Sequencing counts: A combined approach for sequencing and selecting costly unreliable off-line inspections

We study the case of ‘‘inspect-all’’ policy, using off-line quality inspections to prevent non-conforming items from reaching the final consumer, in domains where an item is rejected upon first ‘‘failure’’ classification. Given a set of inspections with known inspection costs and error probabilities of two types (classifying conforming items as non-conforming and vice versa), the goal is to find a sequenced subset of inspections that maximizes the expected overall profit, taking into account the revenue from delivering conforming items, the penalty of delivering non-conforming ones, and the overall cost of the inspections used. Our model allows an additional degree of freedom, in comparison to prior work in this domain, enabling the selection of inspections sequence along the selection of which inspections to use. We present an efficient branch and bound algorithm for finding the optimal solution, and two types of heuristics: greedy-based and preliminary sort-based, differing in their accuracy and calculation time. The optimal and heuristic methods are extensively evaluated, using a factorial experimental design that includes 65 610 problem instances. For each instance we compared the methods performance in terms of reaching optimality, deviation from the optimal solution and calculation-time. The results reflect a substantial influence of the sequence over the expected profit. An interesting finding is that the suggested preliminary sort-based heuristics achieve a relatively accurate solution in a reasonable calculation-time and outperform the commonly used greedy-based heuristics. The usefulness of the different methods is illustrated using sample problems from the biometric inspection security domain. & 2011 Elsevier Ltd. All rights reserved.