Abstract
This paper studies a problem of determining the state of a system through costly tests of its components, where components can be tested simultaneously in batches to exploit economies of scale. This problem is a generalization of the classical sequential testing problem and it has applications in various settings, including machine maintenance, disease diagnosis, and new product development. We prove that the problem is strongly NP-hard, model it as a mixed-integer programming formulation, and we also propose a dynamic program for it. Additionally, we design a tabu search and a hybrid solution method that combines a tabu search metaheuristic and a proximity search matheuristic. Based on extensive computational experiments, we find that the dynamic program can solve instances with up to 25 components within a 15-minute time limit and 16 GB of RAM. With respect to larger instances, the proposed metaheuristic and hybrid method are better than a greedy heuristic.
Published Version
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