Scheduling hybrid flowshops with sequence dependent setup times to minimize makespan and maximum tardiness

  • B. Naderi
  • M. Zandieh
  • V. Roshanaei


This article addresses the problem of scheduling hybrid flowshops where the setup times are sequence dependent to minimize makespan and maximum tardiness. To solve such an NP-hard problem, we introduce a novel simulated annealing (SA) with a new concept, called “Migration mechanism”, and a new operator, called “Giant leap”, to bolster the competitive performance of SA through striking a compromise between the lengths of neighborhood search structures. We hybridize the SA (HSA) with a simple local search to further equip our algorithm with a new strong tool to promote the quality of final solution of our proposed SA. We employ the Taguchi method as an optimization technique to extensively tune different parameters and operators of our algorithm. Taguchi orthogonal array analysis is specifically used to pick the best parameters for the optimum design process with the least number of experiments. We established a benchmark to draw an analogy between the performance of SA with other algorithms. Two basically different objective functions, minimization of makespan and maximum tardiness, are taken into consideration to evaluate the robustness and effectiveness of the proposed HSA. Furthermore, we explore the effects of the increase in the number of jobs on the performance of our algorithm to make sure it is effective in terms of both the acceptability of the solution quality and robustness. The excellence and strength of our HSA are concluded from all the results acquired in various circumstances.


Scheduling Hybrid flowshops Sequence dependent setup time Makespan Maximum tardiness Simulated annealing Local search Taguchi method 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Zandieh M, Fatemi Ghomi SMT, Moattar Husseini SM (2006) An immune algorithm approach to hybrid flow shops scheduling with sequence-dependent setup times. Appl Math Comput 180:111–127, doi: 10.1016/j.amc.2005.11.136 zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Baker KR (1974) Introduction to sequence and scheduling. Wiley, New YorkGoogle Scholar
  3. 3.
    Ruiz R, Maroto C (2006) A genetic algorithm for hybrid flowshops with sequence dependent setup times and machine eligibility. Eur J Oper Res 169:781–800, doi: 10.1016/j.ejor.2004.06.038 zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Conway RW, Maxwell WL (1967) Theory of scheduling. Addison-Wesley, BostonzbMATHGoogle Scholar
  5. 5.
    Sule DR (1997) Industrial scheduling. PWS, BostonzbMATHGoogle Scholar
  6. 6.
    Luh PB, Gou L, Zhang Y, Nagahora T, Tsuji M, Yoneda K, Hasegawa T, Kyoya Y, Kano T (1998) Job shop scheduling with group dependent setups, finite buffers, and long time horizon. Annal Opns Res 76:233–259, doi: 10.1023/A:1018948621875 zbMATHCrossRefGoogle Scholar
  7. 7.
    Gupta JND (1988) Two-stage hybrid flowshop scheduling problem. J Oper Res Soc 39(4):359–364zbMATHCrossRefGoogle Scholar
  8. 8.
    Ng EYK, Ng EWK (2006) Parametric study of the biopotential equation for breast tumors identification using ANOVA and Taguchi method. Med Biol Eng Comput 44:131–139CrossRefGoogle Scholar
  9. 9.
    Jungwattanakit J, Reodecha M, Chaovalitwongse P, Werner F (2007) Algorithms for flexible flow shop problems with unrelated parallel machines, setup times, and dual criteria. Int J Adv Manuf Technol, doi: 10.1007/s00170-007-0977-0
  10. 10.
    Luo F, Sun H, Geng T, Qi N (2008) Application of Taguchi’s method in the optimization of bridging efficiency between confluent and fresh micro carriers in bead-to-bead transfer of Vero cells. Biotechnol Lett 30(4):645–649CrossRefGoogle Scholar
  11. 11.
    Cheng BW, Chang CL (2007) A study on flowshop scheduling problem combining Taguchi experimental design and genetic algorithm. Expert Syst Appl 32:415–421, doi: 10.1016/j.eswa.2005.12.002 CrossRefGoogle Scholar
  12. 12.
    Caprihan R, Wadhwa S (2005) Scheduling of FMSs with information delays: a simulation study. Int J Flex Manuf Syst 17:39–65, doi: 10.1007/s10696-005-5993-5 zbMATHCrossRefGoogle Scholar
  13. 13.
    Ruiz R, Allahverdi A (2007) Some effective heuristics for no-wait flowshops with setup times to minimize total completion time. Ann Oper Res 156:143–171, doi: 10.1007/s10479-007-0227-8 zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Ruiz R, Stützle T (2008) An Iterated Greedy heuristic for the sequence dependent setup times flowshop problem with makespan and weighted tardiness objectives. Eur J Oper Res 187(3):1143–1159, doi: 10.1016/j.ejor.2006.07.029 zbMATHCrossRefGoogle Scholar
  15. 15.
    Johnson SM (1954) Optimal two and three-stage production schedules with setup times included. Nav Res Logist Q 1:61–67, doi: 10.1002/nav.3800010110 CrossRefGoogle Scholar
  16. 16.
    Yoshida T, Hitomi K (1979) Optimal two-stage production with setup times separated. AIIE Trans 11:261–263Google Scholar
  17. 17.
    Gupta JND, Darrow WP (1986) The two-machine sequence dependent flow shop scheduling problem. Eur J Oper Res 24(3):439–446, doi: 10.1016/0377-2217(86)90037-8 zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Kurz ME, Askin RG (2003) Comparing scheduling rules for flexible flow lines. Int J Prod Econ 85:371–388, doi: 10.1016/S0925-5273(03)00123-3 CrossRefGoogle Scholar
  19. 19.
    Kurz ME, Askin RG (2004) Scheduling flexible flow lines with sequence-dependent setup times. Eur J Oper Res 159(1):66–82, doi: 10.1016/S0377-2217(03)00401-6 zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Allahverdi A, Ng CT, Cheng TCE, Kovalyov YM (2008) A survey of scheduling problems with setup times or costs. Eur J Oper Res 187(3):985–1032, doi: 10.1016/j.ejor.2006.06.060 zbMATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Kim YD (1993) Heuristics for flow shop scheduling problems minimizing mean tardiness. J Oper Res Soc 44:19–28zbMATHCrossRefGoogle Scholar
  22. 22.
    Kim YD, Lim HG, Park MW (1996) Search heuristics for a flow shop scheduling problem in a printed circuit board assembly process. Eur J Oper Res 91:124–143, doi: 10.1016/0377-2217(95)00119-0 zbMATHCrossRefGoogle Scholar
  23. 23.
    Phadke MS (1989) Quality engineering using robust design. Prentice-Hall, Upper Saddle RiverGoogle Scholar
  24. 24.
    Adenso-Díaz B (1996) An SA/TS mixture algorithm for the scheduling tardiness problem. Eur J Oper Res 88:516–524, doi: 10.1016/0377-2217(94)00213-4 zbMATHCrossRefGoogle Scholar
  25. 25.
    Vallada E, Ruiz R, Minella G (2008) Minimizing total tardiness in the m-machine flowshop problem: a review and evaluation of heuristics and metaheuristics. Comput Oper Res 35(4):1350–1373, doi: 10.1016/j.cor.2006.08.016 zbMATHCrossRefGoogle Scholar
  26. 26.
    Norman BA, Bean JC (1999) A genetic algorithm methodology for complex scheduling problems. Nav Res Logist 46:199–211, doi: 10.1002/(SICI)1520-6750(199903)46:2<199::AID-NAV5>3.0.CO;2-L zbMATHCrossRefMathSciNetGoogle Scholar
  27. 27.
    Jin Z, Yang Z, Ito T (2006) Metaheuristic algorithms for the multistage hybrid flowshop scheduling problem. Int J Prod Econ 100:322–334, doi: 10.1016/j.ijpe.2004.12.025 CrossRefGoogle Scholar
  28. 28.
    Montgomery DC (2000) Design and analysis of experiments, 5th edn. Wiley, New YorkGoogle Scholar
  29. 29.
    Ruiz R, Maroto C, Alcaraz J (2006) Two new robust genetic algorithms for the flowshop scheduling problem. Omega 34:461–476, doi: 10.1016/ CrossRefGoogle Scholar
  30. 30.
    Ruiz R, Stützle T (2007) A simple and effective iterated greedy algorithm for the permutation flowshop scheduling problem. Eur J Oper Res 177:2033–2049, doi: 10.1016/j.ejor.2005.12.009 zbMATHCrossRefGoogle Scholar
  31. 31.
    Cochran WG, Cox GM (1992) Experimental designs, 2nd edn. Wiley, New YorkzbMATHGoogle Scholar
  32. 32.
    Ross RJ (1989) Taguchi techniques for quality engineering. McGraw-Hill, New YorkGoogle Scholar
  33. 33.
    Lundy M, Mees A (1986) Convergence of an annealing algorithm. Math Program 34:111–124, doi: 10.1007/BF01582166 zbMATHCrossRefMathSciNetGoogle Scholar
  34. 34.
    Hmida AB, Huguet MJ, Lopez P, Haouari M (2007) Climbing depth-bounded discrepancy search for solving hybrid flow shop problems. Eur J Ind Eng 1(2):223–240, doi: 10.1504/EJIE.2007.014110 CrossRefGoogle Scholar
  35. 35.
    Valente JMS (2007) Heuristics for the single machine scheduling problem with early and quadratic tardy penalties. Eur J Ind Eng 1(4):431–448, doi: 10.1504/EJIE.2007.015391 CrossRefGoogle Scholar
  36. 36.
    Li X, Ye N, Xu X, Sawhey R (2007) Influencing factors of job waiting time variance on a single machine. Eur J Ind Eng 1(1):56–73, doi: 10.1504/EJIE.2007.012654 CrossRefGoogle Scholar
  37. 37.
    Rodriguez-Tello E, Hao JK, Torres-Jimenes J (2008) An effective two-stage simulated annealing algorithm for the minimum arrangement problem. Comp Oper Res 35(10):3331–3346, doi: 10.1016/j.cor.2007.03.001 zbMATHCrossRefGoogle Scholar
  38. 38.
    Wu TH, Chang CC, Chung SH (2008) A simulated annealing algorithm for manufacturing cell formation problems. Expert Syst Appl 34(3):1609–1617, doi: 10.1016/j.eswa.2007.01.012 CrossRefGoogle Scholar
  39. 39.
    Ramesh S, Teegavarapu V, Simonovic SP (2002) Optimal operation of reservoir systems using simulated annealing. Water Resour Manag 16(5):401–428, doi: 10.1023/A:1021993222371 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2008

Authors and Affiliations

  1. 1.Department of Industrial EngineeringAmirkabir University of TechnologyTehranIran
  2. 2.Department of Industrial Management, Management and Accounting FacultyShahid Beheshti UniversityTehranIran

Personalised recommendations