Economic optimization in a fixed sequence of unreliable inspections

Given a fixed sequence of unreliable inspection operations with known costs and inspection error probabilities of two types (classifying good items as defective and vice versa), we develop a model for selecting the set of inspections that should be activated in order to minimize expected total costs (inspection and penalties). We present an efficient branch and bound algorithm for finding the optimal solution, and two variations of a greedy heuristic that can be applied jointly to provide very good solutions at a O(n²) computational complexity. The conclusions are backed by a factorial experiment that included 1440 problem instances.