Skip to main content

Two-agent single-machine scheduling with position-dependent processing times

The International Journal of Advanced Manufacturing Technology volume 48, pages 325–331 (2010)Cite this article

Abstract

A new scheduling model in which both two-agent and position-dependent processing times exist simultaneously is considered in this paper. Two agents compete to perform their respective jobs on a common single machine, and each agent has his own criterion to optimize. The job position-dependent processing time is characterized by increasing or decreasing function dependent on the position of a job in the sequence. We introduce an aging effect and a learning effect into the two-agent single-machine scheduling, where the objective is to minimize the total completion time of the first agent with the restriction that the maximum cost of the second agent cannot exceed a given upper bound. We propose the optimal properties for the considered scheduling problems and then present the optimal polynomial time algorithms to solve the two scheduling problems, respectively.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

39,95 €

Price includes VAT (Finland)

References

  1. Agnetis A, Mirchandani PB, Pacciarelli D, Pacifici A (2004) Scheduling problems with two competing agents. Oper Res 52:229–242

    Article  MATH  MathSciNet  Google Scholar 

  2. Ng CT, Cheng TCE, Yuan JJ (2006) A note on the complexity of the problem of two-agent scheduling on a single machine. J Comb Optim 12:387–394

    Article  MATH  MathSciNet  Google Scholar 

  3. Cheng TCE, Ng CT, Yuan JJ (2006) Multi-agent scheduling on a single machine to minimize total weighted number of tardy jobs. Theor Comput Sci 362:273–281

    Article  MATH  MathSciNet  Google Scholar 

  4. Agnetis A, Pacciarelli D, Pacifici A (2007) Multi-agent single machine scheduling. Ann Oper Res 150:3–15

    Article  MATH  MathSciNet  Google Scholar 

  5. Cheng TCE, Ng CT, Yuan JJ (2008) Multi-agent scheduling on a single machine with max-form criteria. Eur J Oper Res 188:603–609

    Article  MATH  MathSciNet  Google Scholar 

  6. Baker KR, Smith JC (2003) A multiple-criterion model for machine scheduling. J Sched 6:7–16

    Article  MATH  MathSciNet  Google Scholar 

  7. Yuan JJ, Shang WP, Feng Q (2005) A note on the scheduling with two families of jobs. J Sched 8:537–542

    Article  MATH  MathSciNet  Google Scholar 

  8. Agnetis A, Pascale G, Pacciarelli D (2009) A Lagrangian approach to single-machine scheduling problems with two competing agents. J Sched 12:401–415

    Article  MATH  MathSciNet  Google Scholar 

  9. Liu P, Tang LX (2008) Two-agent scheduling with linear deteriorating jobs on a single machine. Lect Notes Comput Sci 5092:642–650

    Article  MathSciNet  Google Scholar 

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

    Article  MATH  Google Scholar 

  11. Mosheiov G (2001) Scheduling problems with a learning effect. Eur J Oper Res 132:687–693

    Article  MATH  MathSciNet  Google Scholar 

  12. Mosheiov G (2001) Parallel machine scheduling with a learning effect. J Oper Res Soc 52:1165–1169

    Article  MATH  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  14. Bachman A, Janiak A (2004) Scheduling jobs with position-dependent processing times. J Oper Res Soc 55:257–264

    Article  MATH  Google Scholar 

  15. Wang JB, Xia ZQ (2005) Flowshop scheduling with a learning effect. J Oper Res Soc 56:1325–1330

    Article  MATH  MathSciNet  Google Scholar 

  16. Wu CC, Lee WC, Wang WC (2007) A two-machine flowshop maximum tardiness scheduling problem with a learning effect. Int J Adv Manuf Tech 31:743–750

    Article  Google Scholar 

  17. Wu CC, Lee WC (2007) A note on single-machine scheduling with learning effect and an availability constraint. Int J Adv Manuf Tech 33:540–544

    Article  Google Scholar 

  18. Wang JB (2008) Single-machine scheduling with general learning functions. Comput Math Appl 56:1941–1947

    Article  MATH  MathSciNet  Google Scholar 

  19. Wang JB, Wang LY, Wang D, Wang XY, Guo WJ, Yin N (2009) Single machine scheduling problems with position-dependent processing times. J Appl Math Comput 30:293–304

    Article  MATH  MathSciNet  Google Scholar 

  20. Eren T, Guner E (2009) A bicriteria parallel machine scheduling with a learning effect. Int J Adv Manuf Tech 40:1202–1205

    Article  Google Scholar 

  21. Wang JB, Jiang Y, Wang G (2009) Single-machine scheduling with past-sequence-dependent setup times and effects of deterioration and learning. Int J Adv Manuf Tech 41:1221–1226

    Article  Google Scholar 

  22. Wang LY, Wang JB, Wang D, Yin N, Huang X, Feng EM (2009) Single-machine scheduling with a sum-of-processing-time-based learning effect and deteriorating jobs. Int J Adv Manuf Technol. doi:10.1007/s00170-009-1950-X

    Google Scholar 

  23. Badiru AB (1992) Computational survey of univariate and multivariate learning curve models. IEEE Trans Eng Manage 39:176–188

    Article  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  25. Mosheiov G (2005) A note on scheduling deteriorating jobs. Math Comput Model 41:883–886

    Article  MATH  MathSciNet  Google Scholar 

  26. Zhao CL, Tang HY (2007) Single-machine scheduling problems with an aging effect. J Appl Math Comput 25:305–314

    Article  MATH  MathSciNet  Google Scholar 

  27. Kuo WH, Yang DL (2008) Minimizing the makespan in a single-machine scheduling problem with the cyclic process of an aging effect. J Oper Res Soc 59:416–420

    Article  MATH  Google Scholar 

  28. Chang PC, Chen SH, Mani V (2009) A note on due-date assignment and single machine scheduling with a learning/aging effect. Int J Prod Econ 117:142–149

    Article  Google Scholar 

  29. Graham RL, Lawler EL, Lenstra JK, Rinnooy Kan AHG (1979) Optimization and approximation in deterministic sequencing and scheduling theory: a survey. Ann Discrete Math 5:287–326

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Management, Shenyang University of Technology, Shenyang, 110178, China

    Peng Liu & Xiaoye Zhou

  2. Liaoning Key Laboratory of Manufacturing System and Logistics, The Logistics Institute, Northeastern University, Shenyang, 110004, China

    Lixin Tang

Authors
  1. Peng Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiaoye Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lixin Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Peng Liu.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Liu, P., Zhou, X. & Tang, L. Two-agent single-machine scheduling with position-dependent processing times. Int J Adv Manuf Technol 48, 325–331 (2010). https://doi.org/10.1007/s00170-009-2259-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-009-2259-5

Keywords

  • Scheduling
  • Two-agent
  • Position-dependent processing times
  • Aging effect
  • Learning effect
  • Single machine