Sequencing of imperfect inspection operations subject to constraints on the quality of accepted and rejected units

Several imperfect inspection operations are available in a discrete production environment. A decision regarding acceptance or rejection of the produced items needs to be made without exceeding specified limits for the probabilities of accepted units being non-conforming and rejected units conforming to quality specifications. A branch and bound approach is used to find the inspection sequence resulting in least expected total inspection cost. Following the heuristic construction of a trial solution, a dominance relationship is applied to search the tree of possible sequences for the optimal sequence. A numerical example is included.