Dispatching rules for unrelated parallel machine scheduling with release dates

ORIGINAL ARTICLE

Abstract

In this research, we consider the problem of scheduling n jobs on m unrelated parallel machines with release dates to minimize makespan, total weighted completion time, and total weighted tardiness, individually. The problem is NP-hard in the strong sense. We develop several mixed integer programming models for these scheduling problems to find the optimal solutions for small problem instances. We also propose several dispatching rules to find good solutions quickly for large problem instances. We compare our proposed dispatching rules with other existing dispatching rules. Computational results show that the proposed dispatching rules outperform other existing dispatching rules for problem instances of all sizes.

Keywords Scheduling Unrelated parallel machines Release date Dispatching rule 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Graham RL, Lawler EL, Lenstra JK, Rinnooy Kan AHG (1979) Optimization and approximation in deterministic sequencing and scheduling: a survey. Annals of Discrete Mathematics 5:287–326MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Li CL (1995) A heuristic for parallel machine scheduling with agreeable due dates to minimize the number of late jobs. Comput Oper Res 22:277–283MATHCrossRefGoogle Scholar
  3. 3.
    Chen B, Vestjens APA (1997) Scheduling on identical machines: how good is LPT in an on-line setting? Oper Res Lett 21:165–169MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Kellerer H (1998) Algorithms for multiprocessor scheduling with machine release times. IIE Trans 30(11):991–999Google Scholar
  5. 5.
    Lancia G (2000) Scheduling jobs with release dates and tails on two unrelated parallel machines to minimize the makespan. Eur J Oper Res 120(2):277–288MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Sevaux M, Thomin P (2001) Heuristics and metaheuristics for a parallel machine scheduling problem: a computational evaluation. In: Proceedings of the 4th metaheuristics international conference (MIC 2001), Porto, Portugal, 411–415.Google Scholar
  7. 7.
    Afrati F, Bampis E, Chekuri C, Karger D, Kenyon C, Khanna S, Milis I, Queyranne M, Skutella M, Stein C, Sviridenko M (1999) Approximation schemes for minimizing average weighted completion time with release dates. In Proceedings of the 40th Annual IEEE Symposium on Foundations of Computer Science. IEEE Computer Society, Los Alamitos, CA., 32– 43Google Scholar
  8. 8.
    Bank J, Werner F (2001) Heuristic algorithms for unrelated parallel machine scheduling with a common due date, release dates, and linear earliness and tardiness penalties. Math Comput Modell 33(4–5):363–383MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Carlier J, Pinson E (2004) Jackson's pseudo-preemptive schedule and cumulative scheduling problems. Discret Appl Math 145(1):80–94MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Chou MC, Queyranne M, Simchi-Levi D (2006) The asymptotic performance ratio of an on-line algorithm for uniform parallel machine scheduling with release dates. J Math Program: Series A and B Arch 106(1):137–157MathSciNetMATHCrossRefGoogle Scholar
  11. 11.
    Mönch L, Balasubramanian H, Fowler JW, Pfund ME (2005) Heuristic scheduling of jobs on parallel batch machines with incompatible job families and unequal ready times. Comput Oper Res 32:2731–2750MATHCrossRefGoogle Scholar
  12. 12.
    Mönch L, Zimmermann J, Otto P (2006) Machine learning techniques for scheduling jobs with incompatible families and unequal ready times on parallel batch machines. Eng Appl Artif Intell 19(3):235–245CrossRefGoogle Scholar
  13. 13.
    Nessah R, Yalaoui F, Chu C (2008) A branch-and-bound algorithm to minimize total weighted completion time on identical parallel machines with job release dates. Comput Oper Res 35(4):1176–1190MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    Brucker P, Kravchenko SA (2008) Scheduling jobs with equal processing times and time windows on identical parallel machines. J Sched 11(4):229–237MathSciNetMATHCrossRefGoogle Scholar
  15. 15.
    Wu Y, Ji P (2009) A scheduling problem for PCB assembly: a case with multiple lines. Int J Adv Manuf Technol 43:1189–1201CrossRefGoogle Scholar
  16. 16.
    Damodaran P, Velez-Gallego MC (2010) Heuristics for makespan minimization on parallel batch processing machines with unequal job ready times. Int J Adv Manuf Technol 49:1119–1128CrossRefGoogle Scholar
  17. 17.
    Tang L, Zhang Y (2011) A new Lagrangian relaxation algorithm for scheduling dissimilar parallel machines with release dates. Int J Syst Sci 42(7):1133–1141MathSciNetMATHCrossRefGoogle Scholar
  18. 18.
    Chen C-L (2012) Iterated hybrid metaheuristic algorithms for unrelated parallel machines problem with unequal ready times and sequence-dependent setup times. Int J Adv Manuf Technol 60:693–705CrossRefGoogle Scholar
  19. 19.
    Lenstra JK, Rinnooy Kan AHG, Brucker P (1977) Complexity of machine scheduling problems. Ann Discret Math 1:343–362MathSciNetCrossRefGoogle Scholar
  20. 20.
    Lawler EL (1977) A ‘pseudopolynomial’ time algorithm for sequencing jobs to minimize total tardiness. Ann Discret Math 1:331–342MathSciNetCrossRefGoogle Scholar
  21. 21.
    Pinedo M (2012) Scheduling theory, algorithms, and systems (4th ed.). Upper Saddle, Prentice Hall .Google Scholar
  22. 22.
    Keha AB, Khowala K, Fowler JW (2009) Mixed integer programming formulations for single machine scheduling problems. Comput Ind Eng 56:357–367CrossRefGoogle Scholar
  23. 23.
    Lin YK, Pfund ME, Fowler JW (2011) Heuristics for minimizing regular performance measures in unrelated parallel machine scheduling problems. Comput Oper Res 38(6):901–916MathSciNetMATHCrossRefGoogle Scholar
  24. 24.
    Nawaz M, Enscore EE Jr, Ham I (1983) A heuristic algorithm for the m-machine, n-job flow-shop sequencing problem. Omega 11(1):91–95CrossRefGoogle Scholar
  25. 25.
    Vepsalainen APJ, Morton TE (1987) Priority rules and lead time estimation for job shop scheduling with weighted tardiness costs. Manage Sci 33:1036–1047CrossRefGoogle Scholar
  26. 26.
    Morton TE, Pentico DW (1993) Heuristic scheduling system: with applications to production systems and project management. Wiley, New YorkGoogle Scholar
  27. 27.
    Pfund ME, Fowler JW, Gadkari A, Chen Y (2008) Scheduling jobs on parallel machines with setup times and ready times. Comput Ind Eng 54(4):764–782CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  1. 1.Department of Industrial Engineering and Systems ManagementFeng Chia UniversityTaichungTaiwan

Personalised recommendations