inspection under capacity constraints

We study the inspection process in the context of multistage batch manufacturing, focusing on interstage coordination under capacity limits. The problem is formulated as a constrained Markov decision program. We establish the optimality of a sequential policy that is characterized by a sequence of thresholds, with certain randomization at the thresholds. We further show that such an optimal policy can be completely derived through solving a linear program, and that randomization is needed at no more than two threshold values. We discuss an application in semiconductor wafer fabrication, which motivates our study.