Abstract
We study a new extension of the Sequential Testing problem with a modified cost structure that allows performing of some tests in batches. As in the Sequential Testing problem, we assume a certain dependence between the test results and the conclusion. Namely, we stop testing once a positive result is obtained or all tests are negative. Our extension, motivated by health care applications, considers a fixed cost associated with executing a batch of tests, with the general notion that the more tests are performed in batches, the smaller the total contribution of fixed costs to the sequential testing process. The goal is to minimize the expected cost of testing by finding the optimal choice and sequence of the batches available. The resulting NP-hard model is a variation of the set partitioning problem. We propose various heuristic algorithms for the effective solution of the problem and then demonstrate the performances of the algorithms through extensive numerical experiments.
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Acknowledgments
We would like to thank Hüsnü Yenigün and Uraz Cengiz Türker for helping us with the hardness proof.
Funding This study was funded by TUBITAK (The Scientific and Technological Research Council of Turkey) 1001 program grant number 113M478.
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The authors declare that they have no conflict of interest.
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We gratefully acknowledge the support provided by TUBITAK (The Scientific and Technological Research Council of Turkey) through 1001 program Grant Number 113M478.
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Daldal, R., Özlük, Ö., Selçuk, B. et al. Sequential testing in batches. Ann Oper Res 253, 97–116 (2017). https://doi.org/10.1007/s10479-016-2345-7
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DOI: https://doi.org/10.1007/s10479-016-2345-7