Skip to main content
SpringerLink
Log in

Single-machine scheduling problems with a learning effect matrix

  • Research Paper
  • Published:
Iranian Journal of Science and Technology, Transactions A: Science Aims and scope Submit manuscript

Abstract

Scheduling problems with learning effects have been widely studied in numerous publication. However, the learning effect might accelerate, especially in the steel plates and the human interaction systems. In this paper, we propose a new scheduling model with a learning effect matrix. We show that the makespan and the total completion time problems can be optimally solved in polynomial time. We present heuristic sequencing rules and analyze the worst-case bounds for performance ratios to minimize the total weighted completion time, the maximum lateness, and the total tardiness. We also show that these heuristic rules can be optimal under some agreeable conditions between the normal processing times and job due dates or weights.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Bai J, Wang MZ, Wang JB (2012) Single machine scheduling with a general exponential learning effect. Appl Math Model 36:829–835

  • Biskup D (1999) Single-machines scheduling with learning considerations. Eur J Oper Res 115:173–178

    Article  MATH  Google Scholar 

  • Biskup D (2008) A state-of-the-art review on scheduling with learning effects. Eur J Oper Res 188:315–329

    Article  MathSciNet  MATH  Google Scholar 

  • Cheng TCE, Lai PJ, Wu CC, Lee WC (2009) Single-machine scheduling with sum-of-logarithm-processing-times-based learning considerations. Inf Sci 179:3127–3135

    Article  MathSciNet  MATH  Google Scholar 

  • Cheng TCE, Wang G (2000) Single machine scheduling with learning effect considerations. Ann Oper Res 98:273–290

    Article  MathSciNet  MATH  Google Scholar 

  • Cheng TCE, Kuo WH, Yang DL (2014) Scheduling with a position-weighted learning effect. Optim Lett 8(1):293–306

    Article  MathSciNet  MATH  Google Scholar 

  • Cheng TCE, Wu CC, Lee WC (2008) Some scheduling problems with sum-of-processing-times-based and job-position-based learning effects. Inf Sci 178:2476–2487

    Article  MathSciNet  MATH  Google Scholar 

  • 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

    Article  MathSciNet  MATH  Google Scholar 

  • Koulamas C, Kyparisis GJ (2007) Single-machine and two-machine flowshop scheduling with general learning functions. Eur J Oper Res 178:402C407

    Article  MathSciNet  MATH  Google Scholar 

  • Lai PJ, Lee WC (2011) Single-machine scheduling with general sum-of-processing-time-based and position-based learning effects. Omega Int J Manag Sci 39:467–471

    Article  Google Scholar 

  • Lee WC, Wu CC (2008) Single-machine group scheduling problems with deteriorating setup times and job-processing times. Int J Prod Econ 115:128–133

    Article  Google Scholar 

  • Li L, Yang SW, Wu YB, Huo YZ, Ji P (2013) Single machine scheduling jobs with a truncated sum-of-processing-times-based learning effect. Int J Adv Manuf Technol 67:261–267

    Article  Google Scholar 

  • Low CY, Lin WY (2012) Single machine group scheduling with learning effects and past-sequence-dependent setup times. Int J Syst Sci 43:1–8

    Article  MathSciNet  MATH  Google Scholar 

  • Lu YY, Wang JB (2013) Some single-machine scheduling with sum-of-processing-time-based and job-position-based processing times. Appl Math Model 37:6695–6702

    Article  MathSciNet  Google Scholar 

  • Lu YY, Wang JJ, Huang X (2015) Scheduling jobs with position and sum-of-processing-time based processing times. Appl Math Model 39:4013–4021

    Article  MathSciNet  Google Scholar 

  • Luo KP (2015) A scheduling model with a more general function of learning effects. Comput Ind Eng 82:159–166

    Article  Google Scholar 

  • Ma HF, Shao C, Wang XR (2014) Single machine scheduling with exponential learning functions. Optim Lett 4(8):1273–1285

    Article  MathSciNet  MATH  Google Scholar 

  • Mosheiov G, Sidney JB (2005) Note on scheduling with general learning curves to minimize the number of tardy jobs. J Oper Res Soc 56:110–112

    Article  MATH  Google Scholar 

  • Soroush HM (2015) Scheduling with job-dependent past-sequence-dependent setup times and job-dependent position-based learning effects on a single processor. Eur J Ind Eng 9(3):277–307

    Article  Google Scholar 

  • Vahedi-Nouri B, Fattahi P, Rohaninejad M, Tavakkoli-Moghaddam R (2013) Minimizing the total completion time on a single machine with the learning effect and multiple availability constraints. Appl Math Model 37:3126–3137

    Article  MathSciNet  MATH  Google Scholar 

  • Wang JB, Wang XY, Sun LH, Sun LY (2013) Scheduling jobs with truncated exponential learning functions. Optim Lett 8(7):1857–1873

    Article  MathSciNet  MATH  Google Scholar 

  • Wang JJ, Wang JB, Wang XP (2010) Scheduling problems with exponential learning functions. Int J Innov Comput Inf Control 6:3256–3274

    Google Scholar 

  • Wang JB, Wang MZ (2011) Worst-case behavior of simple sequencing rules in flow shop scheduling with general position-dependent learning effects. Ann Oper Res 191:155–169

    Article  MathSciNet  MATH  Google Scholar 

  • Wang XR, Wang JB, Jin J, Ji P (2014) Single machine scheduling with truncated job-dependent learning effect. Optim Lett 8:669–677

    Article  MathSciNet  MATH  Google Scholar 

  • Wu CC, Yin Y, Cheng SR (2011) Some single-machine scheduling problems with a truncation learning effect. Compt Ind Eng 60:790–795

    Article  Google Scholar 

  • Wright TP (1936) Factors affceting the cost of airplans. J Aeronaut Sci 3:122–128

    Article  Google Scholar 

  • Wu CC, Lee WC (2008) Single-machine scheduling problems with a learning effect. Appl Math Model 32:1191–1197

    Article  MathSciNet  MATH  Google Scholar 

  • Yin Y, Xu D, Sun K, Li H (2009) Some scheduling problems with general position-dependent and time-dependent learning effects. Inf Sci 179:2416–2425

    Article  MathSciNet  MATH  Google Scholar 

  • Yin Y, Wu CC, Wu WH, Chen JC (2013) Single-machine group scheduling with a general learning effect. Eur J Ind Eng 7(3):350–369

    Article  Google Scholar 

  • Zhang XG, Yan GL, Huang WZ, Tang GC (2011) Single-machine scheduling problems with time and position dependent processing times. Ann Oper Res 186:345–356

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

We thank the editors and two anonymous referees for their helpful comments on the earlier version of our paper. This work was supported by National Natural Science Foundation of China (11401065, 71371120, 61302180), the China Postdoctoral Science Foundation funded project (2013M540698, 2014T70854), the Foundation of Chongqing Education Commission (KJ130606) and The Chongqing Municipal Science and Technology Commission of Natural Science Fund Projects (cstc2014jcyjA00003). This paper was supported in part by the Ministry of Science Technology (MOST) of Taiwan under Grant Numbers MOST 105-2221- E-035-053-MY3, MOST 103-2410-H-035-022-MY2, and MOST 105-2816-H-035-001.

Author information

Authors and Affiliations

  1. College of Mathematics Science, Chongqing Normal University, Chongqing, 401331, China

    Xingong Zhang

  2. Department of Business Administration, Fu Jen Catholic University, New Taipei City, Taiwan

    Shang-Chia Liu

  3. Faculty of Science, Kunming University of Science and Technology, Kunming, 650093, China

    Yunqiang Yin

  4. Department of Statistics, Feng Chia University, Taichung, Taiwan

    Chin-Chia Wu

Authors
  1. Xingong Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shang-Chia Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yunqiang Yin
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Chin-Chia Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chin-Chia Wu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, X., Liu, SC., Yin, Y. et al. Single-machine scheduling problems with a learning effect matrix. Iran J Sci Technol Trans Sci 42, 1327–1335 (2018). https://doi.org/10.1007/s40995-016-0080-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40995-016-0080-1

Keywords

Search

Navigation