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Sequential Inspection Under Capacity Constraints

Columbia University, New York, New York
Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong

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.

Subject classifications: dynamic programming; Markov-finite state; constrained Markov decision processes; probability; stochastic model applications; K-submodularity and threshold optimal policy; reliability; quality control; sequential inspection with capacity constraints.