Abstract
In a recent paper (He et al. in J Comb Optim 33(2):626–644, 2017), the authors considered single machine resource allocation scheduling with general truncated job-dependent learning effect. For the convex resource consumption function and limited resource cost, the problem is to minimize the weighted sum of makespan, total completion time, the total absolute deviation in completion time and resource consumption cost. They conjectured that this problem is NP-hard. In this note we show that this problem can be solved in \(O(n^3)\) time. It is also shown that Lemma 4 in He et al. (2017) is incorrect by a counter-example.
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References
Adamopoulos GI, Pappis CP (1996) Single machine scheduling with flow allowances. J Oper Res Soc 47:1280–1285
Azzouz A, Ennigrou M, Said LB (2017) Scheduling problems under learning effects: classification and cartography. Int J Prod Res 56(3):1–20
Biskup D (2008) A state-of-the-art review on scheduling with learning effects. Eur J Oper Res 188:315–329
Graham RL, Lawler EL, Lenstra JK, Rinnooy Kan AHG (1979) Optimization and approximation in deterministic sequencing and scheduling: a survey. Ann Discrete Math 5:287–326
Geng X-N, Wang J-B, Bai D (2019) Common due date assignment scheduling for a no-wait flowshop with convex resource allocation and learning effect. Eng Optim 51(8):1301–1323
He H-Y, Liu M, Wang J-B (2017) Resource constrained scheduling with general truncated job-dependent learning effect. J Comb Optim 33(2):626–644
Panwalker SS, Smith ML, Seidmann A (1982) Common due-date assignment to minimize total penalty for the one machine scheduling problem. Oper Res 30:391–399
Papadimitriou CH, Steiglitz K (1982) Combinatorial optimization: algorithms and complexity. Prentice-Hall, Englewood Cliffs
Seidmann A, Panwalkar SS, Smith ML (1981) Optimal assignment of due dates for a single processor scheduling problem. Int J Prod Res 19:393–399
Shabtay D, Steiner G (2007) A survey of scheduling with controllable processing times. Discrete Appl Math 155(13):1643–1666
Acknowledgements
We thank the two anonymous referees for their helpful comments on earlier version of the article. This work is supported by the National Social Science Foundation under Grant 17BTY049.
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Zou, D., Jiang, C. & Liu, W. Note on the time complexity of resource constrained scheduling with general truncated job-dependent learning effect. J Comb Optim 40, 861–868 (2020). https://doi.org/10.1007/s10878-020-00628-7
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DOI: https://doi.org/10.1007/s10878-020-00628-7