Abstract
Tang et al. (Eur J Oper Res 263:401–411, 2017) have recently introduced a parallel-batching machine scheduling problem with linearly deteriorating jobs of two agents and presented a computational complexity classification of various special cases of this problem, including a number of NP-hardness proofs. We refine these results by demonstrating strong NP-hardness of several special cases, which are proved NP-hard in the ordinary sense in Tang et al. (Eur J Oper Res 263:401–411, 2017). Our reduction employs the problem studied in the first issue of Journal of Scheduling.
References
Brucker, P., Gladky, A., Hoogeveen, H., Kovalyov, M. Y., Potts, C. N., Tautenhahn, T., et al. (1998). Scheduling a batching machine. Journal of Scheduling, 1, 31–54.
Garey, M. R., & Johnson, D. S. (1979). Computers and intractability: A guide to the theory of NP-completeness. San Francisco, CA: W.H. Freeman and Co.
Li, S. S., Ng, C. T., Cheng, T. C. E., & Yuan, J. J. (2011). Parallel-batch scheduling of deteriorating jobs with release dates to minimize the makespan. European Journal of Operational Research, 210, 482–488.
Tang, L., Zhao, X., Liu, J., & Leung, J. Y.-T. (2017). Competitive two-agent scheduling with deteriorating jobs on a single parallel-batching machine. European Journal of Operational Research, 263, 401–411.
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Kovalyov, M.Y., Šešok, D. Two-agent scheduling with deteriorating jobs on a single parallel-batching machine: refining computational complexity. J Sched 22, 603–606 (2019). https://doi.org/10.1007/s10951-019-00613-x
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DOI: https://doi.org/10.1007/s10951-019-00613-x