Abstract
We study single machine scheduling problems with general truncated sum-of-actual-processing-time-based learning effect. In the general truncated learning model, the actual processing time of a job is affected by the sum of actual processing times of previous jobs and by a job-dependent truncation parameter. We show that the single machine problems to minimize makespan and to minimize the sum of weighted completion times are both at least ordinary NP-hard and the single machine problem to minimize maximum lateness is strongly NP-hard. We then show polynomial solvable cases and approximation algorithms for these problems. Computational experiments are also conducted to show the effectiveness of our approximation algorithms.
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References
Agnetis A, Billaut JC, Gawiejnowicz S et al (2014) Multiagent scheduling. Springer, Berlin
Bachman A, Janiak A (2004) Scheduling jobs with position-dependent processing time. J Oper Res Soc 55:257–264
Biskup D (2008) A state-of-the-art review on scheduling with learning effects. Eur J Oper Res 188:315–329
Cheng TCE, Ding Q, Lin BMT (2004) A concise survey of scheduling with time-dependent processing time. Eur J Oper Res 152:1–13
Cheng TCE, Cheng SR, Wu WH, Hsu PH, Wu CC (2011) A two-agent single-machine scheduling problem with truncated sum-of-processing-times-based learning considerations. Comput Ind Eng 60(4):534–541
Cheng TCE, Wu CC, Chen JC, Wu WH, Cheng SR (2013) Two-machine flowshop scheduling with a truncated learning function to minimize the makespan. Int J Prod Econ 141(1):79–86
Garey MR, Johnson DS (1979) Computers and intractability: a guide to the theory of np-completeness. Freeman, San Francisco
Gawiejnowicz S (2008) Time-dependent scheduling. Springer, Berlin, p 390
He H, Liu M, Wang JB (2017) Resource constrained scheduling with general truncated job-dependent learning effect. J Comb Optim 33(2):626–644
Jiang Z, Chen F, Kang H (2013) Single-machine scheduling problem with actual time-dependent and job-dependent learning effect. Eur J Oper Res 227(1):76–80
Kuo WH, Yang DL (2006) Minimizing the total completion time in a single-machine scheduling problem with a time-dependent learning effect. Eur J Oper Res 174:1184–1190
Li DC, Hsu PH, Wu CC (2011) Two-machine flowshop scheduling with truncated learning to minimize the total completion time. Comput Ind Eng 61(3):655–662
Li L, Yang SW, Wu YB (2013) Single machine scheduling jobs with a truncated sum-of-processing-times-based learning effect. Int J Adv Manuf Technol 67(1–4):261–267
Strusevich VA, Rustogi K (2017) Scheduling with time-changing effects and rate-modifying activities. Springer, Cham
Wang XY, Zhou Z, Zhang X (2013a) Several flow shop scheduling problems with truncated position-based learning effect. Comput Oper Res 40(12):2906–2929
Wang JB, Wang XY, Sun LH (2013b) Scheduling jobs with truncated exponential learning functions. Optim Lett 7(8):1857–1873
Wang XR, Wang JB, Jin J (2014) Single machine scheduling with truncated job-dependent learning effect. Optim Lett 8(2):669–677
Wu CC, Yin Y, Cheng SR (2011) Some single-machine scheduling problems with a truncation learning effect. Comput Ind Eng 60(4):790–795
Wu CC, Yin Y, Wu WH, Cheng SR (2012) Some polynomial solvable single-machine scheduling problems with a truncation sum-of-processing-times based learning effect. Eur J Ind Eng 6(4):441–453
Wu CC, Yin Y, Cheng SR (2013) Single-machine and two-machine flowshop scheduling problems with truncated position-based learning functions. J Oper Res Soc 64(1):147–156
Wu CC, Wu WH, Wu WH, Hsu PH, Yin Y, Xu J (2014) A single-machine scheduling with a truncated linear deterioration and ready times. Inf Sci 256(2):109–125
Yang DL, Kuo WH (2007) Single-machine scheduling with an actual time-dependent learning effect. J Oper Res Soc 58:1348–1353
Zhang X, Lin WC, Hsu CJ, Wu CC (2017) Resource constrained scheduling problems with general truncated sum-of-processing time dependent effect under single machine and unrelated parallel machines. Comput Ind Eng 110(1):344–352
Acknowledgements
This work is supported in part by the National Natural Science Foundation of China (Grant Nos. 71971065, 71531005 and 71222104) and a Shuang-Yi-Liu Grant to Department of Management Science, Fudan University, and by Jiangsu Engineering Research Center of Digital Twinning Technology for Key Equipment in Petrochemical Process (DT2020720). The authors are very grateful for the anonymous reviewers for their valuable comments which improve the quality of the paper considerably.
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Jiang, Z., Chen, F. & Zhang, X. Single-machine scheduling problems with general truncated sum-of-actual-processing-time-based learning effect. J Comb Optim 43, 116–139 (2022). https://doi.org/10.1007/s10878-021-00752-y
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DOI: https://doi.org/10.1007/s10878-021-00752-y