Advertisement

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

  • Peng LiuEmail author
  • Xiaoye Zhou
  • Lixin Tang
ORIGINAL 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.

Keywords

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Agnetis A, Mirchandani PB, Pacciarelli D, Pacifici A (2004) Scheduling problems with two competing agents. Oper Res 52:229–242zbMATHCrossRefMathSciNetGoogle Scholar
  2. 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 12:387–394zbMATHCrossRefMathSciNetGoogle Scholar
  3. 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 362:273–281zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Agnetis A, Pacciarelli D, Pacifici A (2007) Multi-agent single machine scheduling. Ann Oper Res 150:3–15zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Cheng TCE, Ng CT, Yuan JJ (2008) Multi-agent scheduling on a single machine with max-form criteria. Eur J Oper Res 188:603–609zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Baker KR, Smith JC (2003) A multiple-criterion model for machine scheduling. J Sched 6:7–16zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Yuan JJ, Shang WP, Feng Q (2005) A note on the scheduling with two families of jobs. J Sched 8:537–542zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Agnetis A, Pascale G, Pacciarelli D (2009) A Lagrangian approach to single-machine scheduling problems with two competing agents. J Sched 12:401–415zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Liu P, Tang LX (2008) Two-agent scheduling with linear deteriorating jobs on a single machine. Lect Notes Comput Sci 5092:642–650CrossRefMathSciNetGoogle Scholar
  10. 10.
    Biskup D (1999) Single-machine scheduling with learning considerations. Eur J Oper Res 115:173–178zbMATHCrossRefGoogle Scholar
  11. 11.
    Mosheiov G (2001) Scheduling problems with a learning effect. Eur J Oper Res 132:687–693zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Mosheiov G (2001) Parallel machine scheduling with a learning effect. J Oper Res Soc 52:1165–1169zbMATHCrossRefGoogle Scholar
  13. 13.
    Cheng TCE, Wang G (2000) Single machine scheduling with learning effect considerations. Ann Oper Res 98:273–290zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Bachman A, Janiak A (2004) Scheduling jobs with position-dependent processing times. J Oper Res Soc 55:257–264zbMATHCrossRefGoogle Scholar
  15. 15.
    Wang JB, Xia ZQ (2005) Flowshop scheduling with a learning effect. J Oper Res Soc 56:1325–1330zbMATHCrossRefMathSciNetGoogle Scholar
  16. 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 31:743–750CrossRefGoogle Scholar
  17. 17.
    Wu CC, Lee WC (2007) A note on single-machine scheduling with learning effect and an availability constraint. Int J Adv Manuf Tech 33:540–544CrossRefGoogle Scholar
  18. 18.
    Wang JB (2008) Single-machine scheduling with general learning functions. Comput Math Appl 56:1941–1947zbMATHCrossRefMathSciNetGoogle Scholar
  19. 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 30:293–304zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Eren T, Guner E (2009) A bicriteria parallel machine scheduling with a learning effect. Int J Adv Manuf Tech 40:1202–1205CrossRefGoogle Scholar
  21. 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 41:1221–1226CrossRefGoogle Scholar
  22. 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. 23.
    Badiru AB (1992) Computational survey of univariate and multivariate learning curve models. IEEE Trans Eng Manage 39:176–188CrossRefGoogle Scholar
  24. 24.
    Biskup D (2008) A state-of-the-art review on scheduling with learning effects. Eur J Oper Res 188:315–329zbMATHCrossRefMathSciNetGoogle Scholar
  25. 25.
    Mosheiov G (2005) A note on scheduling deteriorating jobs. Math Comput Model 41:883–886zbMATHCrossRefMathSciNetGoogle Scholar
  26. 26.
    Zhao CL, Tang HY (2007) Single-machine scheduling problems with an aging effect. J Appl Math Comput 25:305–314zbMATHCrossRefMathSciNetGoogle Scholar
  27. 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 59:416–420zbMATHCrossRefGoogle Scholar
  28. 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 117:142–149CrossRefGoogle Scholar
  29. 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 5:287–326zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2009

Authors and Affiliations

  1. 1.School of ManagementShenyang University of TechnologyShenyangChina
  2. 2.Liaoning Key Laboratory of Manufacturing System and Logistics, The Logistics InstituteNortheastern UniversityShenyangChina

Personalised recommendations