Coordinated quality control in a two-stage system

The authors study a quality control problem in a two-stage system. They ass ume that at each stage units are processed in batches, and the rates are ra ndom variables with known distributions. Final products are supplied to cus tomers under warranties or service contracts, with penalty costs associated with defective units. The focus is on coordinating the inspection procedur es at the two stages. Using a stochastic dynamic programming approach, the authors show that the optimal policy at stage 1 is characterized by a seque nce of thresholds, and at stage 2, by a priority structure, as well as a th reshold structure. The key to optimality is a so-called K-submodularity pro perty, which is a strengthening of the usual notion of submodularity.