, Volume 42, Issue 1, pp 11–21 | Cite as

Minimisation of total tardiness for identical parallel machine scheduling using genetic algorithm



In recent years research on parallel machine scheduling has received an increased attention. This paper considers minimisation of total tardiness for scheduling of n jobs on a set of m parallel machines. A spread-sheet-based genetic algorithm (GA) approach is proposed for the problem. The proposed approach is a domain-independent general purpose approach, which has been effectively used to solve this class of problem. The performance of GA is compared with branch and bound and particle swarm optimisation approaches. Two set of problems having 20 and 25 jobs with number of parallel machines equal to 2, 4, 6, 8 and 10 are solved with the proposed approach. Each combination of number of jobs and machines consists of 125 benchmark problems; thus a total for 2250 problems are solved. The results obtained by the proposed approach are comparable with two earlier approaches. It is also demonstrated that a simple GA can be used to produce results that are comparable with problem-specific approach. The proposed approach can also be used to optimise any objective function without changing the basic GA routine.


Parallel machine scheduling genetic algorithm (GA) total tardiness scheduling 


  1. 1.
    Root G J 1965 Scheduling with deadlines and loss functions on k parallel machines. Manage. Sci. 11(3): 460–475MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Azizoglu M and Kirca O 1998 Tardiness minimization on parallel machines. Int. J. Prod. Econ. 55(2): 163–168CrossRefGoogle Scholar
  3. 3.
    Armentano V A and Yamashita D S 2000 Tabu search for scheduling on identical parallel machines to minimize mean tardiness. J. Intell. Manuf. 11(5): 453–460CrossRefGoogle Scholar
  4. 4.
    Yalaoui F and Chu C 2002 Parallel machine scheduling to minimize total tardiness. Int. J. Prod. Econ. 76(3): 265–279CrossRefGoogle Scholar
  5. 5.
    Bilge Ü, Kıraç F, Kurtulan M and Pekgün P 2004 A tabu search algorithm for parallel machine total tardiness problem. Comput. Oper. Res. 31(3): 397–414CrossRefMATHGoogle Scholar
  6. 6.
    Hu P C 2004 Minimising total tardiness for the worker assignment scheduling problem in identical parallel-machine models. Int. J. Adv. Manuf. Technol. 23(5–6): 383–388CrossRefGoogle Scholar
  7. 7.
    Hu P C 2006 Further study of minimizing total tardiness for the worker assignment scheduling problem in the identical parallel-machine models. Int. J. Adv. Manuf. Technol. 29(1–2): 165–169MathSciNetCrossRefGoogle Scholar
  8. 8.
    Shim S O and Kim Y D 2004 Minimizing total tardiness in an identical-parallel machine scheduling problem. In: Proceedings of the fifth Asia Pacific industrial engineering and management systems conference, Gold Coast, AustraliaGoogle Scholar
  9. 9.
    Shim S O and Kim Y D 2007 Scheduling on parallel identical machines to minimize total tardiness. Eur. J. Oper. Res. 177(1): 135–146MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Anghinolfi D and Paolucci M 2007 Parallel machine total tardiness scheduling with a new hybrid metaheuristic approach. Comput. Oper. Res. 34(11): 3471–3490MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Shim S O and Kim Y D 2008 A branch and bound algorithm for an identical parallel machine scheduling problem with a job splitting property. Comput. Oper. Res. 35(3): 863–875MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Tanaka S and Araki M 2008 A branch-and-bound algorithm with Lagrangian relaxation to minimize total tardiness on identical parallel machines. Int. J. Prod. Econ. 113(1): 446–458CrossRefGoogle Scholar
  13. 13.
    Biskup D, Herrmann J and Gupta J N D 2008 Scheduling identical parallel machines to minimize total tardiness. Int. J. Prod. Econ. 115(1): 134–142CrossRefGoogle Scholar
  14. 14.
    Chaudhry I A and Drake P R 2009 Minimizing total tardiness for the machine scheduling and worker assignment problems in identical parallel machines using genetic algorithms. Int. J. Adv. Manuf. Technol. 42(5–6): 581–594CrossRefGoogle Scholar
  15. 15.
    Niu Q, Zhou T and Wang L 2010. A hybrid particle swarm optimization for parallel machine total tardiness scheduling. Intl. J. Adv. Manuf. Technol. 49(5–8): 723–739CrossRefGoogle Scholar
  16. 16.
    Demirel T, Ozkir V, Demirel N C and Tasdelen B 2011 A genetic algorithm approach for minimizing total tardiness in parallel machine scheduling problems. In: Proceedings of the World Congress on Engineering, 2011, London, UKGoogle Scholar
  17. 17.
    Yalaoui F 2012 Minimizing total tardiness in parallel-machine scheduling with release dates. Int. J. Appl. Evol. Comput. 3(1): 21–46MathSciNetCrossRefGoogle Scholar
  18. 18.
    Wei M, Deng G L, Xu Z H and Gu X S 2012 Parallel machine tardiness scheduling based on improved discrete differential evolution. Adv. Mat. Res. 459: 266–270CrossRefGoogle Scholar
  19. 19.
    Baker K R and Bertrand J W M 1982 A dynamic priority rule for scheduling against due-dates. J. Oper. Manage. 3(1): 37–42CrossRefGoogle Scholar
  20. 20.
    Holland J H 1975 Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor, MIGoogle Scholar
  21. 21.
    Goldberg D E 1989 Genetic algorithms in search, optimization and machine learning. Addison-Wesley Longman Publishing Co., Inc., Boston, MAGoogle Scholar
  22. 22.
    Davis L 1991 Handbook of genetic algorithms. New York: Van Nostrand ReinholdGoogle Scholar
  23. 23.
    Davis L 1985 Job shop scheduling with genetic algorithms. In: Proceedings of the 1st international conference on genetic algorithms, L. Erlbaum Associates IncGoogle Scholar
  24. 24.
    Chaudhry I A and Drake P R 2008 Minimizing flow-time variance in a single-machine system using genetic algorithms. Int. J. Adv. Manuf. Technol. 39(3–4): 355–366CrossRefGoogle Scholar
  25. 25.
    Chaudhry I A 2010 Minimizing flow time for the worker assignment problem in identical parallel machine models using GA. Int. J. Adv. Manuf. Technol. 48(5–8): 747–760CrossRefGoogle Scholar
  26. 26.
    Nanvala H 2011 Use of genetic algorithm based approaches in scheduling of FMS: a review. Int. J. Eng. Sci. Technol. 3(3): 1936–1942Google Scholar
  27. 27.
    Evolver: the genetic algorithm super solver, V 1998 New York, USA: Palisade CorporationGoogle Scholar
  28. 28.
    Chaudhry I A 2012a A genetic algorithm approach for process planning and scheduling in job shop environment. In: Proceedings of the World Congress on Engineering, 2012, London, UKGoogle Scholar
  29. 29.
    Chaudhry I A 2012b Job shop scheduling problem with alternative machines using genetic algorithms. J. Central South Univ. 19(5): 1322–1333CrossRefGoogle Scholar
  30. 30.
    Chaudhry I A and Mahmood S 2012 No-wait flowshop scheduling using genetic algorithm. In: Proceedings of the World Congress on Engineering, 2012, London, UKGoogle Scholar
  31. 31.
    Hayat N and Wirth A 1997 Genetic algorithms and machine scheduling with class setups. Int. J. Comput. Eng. Manage. 5(2): 10–23Google Scholar
  32. 32.
    Hegazy T and Ersahin T 2001 Simplified spreadsheet solutions II: overall schedule optimization. J. Construct. Eng. Manage. 127(6): 469–475CrossRefGoogle Scholar
  33. 33.
    Jeong S J, Lim S J and Kim K S 2006 Hybrid approach to production scheduling using genetic algorithm and simulation. Int. J. Adv. Manuf. Technol. 28(1–2): 129–136CrossRefGoogle Scholar
  34. 34.
    Nassar K 2005 Evolutionary optimization of resource allocation in repetitive construction schedules. ITcon 10: 265–273Google Scholar
  35. 35.
    Ruiz R and Maroto C 2001 Flexible manufacturing in the ceramic tile industry. In: Proceedings of the eighth international workshop on project management and scheduling, Valencia, SpainGoogle Scholar
  36. 36.
    Sadegheih A 2007 Sequence optimization and design of allocation using GA and SA. Appl. Math. Comput. 186(2): 1723–1730MATHGoogle Scholar
  37. 37.
    Shiue Y R and Guh R S 2006 Learning-based multi-pass adaptive scheduling for a dynamic manufacturing cell environment. Robot. Comput. Integr. Manuf. 22(3): 203–216CrossRefGoogle Scholar
  38. 38.
    Saranga H and Kumar U D 2006 Optimization of aircraft maintenance/support infrastructure using genetic algorithms – level of repair analysis. Ann. Oper. Res. 143(1): 91–106CrossRefMATHGoogle Scholar
  39. 39.
    Shum Y S and Gong D C 2007 The application of genetic algorithm in the development of preventive maintenance analytic model. Int. J. Adv. Manuf. Technol. 32(1–2): 169–183CrossRefGoogle Scholar
  40. 40.
    Hegazy T and Kassab M 2003 Resource optimization using combined simulation and genetic algorithms. J. Construct. Eng. Manage. 129(6): 698–705CrossRefGoogle Scholar
  41. 41.
    He D and Grigoryan A 2002 Construction of double sampling s-control charts for agile manufacturing. Qual. Reliab. Eng. Int. 18(4): 343–355CrossRefGoogle Scholar
  42. 42.
    Briand L C, Feng J and Labiche Y 2002 Using genetic algorithms and coupling measures to devise optimal integration test orders. In: Proceedings of the 14th international conference on software engineering and knowledge engineering, ACM, Ischia, Italy, pp. 43–50Google Scholar
  43. 43.
    Barkhi R, Rolland E, Butler J and Fan W 2005 Decision support system induced guidance for model formulation and solution. Decis. Support Syst. 40(2): 269–281CrossRefGoogle Scholar
  44. 44.
    Eusuff M, Ostfeld A and Lansey K 2000 An overview of HANDSS: Hula aggregated numerical decision support system. In: Proceedings of building partnerships, American Society of Civil Engineers, pp. 1–6Google Scholar
  45. 45.
    Cheung S O, Tong T K L and Tam C M 2002 Site pre-cast yard layout arrangement through genetic algorithms. Automat. Construct. 11(1): 35–46CrossRefGoogle Scholar
  46. 46.
    Whitley D and Kauth K 1988 GENITOR: a different genetic algorithm. In: Proceedings of the 1988 Rocky Mountain conference on artificial intelligence Google Scholar
  47. 47.
    Fisher M 1976 A dual algorithm for the one-machine scheduling problem. Math. Program. 11(1): 229–251MathSciNetCrossRefMATHGoogle Scholar
  48. 48.
    Rajendran C 1994 A no-wait flowshop scheduling heuristic to minimize makespan. J. Oper. Res. Soc. 45(4): 472–478CrossRefMATHGoogle Scholar
  49. 49.
    Schuster C J and Framinan J M 2003 Approximative procedures for no-wait job shop scheduling. Oper. Res. Lett. 31(4): 308–318MathSciNetCrossRefMATHGoogle Scholar
  50. 50.
    Grabowski J and Pempera J 2005 Some local search algorithms for no-wait flow-shop problem with makespan criterion. Comput. Oper. Res. 32(8): 2197–2212MathSciNetCrossRefMATHGoogle Scholar
  51. 51.
    Li X, Wang Q and Wu C 2008 Heuristic for no-wait flow shops with makespan minimization. Int. J. Prod. Res. 46(9): 2519–2530CrossRefMATHGoogle Scholar
  52. 52.
    Tseng L Y and Lin Y T 2010 A hybrid genetic algorithm for no-wait flowshop scheduling problem. Int. J. Prod. Econ. 128(1): 144–152CrossRefGoogle Scholar
  53. 53.
    Zhu X, Li X and Wang Q 2008 Hybrid heuristic for m-machine no-wait flowshops to minimize total completion time. In: Shen W, Yong J, Yang Y, Barthès J P and Luo J (Eds) Computer supported cooperative work in design IV, vol 5236. Springer, Berlin–Heidelberg, pp. 192–203CrossRefGoogle Scholar
  54. 54.
    Li X and Wu C 2008 Heuristic for no-wait flow shops with makespan minimization based on total idle-time increments. Sci. China Ser. F: Inf. Sci. 51(7): 896–909MathSciNetCrossRefMATHGoogle Scholar
  55. 55.
    Carlier J 1978 Ordonnancements a contraintes disjonctives. R.A.I.R.O. Recherche operationelle/Oper. Res. 12(4): 333–350MathSciNetMATHGoogle Scholar
  56. 56.
    Reeves C R 1995 A genetic algorithm for flowshop sequencing. Comput. Oper. Res. 22(1): 5–13MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Indian Academy of Sciences 2016

Authors and Affiliations

  1. 1.Department of Industrial Engineering, College of EngineeringUniversity of HailHa’ilSaudi Arabia

Personalised recommendations