Sequential inspection under capacity constraints

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