Abstract
Bender et al. (SPAA 2013) proposed a theoretical framework for testing in contexts where safety mistakes must be avoided. Testing in such a context is made by machines that need to be calibrated on a regular basis. Since calibrations have a non-negligible cost, it is important to study policies minimizing the total calibration cost while performing all the necessary tests. We focus on the single-machine setting, and we study the complexity status of different variants of the problem. First, we extend the model by considering that the jobs have arbitrary processing times, and we propose an optimal polynomial-time algorithm when the preemption of jobs is allowed. Then, we study the case where there are many types of calibrations with their corresponding lengths and costs. We prove that the problem becomes NP-hard for arbitrary processing times even when the preemption of the jobs is allowed. Finally, we focus on the case of unit processing time jobs, and we show that a more general problem, where the recalibration of the machine is not instantaneous, can be solved in polynomial time via dynamic programming.
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Notes
In the edf policy, at any time t, the available jobs are scheduled in order of non-decreasing deadlines.
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A preliminary version of this paper appeared in Proceedings of the 11th International Workshop on Frontiers in Algorithmics (FAW), LNCS 10336, Springer 2020, pp. 1-12(Angel et al. 2017). The second author is supported by the French ANR project ANR-18-CE25-0008. The third author is supported by national key research and development program of China under grant No. 2019YFB2102200, the NSFC No.12071460 and the CAS President’s International Fellowship Initiative No. 2020FYT0002, 2018PT0004. The fourth author is supported by the CAS President’s International Fellowship Initiative No 2019VTA0005 and the ALGONOW project of the THALES program and the Special Account for Research Grants of National and Kapodistrian University of Athens.
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Angel, E., Bampis, E., Chau, V. et al. Calibrations scheduling with arbitrary lengths and activation length. J Sched 24, 459–467 (2021). https://doi.org/10.1007/s10951-021-00688-5
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DOI: https://doi.org/10.1007/s10951-021-00688-5