Abstract
In this paper, we investigate the problem of scheduling weighted jobs on a single machine with a maintenance whose starting time is prior to a given deadline and whose duration is a nondecreasing function of the starting time. We are asked not only to schedule the jobs but also the maintenance such that the total weighted job completion time is minimum. The problem is shown to be weakly NP-hard. In the case that the duration of the maintenance is a concave (and nondecreasing) function of its starting time, we provide two approximation algorithms with approximation ratio of 2 and at most \(1+\sqrt{2}/2+\epsilon\), respectively.
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Luo, W., Chen, L., Zhang, G. (2010). Approximation Algorithms for Scheduling with a Variable Machine Maintenance. In: Chen, B. (eds) Algorithmic Aspects in Information and Management. AAIM 2010. Lecture Notes in Computer Science, vol 6124. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14355-7_22
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DOI: https://doi.org/10.1007/978-3-642-14355-7_22
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