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April  2016, 12(2): 703-717. doi: 10.3934/jimo.2016.12.703

A tabu search algorithm to minimize total weighted tardiness for the job shop scheduling problem

1. 

Department of Industrial Engineering and Systems Management, Feng Chia University, P.O. Box 25-097,Taichung, 40724, Taiwan, ROC, Taiwan

2. 

Planning and Operations Management Group, Singapore Institute of Manufacturing Technology, A-star, 7 Nanyang Avenue, 638075, Singapore

Received  October 2014 Revised  April 2015 Published  June 2015

This research presents a tabu search algorithm with a restart (TSA-R) approach to minimize total weighted tardiness (TWT) for the job shop scheduling problem. Jobs have non-identical due dates. The problem belongs to the class of NP-hard problems. The TSA-R approach uses dispatching rules to obtain an initial solution and searches for new solutions in a neighborhood based on the critical paths of jobs and blocks of operations. The TSA-R applies a new diversification scheme to exploit the initial solutions and its neighborhood structures so as to overcome entrapment issues and to enhance solutions. A computational result based on standard benchmark instances from the literature is presented to show the effectiveness of the proposed tabu search algorithm.
Citation: Y. K. Lin, C. S. Chong. A tabu search algorithm to minimize total weighted tardiness for the job shop scheduling problem. Journal of Industrial & Management Optimization, 2016, 12 (2) : 703-717. doi: 10.3934/jimo.2016.12.703
References:
[1]

E. J. Anderson and J. C. Nyirenda, Two new rules to minimize tardiness in a job shop,, International Journal of Production Research, 28 (1990), 2277.  doi: 10.1080/00207549008942866.  Google Scholar

[2]

V. A. Armentano and C. R. Scrich, Tabu search for minimizing total tardiness in a job shop,, International Journal of Production Research, 63 (2000), 131.  doi: 10.1016/S0925-5273(99)00014-6.  Google Scholar

[3]

M. Asano and H. Ohta, A heuristic for job shop scheduling to minimize total weighted tardiness,, Computers and Industrial Engineering, 42 (2002), 137.  doi: 10.1016/S0360-8352(02)00019-0.  Google Scholar

[4]

K. R. Baker, Sequencing rules and due date assignments in a job shop,, Management Science, 30 (1984), 1093.  doi: 10.1287/mnsc.30.9.1093.  Google Scholar

[5]

K. R. Baker and J. J. Kanet, Job shop scheduling with modified due dates,, Journal of Operations Management, 4 (1983), 11.  doi: 10.1016/0272-6963(83)90022-0.  Google Scholar

[6]

E. Balas, Machine sequencing via disjunctive graph: an implicit enumeration algorithm,, Operations Research, 17 (1969), 941.  doi: 10.1287/opre.17.6.941.  Google Scholar

[7]

K. M. J. Bontridder, Minimizing total weighted tardiness in a generalized job shop,, Journal of Scheduling, 8 (2005), 479.  doi: 10.1007/s10951-005-4779-7.  Google Scholar

[8]

K. Bulbul, A hybrid shifting bottleneck-tabu search heuristic for the job shop total weighted tardiness problem,, Computers and Operations Research, 38 (2011), 967.  doi: 10.1016/j.cor.2010.09.015.  Google Scholar

[9]

G. Calleja and R. Pastor, A dispatching algorithm for flexible job-shop scheduling with transfer batches: an industrial application,, Production Planning and Control, 25 (2014), 93.  doi: 10.1080/09537287.2013.782846.  Google Scholar

[10]

I. Essafi, Y. Mati and S. Dauzere-Peres, A genetic local search algorithm for minimizing total weighted tardiness in the job-shop scheduling problem,, Computers and Operations Research, 35 (2008), 2599.  doi: 10.1016/j.cor.2006.12.019.  Google Scholar

[11]

R. L. Graham, E. L. Lawler, J. K. Lenstra and A. H. G. Rinnooy Kan, Optimization and approximation in deterministic sequencing and scheduling: a survey,, Annals of Discrete Mathematics, 5 (1979), 287.  doi: 10.1016/S0167-5060(08)70356-X.  Google Scholar

[12]

Z. He, T. Yang and D. E. Deal, A multiple-pass heuristic rule for job shop scheduling with due dates,, International Journal of Production Research, 31 (1993), 2677.  doi: 10.1080/00207549308956890.  Google Scholar

[13]

A. S. Jain, B. Rangaswamy and S. Meeran, New and "stronger" job-shop neighborhoods: a focus on the method of Nowicki and Smutnicki (1996),, Journal of Heuristics, 6 (2000), 457.   Google Scholar

[14]

J. J. Kanet and J. C. Hayya, Priority dispatching with operation due dates in a job shop,, Journal of Operations Management, 2 (1982), 167.   Google Scholar

[15]

S. Kreipl, A large step random walk for minimizing total weighted tardiness in a job shop,, Journal of Scheduling, 3 (2000), 125.  doi: 10.1002/(SICI)1099-1425(200005/06)3:3<125::AID-JOS40>3.0.CO;2-C.  Google Scholar

[16]

E. L. Lawler, J. K. Lenstra, A. H. G. Rinnooy Kan and D. B. Shmoys, Sequencing and scheduling: Algorithms and complexity,, in Handbooks in Operations Research and Management Science (eds. S. C. Graves, 4 (1993), 445.   Google Scholar

[17]

H. L. Lu, G. Q. Huang and H. D. Yang, Integrating order review/release and dispatching rules for assembly job shop scheduling using a simulation approach,, International Journal of Production Research, 49 (2011), 647.   Google Scholar

[18]

Y. Mati, S. Dauzere-Peres and C. Lahlou, A general approach for optimizing regular criteria in the job-shop scheduling problem,, European Journal of Operational Research, 212 (2011), 33.  doi: 10.1016/j.ejor.2011.01.046.  Google Scholar

[19]

D. C. Mattfeld and C. Bierwirth, An efficient genetic algorithm for job shop scheduling with tardiness objectives,, European Journal of Operational Research, 155 (2004), 616.  doi: 10.1016/S0377-2217(03)00016-X.  Google Scholar

[20]

E. Nowicki and C. Smutnicki, A fast taboo search algorithm for the job shop problem,, Management Science, 42 (1996), 797.   Google Scholar

[21]

E. Nowicki and C. Smutnicki, An advanced tabu search algorithm for the job shop problem,, Journal of Scheduling, 8 (2005), 145.  doi: 10.1007/s10951-005-6364-5.  Google Scholar

[22]

S. Nguyen, M. Zhang, J. Mark and KC. Tan, A computational study of representations in genetic programming to evolve dispatching rules for the job shop scheduling problem,, IEEE Transactions on Evolutionary Computation, 17 (2013), 621.   Google Scholar

[23]

M. Pinedo and M. Singer, A shifting bottleneck heuristic for minimizing the total weighted tardiness in job shop,, Naval Research Logistics, 46 (1999), 1.  doi: 10.1002/(SICI)1520-6750(199902)46:1<1::AID-NAV1>3.3.CO;2-R.  Google Scholar

[24]

N. Raman and F. B. Talbot, The job shop tardiness problem: A decomposition approach,, European Journal of Operational Research, 69 (1993), 187.   Google Scholar

[25]

M. Singer and M. Pinedo, A computational study of branch and bound techniques for minimizing the total weighted tardiness in job shops,, IIE Transactions, 30 (1998), 109.   Google Scholar

[26]

P. J. M. Van Laarhoven, E. H. L. Aarts and J. K. Lenstra, Job shop scheduling by simulated annealing,, Operations Research, 40 (1992), 113.  doi: 10.1287/opre.40.1.113.  Google Scholar

[27]

A. P. J. Vepsalainen and T. E. Morton, Priority rules for job shops with weighted tardiness costs,, Management Science, 33 (1987), 1035.   Google Scholar

[28]

T. Yang, Z. He and K. K. Cho, An effective heuristic method for generalized job shop scheduling with due dates,, Computers and Industrial Engineering, 26 (1994), 647.   Google Scholar

[29]

C. Zhang, X. Shao, Y. Rao and H. Qiu, Some new results on tabu search algorithm applied to the job-shop scheduling problem, Tabu Search, Wassim Jaziri (Ed.), InTech, Available from: http://www.intechopen.com/articles/show/title/some_new_results_on_tabu_search_algorithm_applied_to_the_job-shop_scheduling_problem, (2008)., (2008).   Google Scholar

[30]

R. Zhang, A genetic local search algorithm based on insertion neighborhood for the job shop scheduling problem,, Advances in Information Sciences and Services, 3 (2011), 117.   Google Scholar

[31]

R. Zhang and C. Wu, A divide-and-conquer strategy with particle swarm optimization for the job shop scheduling problem,, Engineering Optimization, 42 (): 641.  doi: 10.1080/03052150903369845.  Google Scholar

[32]

R. Zhang and C. Wu, A hybrid immune simulated annealing algorithm for the job shop scheduling problem,, Applied Soft Computing, 10 (): 79.   Google Scholar

[33]

R. Zhang and C. Wu, A simulated annealing algorithm based on block properties for the job shop scheduling problem with total weighted tardiness objective,, Computers and Operations Research, 38 (2011), 854.  doi: 10.1016/j.cor.2010.09.014.  Google Scholar

[34]

R. Zhang, S. Song and C. Wu, A hybrid artificial bee colony algorithm for the job shop scheduling problem,, International Journal of Production Economics, 141 (2013), 167.   Google Scholar

[35]

H. Zhou, W. Cheung and L. C. Leung, Minimizing weighted tardiness of job-shop scheduling using a hybrid genetic algorithm,, European Journal of Operational Research, 194 (2009), 637.   Google Scholar

show all references

References:
[1]

E. J. Anderson and J. C. Nyirenda, Two new rules to minimize tardiness in a job shop,, International Journal of Production Research, 28 (1990), 2277.  doi: 10.1080/00207549008942866.  Google Scholar

[2]

V. A. Armentano and C. R. Scrich, Tabu search for minimizing total tardiness in a job shop,, International Journal of Production Research, 63 (2000), 131.  doi: 10.1016/S0925-5273(99)00014-6.  Google Scholar

[3]

M. Asano and H. Ohta, A heuristic for job shop scheduling to minimize total weighted tardiness,, Computers and Industrial Engineering, 42 (2002), 137.  doi: 10.1016/S0360-8352(02)00019-0.  Google Scholar

[4]

K. R. Baker, Sequencing rules and due date assignments in a job shop,, Management Science, 30 (1984), 1093.  doi: 10.1287/mnsc.30.9.1093.  Google Scholar

[5]

K. R. Baker and J. J. Kanet, Job shop scheduling with modified due dates,, Journal of Operations Management, 4 (1983), 11.  doi: 10.1016/0272-6963(83)90022-0.  Google Scholar

[6]

E. Balas, Machine sequencing via disjunctive graph: an implicit enumeration algorithm,, Operations Research, 17 (1969), 941.  doi: 10.1287/opre.17.6.941.  Google Scholar

[7]

K. M. J. Bontridder, Minimizing total weighted tardiness in a generalized job shop,, Journal of Scheduling, 8 (2005), 479.  doi: 10.1007/s10951-005-4779-7.  Google Scholar

[8]

K. Bulbul, A hybrid shifting bottleneck-tabu search heuristic for the job shop total weighted tardiness problem,, Computers and Operations Research, 38 (2011), 967.  doi: 10.1016/j.cor.2010.09.015.  Google Scholar

[9]

G. Calleja and R. Pastor, A dispatching algorithm for flexible job-shop scheduling with transfer batches: an industrial application,, Production Planning and Control, 25 (2014), 93.  doi: 10.1080/09537287.2013.782846.  Google Scholar

[10]

I. Essafi, Y. Mati and S. Dauzere-Peres, A genetic local search algorithm for minimizing total weighted tardiness in the job-shop scheduling problem,, Computers and Operations Research, 35 (2008), 2599.  doi: 10.1016/j.cor.2006.12.019.  Google Scholar

[11]

R. L. Graham, E. L. Lawler, J. K. Lenstra and A. H. G. Rinnooy Kan, Optimization and approximation in deterministic sequencing and scheduling: a survey,, Annals of Discrete Mathematics, 5 (1979), 287.  doi: 10.1016/S0167-5060(08)70356-X.  Google Scholar

[12]

Z. He, T. Yang and D. E. Deal, A multiple-pass heuristic rule for job shop scheduling with due dates,, International Journal of Production Research, 31 (1993), 2677.  doi: 10.1080/00207549308956890.  Google Scholar

[13]

A. S. Jain, B. Rangaswamy and S. Meeran, New and "stronger" job-shop neighborhoods: a focus on the method of Nowicki and Smutnicki (1996),, Journal of Heuristics, 6 (2000), 457.   Google Scholar

[14]

J. J. Kanet and J. C. Hayya, Priority dispatching with operation due dates in a job shop,, Journal of Operations Management, 2 (1982), 167.   Google Scholar

[15]

S. Kreipl, A large step random walk for minimizing total weighted tardiness in a job shop,, Journal of Scheduling, 3 (2000), 125.  doi: 10.1002/(SICI)1099-1425(200005/06)3:3<125::AID-JOS40>3.0.CO;2-C.  Google Scholar

[16]

E. L. Lawler, J. K. Lenstra, A. H. G. Rinnooy Kan and D. B. Shmoys, Sequencing and scheduling: Algorithms and complexity,, in Handbooks in Operations Research and Management Science (eds. S. C. Graves, 4 (1993), 445.   Google Scholar

[17]

H. L. Lu, G. Q. Huang and H. D. Yang, Integrating order review/release and dispatching rules for assembly job shop scheduling using a simulation approach,, International Journal of Production Research, 49 (2011), 647.   Google Scholar

[18]

Y. Mati, S. Dauzere-Peres and C. Lahlou, A general approach for optimizing regular criteria in the job-shop scheduling problem,, European Journal of Operational Research, 212 (2011), 33.  doi: 10.1016/j.ejor.2011.01.046.  Google Scholar

[19]

D. C. Mattfeld and C. Bierwirth, An efficient genetic algorithm for job shop scheduling with tardiness objectives,, European Journal of Operational Research, 155 (2004), 616.  doi: 10.1016/S0377-2217(03)00016-X.  Google Scholar

[20]

E. Nowicki and C. Smutnicki, A fast taboo search algorithm for the job shop problem,, Management Science, 42 (1996), 797.   Google Scholar

[21]

E. Nowicki and C. Smutnicki, An advanced tabu search algorithm for the job shop problem,, Journal of Scheduling, 8 (2005), 145.  doi: 10.1007/s10951-005-6364-5.  Google Scholar

[22]

S. Nguyen, M. Zhang, J. Mark and KC. Tan, A computational study of representations in genetic programming to evolve dispatching rules for the job shop scheduling problem,, IEEE Transactions on Evolutionary Computation, 17 (2013), 621.   Google Scholar

[23]

M. Pinedo and M. Singer, A shifting bottleneck heuristic for minimizing the total weighted tardiness in job shop,, Naval Research Logistics, 46 (1999), 1.  doi: 10.1002/(SICI)1520-6750(199902)46:1<1::AID-NAV1>3.3.CO;2-R.  Google Scholar

[24]

N. Raman and F. B. Talbot, The job shop tardiness problem: A decomposition approach,, European Journal of Operational Research, 69 (1993), 187.   Google Scholar

[25]

M. Singer and M. Pinedo, A computational study of branch and bound techniques for minimizing the total weighted tardiness in job shops,, IIE Transactions, 30 (1998), 109.   Google Scholar

[26]

P. J. M. Van Laarhoven, E. H. L. Aarts and J. K. Lenstra, Job shop scheduling by simulated annealing,, Operations Research, 40 (1992), 113.  doi: 10.1287/opre.40.1.113.  Google Scholar

[27]

A. P. J. Vepsalainen and T. E. Morton, Priority rules for job shops with weighted tardiness costs,, Management Science, 33 (1987), 1035.   Google Scholar

[28]

T. Yang, Z. He and K. K. Cho, An effective heuristic method for generalized job shop scheduling with due dates,, Computers and Industrial Engineering, 26 (1994), 647.   Google Scholar

[29]

C. Zhang, X. Shao, Y. Rao and H. Qiu, Some new results on tabu search algorithm applied to the job-shop scheduling problem, Tabu Search, Wassim Jaziri (Ed.), InTech, Available from: http://www.intechopen.com/articles/show/title/some_new_results_on_tabu_search_algorithm_applied_to_the_job-shop_scheduling_problem, (2008)., (2008).   Google Scholar

[30]

R. Zhang, A genetic local search algorithm based on insertion neighborhood for the job shop scheduling problem,, Advances in Information Sciences and Services, 3 (2011), 117.   Google Scholar

[31]

R. Zhang and C. Wu, A divide-and-conquer strategy with particle swarm optimization for the job shop scheduling problem,, Engineering Optimization, 42 (): 641.  doi: 10.1080/03052150903369845.  Google Scholar

[32]

R. Zhang and C. Wu, A hybrid immune simulated annealing algorithm for the job shop scheduling problem,, Applied Soft Computing, 10 (): 79.   Google Scholar

[33]

R. Zhang and C. Wu, A simulated annealing algorithm based on block properties for the job shop scheduling problem with total weighted tardiness objective,, Computers and Operations Research, 38 (2011), 854.  doi: 10.1016/j.cor.2010.09.014.  Google Scholar

[34]

R. Zhang, S. Song and C. Wu, A hybrid artificial bee colony algorithm for the job shop scheduling problem,, International Journal of Production Economics, 141 (2013), 167.   Google Scholar

[35]

H. Zhou, W. Cheung and L. C. Leung, Minimizing weighted tardiness of job-shop scheduling using a hybrid genetic algorithm,, European Journal of Operational Research, 194 (2009), 637.   Google Scholar

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