Abstract
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.
Similar content being viewed by others
References
Root G J 1965 Scheduling with deadlines and loss functions on k parallel machines. Manage. Sci. 11(3): 460–475
Azizoglu M and Kirca O 1998 Tardiness minimization on parallel machines. Int. J. Prod. Econ. 55(2): 163–168
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): 453–460
Yalaoui F and Chu C 2002 Parallel machine scheduling to minimize total tardiness. Int. J. Prod. Econ. 76(3): 265–279
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): 397–414
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): 383–388
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): 165–169
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, Australia
Shim S O and Kim Y D 2007 Scheduling on parallel identical machines to minimize total tardiness. Eur. J. Oper. Res. 177(1): 135–146
Anghinolfi D and Paolucci M 2007 Parallel machine total tardiness scheduling with a new hybrid metaheuristic approach. Comput. Oper. Res. 34(11): 3471–3490
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): 863–875
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): 446–458
Biskup D, Herrmann J and Gupta J N D 2008 Scheduling identical parallel machines to minimize total tardiness. Int. J. Prod. Econ. 115(1): 134–142
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): 581–594
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): 723–739
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, UK
Yalaoui F 2012 Minimizing total tardiness in parallel-machine scheduling with release dates. Int. J. Appl. Evol. Comput. 3(1): 21–46
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: 266–270
Baker K R and Bertrand J W M 1982 A dynamic priority rule for scheduling against due-dates. J. Oper. Manage. 3(1): 37–42
Holland J H 1975 Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor, MI
Goldberg D E 1989 Genetic algorithms in search, optimization and machine learning. Addison-Wesley Longman Publishing Co., Inc., Boston, MA
Davis L 1991 Handbook of genetic algorithms. New York: Van Nostrand Reinhold
Davis L 1985 Job shop scheduling with genetic algorithms. In: Proceedings of the 1st international conference on genetic algorithms, L. Erlbaum Associates Inc
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): 355–366
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): 747–760
Nanvala H 2011 Use of genetic algorithm based approaches in scheduling of FMS: a review. Int. J. Eng. Sci. Technol. 3(3): 1936–1942
Evolver: the genetic algorithm super solver, V 1998 New York, USA: Palisade Corporation
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, UK
Chaudhry I A 2012b Job shop scheduling problem with alternative machines using genetic algorithms. J. Central South Univ. 19(5): 1322–1333
Chaudhry I A and Mahmood S 2012 No-wait flowshop scheduling using genetic algorithm. In: Proceedings of the World Congress on Engineering, 2012, London, UK
Hayat N and Wirth A 1997 Genetic algorithms and machine scheduling with class setups. Int. J. Comput. Eng. Manage. 5(2): 10–23
Hegazy T and Ersahin T 2001 Simplified spreadsheet solutions II: overall schedule optimization. J. Construct. Eng. Manage. 127(6): 469–475
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): 129–136
Nassar K 2005 Evolutionary optimization of resource allocation in repetitive construction schedules. ITcon 10: 265–273
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, Spain
Sadegheih A 2007 Sequence optimization and design of allocation using GA and SA. Appl. Math. Comput. 186(2): 1723–1730
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): 203–216
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): 91–106
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): 169–183
Hegazy T and Kassab M 2003 Resource optimization using combined simulation and genetic algorithms. J. Construct. Eng. Manage. 129(6): 698–705
He D and Grigoryan A 2002 Construction of double sampling s-control charts for agile manufacturing. Qual. Reliab. Eng. Int. 18(4): 343–355
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. 43–50
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): 269–281
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. 1–6
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): 35–46
Whitley D and Kauth K 1988 GENITOR: a different genetic algorithm. In: Proceedings of the 1988 Rocky Mountain conference on artificial intelligence
Fisher M 1976 A dual algorithm for the one-machine scheduling problem. Math. Program. 11(1): 229–251
Rajendran C 1994 A no-wait flowshop scheduling heuristic to minimize makespan. J. Oper. Res. Soc. 45(4): 472–478
Schuster C J and Framinan J M 2003 Approximative procedures for no-wait job shop scheduling. Oper. Res. Lett. 31(4): 308–318
Grabowski J and Pempera J 2005 Some local search algorithms for no-wait flow-shop problem with makespan criterion. Comput. Oper. Res. 32(8): 2197–2212
Li X, Wang Q and Wu C 2008 Heuristic for no-wait flow shops with makespan minimization. Int. J. Prod. Res. 46(9): 2519–2530
Tseng L Y and Lin Y T 2010 A hybrid genetic algorithm for no-wait flowshop scheduling problem. Int. J. Prod. Econ. 128(1): 144–152
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. 192–203
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): 896–909
Carlier J 1978 Ordonnancements a contraintes disjonctives. R.A.I.R.O. Recherche operationelle/Oper. Res. 12(4): 333–350
Reeves C R 1995 A genetic algorithm for flowshop sequencing. Comput. Oper. Res. 22(1): 5–13
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
CHAUDHRY, I.A., ELBADAWI, I.A.Q. Minimisation of total tardiness for identical parallel machine scheduling using genetic algorithm. Sādhanā 42, 11–21 (2017). https://doi.org/10.1007/s12046-016-0575-7
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12046-016-0575-7