Abstract
We study the scheduling problem with calibrations. We are given a set of n jobs that need to be scheduled on a set of m machines. However, a machine can schedule jobs only if a calibration has been performed beforehand and the machine is considered as valid during a fixed time period of T, after which it must be recalibrated before running more jobs. In this paper, we investigate the batch calibrations, calibrations occur in batch and at the same moment. It is then not possible to perform any calibrations during a period of T. We consider different cost function depending on the number of machines we calibrate at a given time. Moreover, jobs have release time, deadline and unit processing time. The objective is to schedule all jobs with the minimum cost of calibrations. We give a dynamic programming to solve the case with arbitrary cost function. Then, we propose several faster approximation algorithm for different cost function.
Vincent Chau is supported by Shenzhen research grants (KQJSCX 20180330170311901, JCYJ20180305180840138 and GGFW2017073114031767), NSFC (No. 61433012), Hong Kong GRF 17210017 and Shenzhen Discipline Construction Project for Urban Computing and Data Intelligence. Minming Li and Ruilong Zhang are supported by a grant from Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CityU 11268616). Yingchao Zhao is supported by Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. UGC/FDS11/E03/16).
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Chau, V., Li, M., Wang, Y., Zhang, R., Zhao, Y. (2019). Minimizing the Cost of Batch Calibrations. In: Du, DZ., Duan, Z., Tian, C. (eds) Computing and Combinatorics. COCOON 2019. Lecture Notes in Computer Science(), vol 11653. Springer, Cham. https://doi.org/10.1007/978-3-030-26176-4_7
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