A greedy heuristic and simulated annealing approach for a bicriteria flowshop scheduling problem with precedence constraints—a practical manufacturing case

Original Article

Abstract

This paper considers a flowshop scheduling problem with two criteria, where the primary (dominant) criterion is the minimization of material waste and the secondary criterion is the minimization of the total tardiness time. The decision maker does not authorize trade-offs between the criteria. In view of the nature of this problem, a hierarchical (lexicographical) optimization approach is followed. An effective greedy heuristic is proposed to minimize the material waste and a simulated annealing (SA) algorithm is developed to minimize the total tardiness time, subjective to the constraint computed for the primary criterion. The solution accuracy is compared with the optimal solution obtained by complete enumeration for randomly generated problem sets. From the results, it is observed that the greedy heuristic produces the optimal solution and the SA solution does not differ significantly from the optimal solution.

Keywords

Flowshop scheduling Lexicographical optimization Simulated annealing Multicriteria scheduling 

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References

  1. 1.
    Evans GW (1984) An overview of techniques for solving multiobjective mathematical programs. Manage Sci 30:1268–1282MATHCrossRefGoogle Scholar
  2. 2.
    Fry TD, Armstrong RD, Lewis H (1999) A framework for single machine multiple objective sequencing research. Omega 17:595–607CrossRefGoogle Scholar
  3. 3.
    Nagar A, Heragu SS, Haddock J (1995) A branch and bound approach for a two-machine flowshop scheduling problem. J Oper Res Soc 46:721–734MATHGoogle Scholar
  4. 4.
    Sridhar J, Rajendran C, (1996) Scheduling in flowshop and cellular manufacturing systems with multiple objectives—a genetic algorithmic approach. Prod Plan Control 7:374–382CrossRefGoogle Scholar
  5. 5.
    Framinan JM, Leisten R, Ruiz-Usano R (2002) Efficient heuristics for flowshop sequencing with the objectives of makespan and flowtime minimisation. Eur J Oper Res 141:559–569MATHCrossRefGoogle Scholar
  6. 6.
    T’kindt V, Billaut J-C, Proust C (2001) Solving a bicriteria scheduling problem on unrelated parallel machines occurring in the glass bottle industry. Eur J Oper Res 135:42–49MATHCrossRefGoogle Scholar
  7. 7.
    Marler RT, Arora JS (2004) Survey of multi-objective optimization methods for engineering. Struct Multidisc Optim 26:369–395MathSciNetCrossRefGoogle Scholar
  8. 8.
    T’kindt V, Billaut J-C (2001) Multicriteria scheduling problems: a survey. RAIRO Oper Res 35:143–163MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Hoogeveen H (2005) Multicriteria scheduling. Eur J Oper Res 167:592–623MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Nawaz M, Enscore E, Ham L (1983) A heuristic for the m-machine n-job flowshop sequencing problem. Omega II:91–95CrossRefGoogle Scholar
  11. 11.
    Panneerselvam R (2006) Simple heuristic to minimize total tardiness in a single machine scheduling problem. Int J Adv Manuf Tech 30:722–726CrossRefGoogle Scholar
  12. 12.
    Reeves CR (1995) A genetic algorithm for flowshop sequencing. Comput Oper Res 22:5–13MATHCrossRefGoogle Scholar
  13. 13.
    Rajendran C, Ziegler H (2004) Ant-colony algorithms for permutation flowshop scheduling to minimize makespan/total flowtime of jobs. Eur J Oper Res 155:426–38MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    Noorul Haq A, Saravanan M, Vivekraj AR, Prasad T (2006) A scatter search algorithm for general flowshop scheduling problem. Int J Adv Manuf Tech 31:731–736CrossRefGoogle Scholar
  15. 15.
    Suman B (2002) Multiobjective simulated annealing—a metaheuristic technique for multiobjective optimization of a constrained problem. Found Comput Decis Soc 27:171–191Google Scholar
  16. 16.
    Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 20:671–680MathSciNetCrossRefGoogle Scholar
  17. 17.
    Eglese RW (1990) Simulated annealing: a tool for operational research. Eur J Oper Res 46:271–281MathSciNetMATHCrossRefGoogle Scholar
  18. 18.
    Ehrgott M, Gandibleux X (2000) A survey and annotated bibliography of multiobjective combinatorial optimization. OR Spektrum 22:425–460MathSciNetMATHCrossRefGoogle Scholar
  19. 19.
    Van Laarhoven PJM, Aarts EHL, Lenstra JK (1992) Job shop scheduling by simulated annealing. Oper Res 40:113–125MathSciNetMATHCrossRefGoogle Scholar
  20. 20.
    Liaw CF (1999) Applying simulated annealing to the open shop scheduling problem. IIE T 31:457–465Google Scholar
  21. 21.
    Dipak L, Chakraborty UK (2009) An efficient hybrid heuristic for makespan minimization in permutation flow shop scheduling. Int J Adv Manuf Tech 44:559–569CrossRefGoogle Scholar
  22. 22.
    Varadharajan TK, Rajendran C (2005) A multi-objective simulated-annealing algorithm for scheduling in flowshops to minimize the makespan and total flowtime of jobs. Eur J Oper Res 167:772–795MathSciNetMATHCrossRefGoogle Scholar
  23. 23.
    Suman B, Kumar P (2006) A survey of simulated annealing as a tool for single and multiobjective optimization. J Oper Res Soc 57:1143–1160MATHCrossRefGoogle Scholar
  24. 24.
    Rajasekaran S (1990) On the convergence time of simulated annealing. University of Pennsylvania Department of Computer and Information Science, Technical Report no. MS-CIS-90-89Google Scholar
  25. 25.
    Bertsimas D, Tsitsiklis J (1993) Simulated annealing. Statistical Science 8(1):10–15CrossRefGoogle Scholar
  26. 26.
    Ben-Daya M, Al-Fawzan M (1996) A simulated annealing approach for the one-machine mean tardiness scheduling problem. Eur J Oper Res 93:61–67MATHCrossRefGoogle Scholar
  27. 27.
    Parthasarathy S, Rajendran C (1997) A simulated annealing heuristic for scheduling to minimize mean weighted tardiness in a flowshop with sequence-dependent setup times of jobs—a case study. Prod Plan Control 8:475–483CrossRefGoogle Scholar
  28. 28.
    Potts CN, Van Wassenhove LN (1991) Single machine tardiness sequencing heuristics. IIE T 23(4):346–354CrossRefGoogle Scholar
  29. 29.
    Johnson DS, Aragon CR, Mcgeoch LA, Schevon C (1989) Optimisation by simulated annealing: an experimental valuation. Part I, graph partitioning, Oper Res 37:865–891MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.Centre for Intelligent Systems ResearchInstitute of Technology and Research Innovation, Deakin UniversityVictoriaAustralia

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