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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

Y. K. Lin 1, and  C. S. Chong 2,

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.
Keywords: Scheduling, total weighted tardiness., job shop, tabu search.
Mathematics Subject Classification: Primary: 90B35; Secondary: 68M2.
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 and 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), 2277-2292. doi: 10.1080/00207549008942866.

[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), 131-140. doi: 10.1016/S0925-5273(99)00014-6.

[3]

M. Asano and H. Ohta, A heuristic for job shop scheduling to minimize total weighted tardiness, Computers and Industrial Engineering, 42 (2002), 137-147. doi: 10.1016/S0360-8352(02)00019-0.

[4]

K. R. Baker, Sequencing rules and due date assignments in a job shop, Management Science, 30 (1984), 1093-1104. doi: 10.1287/mnsc.30.9.1093.

[5]

K. R. Baker and J. J. Kanet, Job shop scheduling with modified due dates, Journal of Operations Management, 4 (1983), 11-22. doi: 10.1016/0272-6963(83)90022-0.

[6]

E. Balas, Machine sequencing via disjunctive graph: an implicit enumeration algorithm, Operations Research, 17 (1969), 941-957. doi: 10.1287/opre.17.6.941.

[7]

K. M. J. Bontridder, Minimizing total weighted tardiness in a generalized job shop, Journal of Scheduling, 8 (2005), 479-496. doi: 10.1007/s10951-005-4779-7.

[8]

K. Bulbul, A hybrid shifting bottleneck-tabu search heuristic for the job shop total weighted tardiness problem, Computers and Operations Research, 38 (2011), 967-983. doi: 10.1016/j.cor.2010.09.015.

[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), 93-109. doi: 10.1080/09537287.2013.782846.

[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), 2599-2616. doi: 10.1016/j.cor.2006.12.019.

[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), 287-326. doi: 10.1016/S0167-5060(08)70356-X.

[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), 2677-2692. doi: 10.1080/00207549308956890.

[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), 457-480.

[14]

J. J. Kanet and J. C. Hayya, Priority dispatching with operation due dates in a job shop, Journal of Operations Management, 2 (1982), 167-175.

[15]

S. Kreipl, A large step random walk for minimizing total weighted tardiness in a job shop, Journal of Scheduling, 3 (2000), 125-138. doi: 10.1002/(SICI)1099-1425(200005/06)3:3<125::AID-JOS40>3.0.CO;2-C.

[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, A. H. G. Rinnooy Kan and P. H. Zipkin), 4 (1993), 445-522.

[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), 647-669.

[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), 33-42. doi: 10.1016/j.ejor.2011.01.046.

[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), 616-630. doi: 10.1016/S0377-2217(03)00016-X.

[20]

E. Nowicki and C. Smutnicki, A fast taboo search algorithm for the job shop problem, Management Science, 42 (1996), 797-813.

[21]

E. Nowicki and C. Smutnicki, An advanced tabu search algorithm for the job shop problem, Journal of Scheduling, 8 (2005), 145-159. doi: 10.1007/s10951-005-6364-5.

[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), 621-639.

[23]

M. Pinedo and M. Singer, A shifting bottleneck heuristic for minimizing the total weighted tardiness in job shop, Naval Research Logistics, 46 (1999), 1-17. doi: 10.1002/(SICI)1520-6750(199902)46:1<1::AID-NAV1>3.3.CO;2-R.

[24]

N. Raman and F. B. Talbot, The job shop tardiness problem: A decomposition approach, European Journal of Operational Research, 69 (1993), 187-199.

[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), 109-118.

[26]

P. J. M. Van Laarhoven, E. H. L. Aarts and J. K. Lenstra, Job shop scheduling by simulated annealing, Operations Research, 40 (1992), 113-125. doi: 10.1287/opre.40.1.113.

[27]

A. P. J. Vepsalainen and T. E. Morton, Priority rules for job shops with weighted tardiness costs, Management Science, 33 (1987), 1035-1047.

[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), 647-660.

[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).

[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), 117-125.

[31]

R. Zhang and C. Wu, A divide-and-conquer strategy with particle swarm optimization for the job shop scheduling problem, Engineering Optimization, 42 (2010a), 641-670. doi: 10.1080/03052150903369845.

[32]

R. Zhang and C. Wu, A hybrid immune simulated annealing algorithm for the job shop scheduling problem, Applied Soft Computing, 10 (2010b), 79-89.

[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), 854-867. doi: 10.1016/j.cor.2010.09.014.

[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), 167-178.

[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), 637-649.

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), 2277-2292. doi: 10.1080/00207549008942866.

[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), 131-140. doi: 10.1016/S0925-5273(99)00014-6.

[3]

M. Asano and H. Ohta, A heuristic for job shop scheduling to minimize total weighted tardiness, Computers and Industrial Engineering, 42 (2002), 137-147. doi: 10.1016/S0360-8352(02)00019-0.

[4]

K. R. Baker, Sequencing rules and due date assignments in a job shop, Management Science, 30 (1984), 1093-1104. doi: 10.1287/mnsc.30.9.1093.

[5]

K. R. Baker and J. J. Kanet, Job shop scheduling with modified due dates, Journal of Operations Management, 4 (1983), 11-22. doi: 10.1016/0272-6963(83)90022-0.

[6]

E. Balas, Machine sequencing via disjunctive graph: an implicit enumeration algorithm, Operations Research, 17 (1969), 941-957. doi: 10.1287/opre.17.6.941.

[7]

K. M. J. Bontridder, Minimizing total weighted tardiness in a generalized job shop, Journal of Scheduling, 8 (2005), 479-496. doi: 10.1007/s10951-005-4779-7.

[8]

K. Bulbul, A hybrid shifting bottleneck-tabu search heuristic for the job shop total weighted tardiness problem, Computers and Operations Research, 38 (2011), 967-983. doi: 10.1016/j.cor.2010.09.015.

[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), 93-109. doi: 10.1080/09537287.2013.782846.

[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), 2599-2616. doi: 10.1016/j.cor.2006.12.019.

[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), 287-326. doi: 10.1016/S0167-5060(08)70356-X.

[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), 2677-2692. doi: 10.1080/00207549308956890.

[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), 457-480.

[14]

J. J. Kanet and J. C. Hayya, Priority dispatching with operation due dates in a job shop, Journal of Operations Management, 2 (1982), 167-175.

[15]

S. Kreipl, A large step random walk for minimizing total weighted tardiness in a job shop, Journal of Scheduling, 3 (2000), 125-138. doi: 10.1002/(SICI)1099-1425(200005/06)3:3<125::AID-JOS40>3.0.CO;2-C.

[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, A. H. G. Rinnooy Kan and P. H. Zipkin), 4 (1993), 445-522.

[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), 647-669.

[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), 33-42. doi: 10.1016/j.ejor.2011.01.046.

[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), 616-630. doi: 10.1016/S0377-2217(03)00016-X.

[20]

E. Nowicki and C. Smutnicki, A fast taboo search algorithm for the job shop problem, Management Science, 42 (1996), 797-813.

[21]

E. Nowicki and C. Smutnicki, An advanced tabu search algorithm for the job shop problem, Journal of Scheduling, 8 (2005), 145-159. doi: 10.1007/s10951-005-6364-5.

[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), 621-639.

[23]

M. Pinedo and M. Singer, A shifting bottleneck heuristic for minimizing the total weighted tardiness in job shop, Naval Research Logistics, 46 (1999), 1-17. doi: 10.1002/(SICI)1520-6750(199902)46:1<1::AID-NAV1>3.3.CO;2-R.

[24]

N. Raman and F. B. Talbot, The job shop tardiness problem: A decomposition approach, European Journal of Operational Research, 69 (1993), 187-199.

[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), 109-118.

[26]

P. J. M. Van Laarhoven, E. H. L. Aarts and J. K. Lenstra, Job shop scheduling by simulated annealing, Operations Research, 40 (1992), 113-125. doi: 10.1287/opre.40.1.113.

[27]

A. P. J. Vepsalainen and T. E. Morton, Priority rules for job shops with weighted tardiness costs, Management Science, 33 (1987), 1035-1047.

[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), 647-660.

[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).

[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), 117-125.

[31]

R. Zhang and C. Wu, A divide-and-conquer strategy with particle swarm optimization for the job shop scheduling problem, Engineering Optimization, 42 (2010a), 641-670. doi: 10.1080/03052150903369845.

[32]

R. Zhang and C. Wu, A hybrid immune simulated annealing algorithm for the job shop scheduling problem, Applied Soft Computing, 10 (2010b), 79-89.

[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), 854-867. doi: 10.1016/j.cor.2010.09.014.

[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), 167-178.

[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), 637-649.

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