Abstract
We study a parallel-machine scheduling problem in which job rejection is allowed and the actual processing time of a job depends on the sum of certain parameters associated with the jobs scheduled earlier. The goal is to minimize the sum of the makespan of the accepted jobs and total rejection penalty of the rejected jobs. When the number of machines is fixed, we develop an exact dynamic programming algorithm and a fully polynomial-time approximation scheme for solving it. When the number of machines is restricted to one, we reformulate the problem as a variant of a half-product problem, which allows us to design a fully polynomial-time approximation scheme with the best possible running time.
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Acknowledgements
The authors would like to thank two anonymous reviewers for their helpful and detailed comments. This research was supported in part by the National Natural Science Foundation of China under Grant Nos. (11501279 and 11701595) and the Young Backbone Teachers training program of Zhongyuan University of Technology.
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Li, SS., Chen, RX., Feng, Q. et al. Parallel-machine scheduling with job-dependent cumulative deterioration effect and rejection. J Comb Optim 38, 957–971 (2019). https://doi.org/10.1007/s10878-019-00429-7
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DOI: https://doi.org/10.1007/s10878-019-00429-7