American Institute of Mathematical Sciences

Advanced
  • Previous Article
    Optimality conditions for $ E $-differentiable vector optimization problems with the multiple interval-valued objective function
  • JIMO Home
  • This Issue
  • Next Article
    Distributionally robust chance constrained problems under general moments information
November  2020, 16(6): 2943-2969. doi: 10.3934/jimo.2019088

An enhanced Genetic Algorithm with an innovative encoding strategy for flexible job-shop scheduling with operation and processing flexibility

Xuewen Huang 1, , Xiaotong Zhang 1, , Sardar M. N. Islam 2,, and  Carlos A. Vega-Mejía 2,3,

1. 

Faculty of Management and Economics, Dalian University of Technology, Dalian, Liaoning 116023, China
2. 

ISILC, Victoria University, Melbourne, Australia
3. 

Operations & Supply Chain Management Research Group, Universidad de La Sabana, Bogotá, Colombia

* Corresponding author: Sardar M. N. Islam

Received  November 2017 Revised  March 2019 Published  November 2020 Early access  July 2019

Fund Project: Xuewen Huang is supported by the National Science and Technology Plan of China under Grant No. 2015BAF09B01 and the China Scholarship under Grant No. 201606060170

This paper considers the Flexible Job-shop Scheduling Problem with Operation and Processing flexibility (FJSP-OP) with the objective of minimizing the makespan. A Genetic Algorithm based approach is presented to solve the FJSP-OP. For the performance improvement, a new and concise Four-Tuple Scheme (FTS) is proposed for modeling a job with operation and processing flexibility. Then, with the FTS, an enhanced Genetic Algorithm employing a more efficient encoding strategy is developed. The use of this encoding strategy ensures that the classic genetic operators can be adopted to the utmost extent without generating infeasible offspring. Experiments have validated the proposed approach, and the results have shown the effectiveness and high performance of the proposed approach.

Keywords: IPPS, flexible job-shop scheduling, operation flexibility, processing flexibility, Genetic Algorithm.
Mathematics Subject Classification: Primary: 90B35, 90C59; Secondary: 68M20.
Citation: Xuewen Huang, Xiaotong Zhang, Sardar M. N. Islam, Carlos A. Vega-Mejía. An enhanced Genetic Algorithm with an innovative encoding strategy for flexible job-shop scheduling with operation and processing flexibility. Journal of Industrial & Management Optimization, 2020, 16 (6) : 2943-2969. doi: 10.3934/jimo.2019088
References:
[1]

A. Azzouz, M. Ennigrou and L. B. Said, A hybrid algorithm for flexible job-shop scheduling problem with setup times, Int. J. of Prod. Mgmt. & Eng., 5 (2017), 23-30.  doi: 10.4995/ijpme.2017.6618.  Google Scholar

[2]

K. R. Baker, Introduction to Sequencing and Scheduling, Wiley, New York, 1974. Google Scholar

[3]

W. Banzhaf, The "molecula" traveling salesman, Bio. Cyber., 64 (1990), 7-14.   Google Scholar

[4]

A. Baykasoglu, Linguistic-based meta-heuristic optimization model for flexible job shop scheduling, Int. J. of Prod. Research, 40 (2002), 4523-4543.  doi: 10.1080/00207540210147043.  Google Scholar

[5]

A. Baykasoglu, L. Ozbakir and A. Sonmez, Using multiple objective tabu search and grammars to model and solve multi-objective flexible job shop scheduling problems, J. of Intell. Manufacturing, 15 (2004), 777-785.  doi: 10.1023/B:JIMS.0000042663.16199.84.  Google Scholar

[6]

S. Benjaafar and R. S. Ramakrishnan, Modelling, measurement and evaluation of sequencing flexibility in manufacturing systems, Int. J. of Prod. Research, 34 (1996), 1195-1220.  doi: 10.1080/00207549608904961.  Google Scholar

[7]

C. Bierwirth, D. C. Mattfeld and H. Kopfer, On permutation representations for scheduling problems, in International Conference on Parallel Problem Solving from Nature, Lecture Notes in Computer Science, 1141, Springer, Berlin, 1996,310–318. doi: 10.1007/3-540-61723-X_995.  Google Scholar

[8]

C. Bierwirth and D. Mattfeld, Production scheduling and rescheduling with genetic algorithms, Evol. Computation, 7 (1999), 1-17.  doi: 10.1162/evco.1999.7.1.1.  Google Scholar

[9]

P. Brandimarte, Routing and scheduling in a flexible job shop by tabu search, Annals of Ops. Research, 41 (1993), 157-183.  doi: 10.1007/BF02023073.  Google Scholar

[10]

I. A. Chaudhry and M. Usman, Integrated process planning and scheduling using genetic algorithms, Tehnicki Vjesnik, 24 (2017), 1401-1409.  doi: 10.17559/TV-20151121212910.  Google Scholar

[11]

R. Cheng, M. Gen and Y. Tsujimura, A tutorial survey of job-shop scheduling problems using genetic algorithms-Ⅰ. Representation, Comp. & Indust. Engineering, 30 (1996), 983-997.  doi: 10.1016/0360-8352(96)00047-2.  Google Scholar

[12]

R. Cheng, M. Gen and Y. Tsujimura, A tutorial survey of job-shop scheduling problems using genetic algorithms: Part Ⅱ. Hybrid genetic search strategies, Comp. & Indust. Engineering, 37 (1999), 51-55.  doi: 10.1016/s0360-8352(99)00022-4.  Google Scholar

[13]

G. Chryssolouris, S. Chan and W. Cobb, Decision making on the factory floor: An integrated approach to process planning and scheduling, Robotics & Comp. Integ. Manufacturing, 1 (1984), 315-319.  doi: 10.1016/0736-5845(84)90020-6.  Google Scholar

[14]

G. Chryssolouris, S. Chan and N. P. Suh, An integrated approach to process planning and scheduling, CIRP Annals - Manufacturing Tech., 34 (1985), 413-417.  doi: 10.1016/S0007-8506(07)61801-0.  Google Scholar

[15]

D. A. Dabney, L. Green and V. Topalli, A priority-based heuristic algorithm (PBHA) for optimizing integrated process planning and scheduling problem, J. of Criminal Justice Edu., 2 (2015), 44-68.  doi: 10.1080/23311916.2015.1070494.  Google Scholar

[16]

L. Davis, Job shop scheduling with genetic algorithms, In: International Conference on Genetic Algorithms, L. Erlbaum Asssociates Inc., Hillsdale, 1985, 136–140. Google Scholar

[17]

H. H. Doh, J. M. Yu, J. S. Kim, D. H. Lee and S. H. Nam, A priority scheduling approach for flexible job shops with multiple process plans, Int. J. of Prod. Research, 51 (2013), 3748-3764.  doi: 10.1080/00207543.2013.765074.  Google Scholar

[18]

D. B. Fogel, An evolutionary approach to the traveling salesman problem, Bio. Cybernetics, 60 (1988), 139-144.  doi: 10.1007/BF00202901.  Google Scholar

[19]

J. Gao, M. Gen, L. Sun and X. Zhao, A hybrid of genetic algorithm and bottleneck shifting for multiobjective flexible job shop scheduling problems, Comp. & Indust. Engineering, 53 (2007), 149-162.  doi: 10.1016/j.cie.2007.04.010.  Google Scholar

[20]

K. Z. Gao, P. N. Suganthan, T. J. Chua, C. S. Chong, T. X. Cai and Q. K. Pan, A two-stage artificial bee colony algorithm scheduling flexible job-shop scheduling problem with new job insertion, Expert Syst. with Appl., 42 (2015), 7652-7663.  doi: 10.1016/j.eswa.2015.06.004.  Google Scholar

[21]

M. Gen, Y. Tsujimura and E. Kubota, Solving job-shop scheduling problems by genetic algorithm, in IEEE International Conference on Systems, (1994), 576–579. doi: 10.1109/ICSMC.1994.400072.  Google Scholar

[22]

M. Gen and R. Cheng, Genetic Algorithms and Engineering Optimization, John Wiley & Sons, 2000. doi: 10.1002/9780470172261.  Google Scholar

[23]

D. E. Goldberg and R. Lingle, Alleles, loci and the traveling salesman problem, Proc. of 1st Int. Conf. on Genetic Algorithms and Their Applications, 12 (1985), 154-159.   Google Scholar

[24]

N. B. Ho, J. C. Tay and M. K. Lai, An effective architecture for learning and evolving flexible job-shop schedules, European J. of Oper. Research, 179 (2007), 316-333.  doi: 10.1016/j.ejor.2006.04.007.  Google Scholar

[25]

Y. C. Ho and C. L. Moodie, Solving cell formation problems in a manufacturing environment with flexible processing and routing capabilities, Int. J. of Prod. Research, 34 (1996), 2901-2923.  doi: 10.1080/00207549608905065.  Google Scholar

[26] J. H. Holland, Adaptation in Natural and Artificial Systems, University of Michigan Press, Ann Arbor, Mich., 1975.   Google Scholar
[27]

K. Ida and K. Oka, Flexible job-shop scheduling problem by genetic algorithm, Electrical Engineering in Japan, 177 (2011), 28-35.  doi: 10.1002/eej.21194.  Google Scholar

[28]

L. Jin, Q. Tang, C. Zhang, X. Shao and G. Tian, More MILP models for integrated process planning and scheduling, Int. J. of Prod. Research, 54 (2016), 4387-4402.  doi: 10.1080/00207543.2016.1140917.  Google Scholar

[29]

B. Khoshnevis and Q. M. Chen, Integration of process planning and scheduling functions, J. of Intell. Manufacturing, 2 (1991), 165-175.  doi: 10.1007/BF01471363.  Google Scholar

[30]

Y. K. Kim, J. Y. Kim and K. S. Shin, An asymmetric multileveled symbiotic evolutionary algorithm for integrated FMS scheduling, J. of Intell. Manufacturing, 18 (2007), 631-645.  doi: 10.1007/s10845-007-0037-5.  Google Scholar

[31]

Y. K. Kim, K. Park and J. Ko, A symbiotic evolutionary algorithm for the integration of process planning and job shop scheduling, Comp. & Ops. Research, 30 (2003), 1151-1171.  doi: 10.1016/S0305-0548(02)00063-1.  Google Scholar

[32]

T. Kis, Job-shop scheduling with processing alternatives, European J. of Oper. Research, 151 (2003), 307-332.  doi: 10.1016/S0377-2217(02)00828-7.  Google Scholar

[33]

R. Kumar, M. K. Tiwari and R. Shankar, Scheduling of flexible manufacturing systems: An ant colony optimization approach, Proceedings of the Inst. of Mech. Engineers Part B: J. of Engineering Manufacture, 217 (2003), 1443-1453.  doi: 10.1243/095440503322617216.  Google Scholar

[34]

A. Ławrynowicz, Integration of production planning and scheduling using an expert system and a genetic algorithm, J. of the Oper. Research Society, 59 (2008), 455-463.  doi: 10.1057/palgrave.jors.2602423.  Google Scholar

[35]

H. Lee and S. S. Kim, Integration of process planning and scheduling using simulation based genetic algorithms, The Int. J. of Adv. Manufacturing Tech., 18 (2001), 586-590.  doi: 10.1007/s001700170035.  Google Scholar

[36]

K. M. Lee, T. Yamakawa and K. M. Lee, A genetic algorithm for general machine scheduling problems, Int. J. of Knowledge-Based Intell. Electronic Systems, 2 (1998), 60-66.  doi: 10.1109/KES.1998.725893.  Google Scholar

[37]

X. Y. Li and L. Gao, An effective hybrid genetic algorithm and tabu search for flexible job shop scheduling problem, Int. J. of Prod. Economics, 174 (2016), 93-110.  doi: 10.1016/j.ijpe.2016.01.016.  Google Scholar

[38]

X. Y. Li, L. Gao, X. Shao, C. Zhang and C. Wang, Mathematical modeling and evolutionary algorithm-based approach for integrated process planning and scheduling, Comp. & Ops. Research, 37 (2010), 656-667.  doi: 10.1016/j.cor.2009.06.008.  Google Scholar

[39]

X. Y. Li, L. Gao and X. Y. Shao, An active learning genetic algorithm for integrated process planning and scheduling, Expert Syst. with Appl., 39 (2012), 6683-6691.  doi: 10.1016/j.eswa.2011.11.074.  Google Scholar

[40]

X. Y. Li, X. Y. Shao, L. Gao and W. Qian, An effective hybrid algorithm for integrated process planning and scheduling, Int. J. of Prod. Economics, 126 (2010), 289-298.  doi: 10.1016/j.ijpe.2010.04.001.  Google Scholar

[41]

X. Y. Li, C. Zhang, L. Gao, W. Li and X. Y. Shao, An agent-based approach for integrated process planning and scheduling, Expert Syst. with Appl., 37 (2010), 1256-1264.  doi: 10.1016/j.eswa.2009.06.014.  Google Scholar

[42]

Y. J. Lin and J. J. Solberg, Effectiveness of flexible routing control, Int. J. of Flexible Manufacturing Syst., 3 (1991), 189-211.  doi: 10.1007/BF00170206.  Google Scholar

[43]

M. Liu, S. Yi and P. Wen, Quantum-inspired hybrid algorithm for integrated process planning and scheduling, Proceedings of the Inst. of Mech. Engineers Part B: J. of Engineering Manufacture, 232 (2016), 1-18.  doi: 10.1177/0954405416661006.  Google Scholar

[44]

G. Luo, X. Wen, H. Li, W. Ming and G. Xie, An effective multi-objective genetic algorithm based on immune principle and external archive for multi-objective integrated process planning and scheduling, Int. J. of Adv. Manufacturing Tech., 91 (2017), 3145-3158.  doi: 10.1007/s00170-017-0020-z.  Google Scholar

[45]

V. K. Manupati, G. D. Putnik, M. K. Tiwari, P. Ávila and M. M. Cruz-Cunha, Integration of process planning and scheduling using mobile-agent based approach in a networked manufacturing environment, Comp. & Industrial Engineering, 94 (2016), 63-73.  doi: 10.1016/j.cie.2016.01.017.  Google Scholar

[46]

Z. Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs, Second edition, Springer-Verlag, Berlin, 1994. doi: 10.1007/978-3-662-02830-8.  Google Scholar

[47]

C. Moon, Y. H. Lee, C. S. Jeong and Y. S. Yun, Integrated process planning and scheduling in a supply chain, Comp. & Indust. Engineering, 54 (2008), 1048-1061.  doi: 10.1016/j.cie.2007.06.018.  Google Scholar

[48]

N. Morad and A. Zalzala, Genetic algorithms in integrated process planning and scheduling, J. of Intell. Manufacturing, 10 (1999), 169-179.  doi: 10.1023/a:1008976720878.  Google Scholar

[49]

H. E. Nouri, O. B. Driss and K. Ghédira, Solving the flexible job shop problem by hybrid metaheuristics-based multiagent model, J. of Indust. Engineering Int., 14 (2018), 1-14.  doi: 10.1007/s40092-017-0204-z.  Google Scholar

[50]

M. Nouiri, A. Bekrar, A. Jemai, S. Niar and A. C. Ammari, An effective and distributed particle swarm optimization algorithm for flexible job-shop scheduling problem, J. of Intell. Manufacturing, 29 (2018), 603-615.  doi: 10.1007/s10845-015-1039-3.  Google Scholar

[51]

C. Özgüven, L. Özbakır and Y. Yavuz, Mathematical models for job-shop scheduling problems with routing and process plan flexibility, Appl. Math. Modelling, 34 (2010), 1539-1548.  doi: 10.1016/j.apm.2009.09.002.  Google Scholar

[52]

J. J. Palacios, M. A. González, C. R. Vela, I. González-Rodríguez and J. Puente, Genetic tabu search for the fuzzy flexible job shop problem, Comp. & Ops. Research, 54 (2015), 74-89.  doi: 10.1016/j.cor.2014.08.023.  Google Scholar

[53]

M. Petroviä, J. Petronijeviä, M. Mitiä, N. Vukoviä, Z. Miljkoviä and B. Babiä, The ant lion optimization algorithm for integrated process planning and scheduling, Appl. Mechanics & Materials, 834 (2016), 187-192.   Google Scholar

[54]

R. K. Phanden, A. Jain and R. Verma, Integration of process planning and scheduling: A state-of-the-art review, Int. J. of Comp. Integrated Manufacturing, 24 (2011), 517-534.  doi: 10.1080/0951192X.2011.562543.  Google Scholar

[55]

L. Qiao and S. Lv, An improved genetic algorithm for integrated process planning and scheduling, The Int. J. of Adv. Manufacturing Tech., 58 (2012), 727-740.  doi: 10.1007/s00170-011-3409-0.  Google Scholar

[56]

A. Rajabinasab and S. Mansour, Dynamic flexible job shop scheduling with alternative process plans: An agent-based approach, The Int. J. of Adv. Manufacturing Tech., 54 (2011), 1091-1107.  doi: 10.1007/s00170-010-2986-7.  Google Scholar

[57]

C. Saygin and S. E. Kilic, Integrating flexible process plans with scheduling in flexible manufacturing systems, The Int. J. of Adv. Manufacturing Tech., 15 (1999), 268-280.  doi: 10.1007/s001700050066.  Google Scholar

[58]

X. Y. Shao, X. Y. Li, L. Gao and C. Y. Zhang, Integration of process planning and scheduling-a modified genetic algorithm-based approach, Comp. & Ops. Research, 36 (2009), 2082-2096.  doi: 10.1016/j.cor.2008.07.006.  Google Scholar

[59]

O. Sobeyko and L. Mã¶Nch, Integrated process planning and scheduling for large-scale flexible job shops using metaheuristics, Int. J. of Prod. Research, 55 (2017), 392-409.  doi: 10.1080/00207543.2016.1182227.  Google Scholar

[60]

D. Sreeramulu, Y. Sagar, P. Suman and A. S. Kumar, Integration of process planning and scheduling of a manufacturing systems using petri nets and genetic algorithm, Indian J. of Science & Tech., 9 (2016), 2-8.  doi: 10.17485/ijst/2016/v9i41/100874.  Google Scholar

[61]

G. Syswerda, Uniform Crossover in Genetic Algorithms, International Conference on Genetic Algorithms, (1989), 2–9. Google Scholar

[62]

Z. Wang and T. Ju, The research about integration of process planning and production scheduling based on genetic algorithm, International Conference on Computer Science and Software Engineering, (2008), 9–12. doi: 10.1109/CSSE.2008.845.  Google Scholar

[63]

T. N. Wong, C. W. Leung, K. L. Mak and R. Y. K. Fung, An agent-based negotiation approach to integrate process planning and scheduling, Int. J. of Prod. Research, 44 (2006), 1331-1351.  doi: 10.1080/00207540500409723.  Google Scholar

[64]

T. N. Wong, C. W. Leung, K. L. Mak and R. Y. K. Fung, Integrated process planning and scheduling/rescheduling-an agent-based approach, Int. J. of Prod. Research, 44 (2006), 3627-3655.  doi: 10.1080/00207540600675801.  Google Scholar

[65]

T. N. Wong, S. C. Zhang, G. Wang and L. P. Zhang, Integrated process planning and scheduling – multi-agent system with two-stage ant colony optimisation algorithm, Int. J. of Prod. Research, 50 (2012), 6188-6201.  doi: 10.1080/00207543.2012.720393.  Google Scholar

[66]

H. Xia, X. Li and L. Gao, A hybrid genetic algorithm with variable neighborhood search for dynamic integrated process planning and scheduling, Comp. & Indust. Engineering, 102 (2016), 99-112.  doi: 10.1016/j.cie.2016.10.015.  Google Scholar

[67]

L. Yin, L. Gao, X. Li and H. Xia, An improved genetic algorithm with rolling window technology for dynamic integrated process planning and scheduling problem, IEEE International Conference on Computer Supported Cooperative Work in Design, (2017), 414–419. doi: 10.1109/CSCWD.2017.8066730.  Google Scholar

[68]

Y. Yuan and H. Xu, Multiobjective flexible job shop scheduling using memetic algorithms, IEEE Transactions on Automation Science and Engineering, 12 (2015), 336-353.  doi: 10.1109/TASE.2013.2274517.  Google Scholar

[69]

G. Zhang, L. Zhang, X. Song, Y. Wang and C. Zhou, A variable neighborhood search based genetic algorithm for flexible job shop scheduling problem, Cluster Computing, (2018), 1–12. doi: 10.1007/s10586-017-1420-4.  Google Scholar

[70]

S. Zhang and T. N. Wong, Integrated process planning and scheduling: An enhanced ant colony optimization heuristic with parameter tuning, J. of Intell. Manufacturing, 29 (2018), 585-601.  doi: 10.1007/s10845-014-1023-3.  Google Scholar

[71]

L. Zhang and T. N. Wong, An object-coding genetic algorithm for integrated process planning and scheduling, European J. of Oper. Research, 244 (2015), 434-444.  doi: 10.1016/j.ejor.2015.01.032.  Google Scholar

[72]

S. Zhang, Z. Yu, W. Zhang, D. Yu and Y. Xu, An extended genetic algorithm for distributed integration of fuzzy process planning and scheduling, Math. Problems in Engineering, 3 (2016), 1-13.  doi: 10.1155/2016/3763512.  Google Scholar

show all references

References:
[1]

A. Azzouz, M. Ennigrou and L. B. Said, A hybrid algorithm for flexible job-shop scheduling problem with setup times, Int. J. of Prod. Mgmt. & Eng., 5 (2017), 23-30.  doi: 10.4995/ijpme.2017.6618.  Google Scholar

[2]

K. R. Baker, Introduction to Sequencing and Scheduling, Wiley, New York, 1974. Google Scholar

[3]

W. Banzhaf, The "molecula" traveling salesman, Bio. Cyber., 64 (1990), 7-14.   Google Scholar

[4]

A. Baykasoglu, Linguistic-based meta-heuristic optimization model for flexible job shop scheduling, Int. J. of Prod. Research, 40 (2002), 4523-4543.  doi: 10.1080/00207540210147043.  Google Scholar

[5]

A. Baykasoglu, L. Ozbakir and A. Sonmez, Using multiple objective tabu search and grammars to model and solve multi-objective flexible job shop scheduling problems, J. of Intell. Manufacturing, 15 (2004), 777-785.  doi: 10.1023/B:JIMS.0000042663.16199.84.  Google Scholar

[6]

S. Benjaafar and R. S. Ramakrishnan, Modelling, measurement and evaluation of sequencing flexibility in manufacturing systems, Int. J. of Prod. Research, 34 (1996), 1195-1220.  doi: 10.1080/00207549608904961.  Google Scholar

[7]

C. Bierwirth, D. C. Mattfeld and H. Kopfer, On permutation representations for scheduling problems, in International Conference on Parallel Problem Solving from Nature, Lecture Notes in Computer Science, 1141, Springer, Berlin, 1996,310–318. doi: 10.1007/3-540-61723-X_995.  Google Scholar

[8]

C. Bierwirth and D. Mattfeld, Production scheduling and rescheduling with genetic algorithms, Evol. Computation, 7 (1999), 1-17.  doi: 10.1162/evco.1999.7.1.1.  Google Scholar

[9]

P. Brandimarte, Routing and scheduling in a flexible job shop by tabu search, Annals of Ops. Research, 41 (1993), 157-183.  doi: 10.1007/BF02023073.  Google Scholar

[10]

I. A. Chaudhry and M. Usman, Integrated process planning and scheduling using genetic algorithms, Tehnicki Vjesnik, 24 (2017), 1401-1409.  doi: 10.17559/TV-20151121212910.  Google Scholar

[11]

R. Cheng, M. Gen and Y. Tsujimura, A tutorial survey of job-shop scheduling problems using genetic algorithms-Ⅰ. Representation, Comp. & Indust. Engineering, 30 (1996), 983-997.  doi: 10.1016/0360-8352(96)00047-2.  Google Scholar

[12]

R. Cheng, M. Gen and Y. Tsujimura, A tutorial survey of job-shop scheduling problems using genetic algorithms: Part Ⅱ. Hybrid genetic search strategies, Comp. & Indust. Engineering, 37 (1999), 51-55.  doi: 10.1016/s0360-8352(99)00022-4.  Google Scholar

[13]

G. Chryssolouris, S. Chan and W. Cobb, Decision making on the factory floor: An integrated approach to process planning and scheduling, Robotics & Comp. Integ. Manufacturing, 1 (1984), 315-319.  doi: 10.1016/0736-5845(84)90020-6.  Google Scholar

[14]

G. Chryssolouris, S. Chan and N. P. Suh, An integrated approach to process planning and scheduling, CIRP Annals - Manufacturing Tech., 34 (1985), 413-417.  doi: 10.1016/S0007-8506(07)61801-0.  Google Scholar

[15]

D. A. Dabney, L. Green and V. Topalli, A priority-based heuristic algorithm (PBHA) for optimizing integrated process planning and scheduling problem, J. of Criminal Justice Edu., 2 (2015), 44-68.  doi: 10.1080/23311916.2015.1070494.  Google Scholar

[16]

L. Davis, Job shop scheduling with genetic algorithms, In: International Conference on Genetic Algorithms, L. Erlbaum Asssociates Inc., Hillsdale, 1985, 136–140. Google Scholar

[17]

H. H. Doh, J. M. Yu, J. S. Kim, D. H. Lee and S. H. Nam, A priority scheduling approach for flexible job shops with multiple process plans, Int. J. of Prod. Research, 51 (2013), 3748-3764.  doi: 10.1080/00207543.2013.765074.  Google Scholar

[18]

D. B. Fogel, An evolutionary approach to the traveling salesman problem, Bio. Cybernetics, 60 (1988), 139-144.  doi: 10.1007/BF00202901.  Google Scholar

[19]

J. Gao, M. Gen, L. Sun and X. Zhao, A hybrid of genetic algorithm and bottleneck shifting for multiobjective flexible job shop scheduling problems, Comp. & Indust. Engineering, 53 (2007), 149-162.  doi: 10.1016/j.cie.2007.04.010.  Google Scholar

[20]

K. Z. Gao, P. N. Suganthan, T. J. Chua, C. S. Chong, T. X. Cai and Q. K. Pan, A two-stage artificial bee colony algorithm scheduling flexible job-shop scheduling problem with new job insertion, Expert Syst. with Appl., 42 (2015), 7652-7663.  doi: 10.1016/j.eswa.2015.06.004.  Google Scholar

[21]

M. Gen, Y. Tsujimura and E. Kubota, Solving job-shop scheduling problems by genetic algorithm, in IEEE International Conference on Systems, (1994), 576–579. doi: 10.1109/ICSMC.1994.400072.  Google Scholar

[22]

M. Gen and R. Cheng, Genetic Algorithms and Engineering Optimization, John Wiley & Sons, 2000. doi: 10.1002/9780470172261.  Google Scholar

[23]

D. E. Goldberg and R. Lingle, Alleles, loci and the traveling salesman problem, Proc. of 1st Int. Conf. on Genetic Algorithms and Their Applications, 12 (1985), 154-159.   Google Scholar

[24]

N. B. Ho, J. C. Tay and M. K. Lai, An effective architecture for learning and evolving flexible job-shop schedules, European J. of Oper. Research, 179 (2007), 316-333.  doi: 10.1016/j.ejor.2006.04.007.  Google Scholar

[25]

Y. C. Ho and C. L. Moodie, Solving cell formation problems in a manufacturing environment with flexible processing and routing capabilities, Int. J. of Prod. Research, 34 (1996), 2901-2923.  doi: 10.1080/00207549608905065.  Google Scholar

[26] J. H. Holland, Adaptation in Natural and Artificial Systems, University of Michigan Press, Ann Arbor, Mich., 1975.   Google Scholar
[27]

K. Ida and K. Oka, Flexible job-shop scheduling problem by genetic algorithm, Electrical Engineering in Japan, 177 (2011), 28-35.  doi: 10.1002/eej.21194.  Google Scholar

[28]

L. Jin, Q. Tang, C. Zhang, X. Shao and G. Tian, More MILP models for integrated process planning and scheduling, Int. J. of Prod. Research, 54 (2016), 4387-4402.  doi: 10.1080/00207543.2016.1140917.  Google Scholar

[29]

B. Khoshnevis and Q. M. Chen, Integration of process planning and scheduling functions, J. of Intell. Manufacturing, 2 (1991), 165-175.  doi: 10.1007/BF01471363.  Google Scholar

[30]

Y. K. Kim, J. Y. Kim and K. S. Shin, An asymmetric multileveled symbiotic evolutionary algorithm for integrated FMS scheduling, J. of Intell. Manufacturing, 18 (2007), 631-645.  doi: 10.1007/s10845-007-0037-5.  Google Scholar

[31]

Y. K. Kim, K. Park and J. Ko, A symbiotic evolutionary algorithm for the integration of process planning and job shop scheduling, Comp. & Ops. Research, 30 (2003), 1151-1171.  doi: 10.1016/S0305-0548(02)00063-1.  Google Scholar

[32]

T. Kis, Job-shop scheduling with processing alternatives, European J. of Oper. Research, 151 (2003), 307-332.  doi: 10.1016/S0377-2217(02)00828-7.  Google Scholar

[33]

R. Kumar, M. K. Tiwari and R. Shankar, Scheduling of flexible manufacturing systems: An ant colony optimization approach, Proceedings of the Inst. of Mech. Engineers Part B: J. of Engineering Manufacture, 217 (2003), 1443-1453.  doi: 10.1243/095440503322617216.  Google Scholar

[34]

A. Ławrynowicz, Integration of production planning and scheduling using an expert system and a genetic algorithm, J. of the Oper. Research Society, 59 (2008), 455-463.  doi: 10.1057/palgrave.jors.2602423.  Google Scholar

[35]

H. Lee and S. S. Kim, Integration of process planning and scheduling using simulation based genetic algorithms, The Int. J. of Adv. Manufacturing Tech., 18 (2001), 586-590.  doi: 10.1007/s001700170035.  Google Scholar

[36]

K. M. Lee, T. Yamakawa and K. M. Lee, A genetic algorithm for general machine scheduling problems, Int. J. of Knowledge-Based Intell. Electronic Systems, 2 (1998), 60-66.  doi: 10.1109/KES.1998.725893.  Google Scholar

[37]

X. Y. Li and L. Gao, An effective hybrid genetic algorithm and tabu search for flexible job shop scheduling problem, Int. J. of Prod. Economics, 174 (2016), 93-110.  doi: 10.1016/j.ijpe.2016.01.016.  Google Scholar

[38]

X. Y. Li, L. Gao, X. Shao, C. Zhang and C. Wang, Mathematical modeling and evolutionary algorithm-based approach for integrated process planning and scheduling, Comp. & Ops. Research, 37 (2010), 656-667.  doi: 10.1016/j.cor.2009.06.008.  Google Scholar

[39]

X. Y. Li, L. Gao and X. Y. Shao, An active learning genetic algorithm for integrated process planning and scheduling, Expert Syst. with Appl., 39 (2012), 6683-6691.  doi: 10.1016/j.eswa.2011.11.074.  Google Scholar

[40]

X. Y. Li, X. Y. Shao, L. Gao and W. Qian, An effective hybrid algorithm for integrated process planning and scheduling, Int. J. of Prod. Economics, 126 (2010), 289-298.  doi: 10.1016/j.ijpe.2010.04.001.  Google Scholar

[41]

X. Y. Li, C. Zhang, L. Gao, W. Li and X. Y. Shao, An agent-based approach for integrated process planning and scheduling, Expert Syst. with Appl., 37 (2010), 1256-1264.  doi: 10.1016/j.eswa.2009.06.014.  Google Scholar

[42]

Y. J. Lin and J. J. Solberg, Effectiveness of flexible routing control, Int. J. of Flexible Manufacturing Syst., 3 (1991), 189-211.  doi: 10.1007/BF00170206.  Google Scholar

[43]

M. Liu, S. Yi and P. Wen, Quantum-inspired hybrid algorithm for integrated process planning and scheduling, Proceedings of the Inst. of Mech. Engineers Part B: J. of Engineering Manufacture, 232 (2016), 1-18.  doi: 10.1177/0954405416661006.  Google Scholar

[44]

G. Luo, X. Wen, H. Li, W. Ming and G. Xie, An effective multi-objective genetic algorithm based on immune principle and external archive for multi-objective integrated process planning and scheduling, Int. J. of Adv. Manufacturing Tech., 91 (2017), 3145-3158.  doi: 10.1007/s00170-017-0020-z.  Google Scholar

[45]

V. K. Manupati, G. D. Putnik, M. K. Tiwari, P. Ávila and M. M. Cruz-Cunha, Integration of process planning and scheduling using mobile-agent based approach in a networked manufacturing environment, Comp. & Industrial Engineering, 94 (2016), 63-73.  doi: 10.1016/j.cie.2016.01.017.  Google Scholar

[46]

Z. Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs, Second edition, Springer-Verlag, Berlin, 1994. doi: 10.1007/978-3-662-02830-8.  Google Scholar

[47]

C. Moon, Y. H. Lee, C. S. Jeong and Y. S. Yun, Integrated process planning and scheduling in a supply chain, Comp. & Indust. Engineering, 54 (2008), 1048-1061.  doi: 10.1016/j.cie.2007.06.018.  Google Scholar

[48]

N. Morad and A. Zalzala, Genetic algorithms in integrated process planning and scheduling, J. of Intell. Manufacturing, 10 (1999), 169-179.  doi: 10.1023/a:1008976720878.  Google Scholar

[49]

H. E. Nouri, O. B. Driss and K. Ghédira, Solving the flexible job shop problem by hybrid metaheuristics-based multiagent model, J. of Indust. Engineering Int., 14 (2018), 1-14.  doi: 10.1007/s40092-017-0204-z.  Google Scholar

[50]

M. Nouiri, A. Bekrar, A. Jemai, S. Niar and A. C. Ammari, An effective and distributed particle swarm optimization algorithm for flexible job-shop scheduling problem, J. of Intell. Manufacturing, 29 (2018), 603-615.  doi: 10.1007/s10845-015-1039-3.  Google Scholar

[51]

C. Özgüven, L. Özbakır and Y. Yavuz, Mathematical models for job-shop scheduling problems with routing and process plan flexibility, Appl. Math. Modelling, 34 (2010), 1539-1548.  doi: 10.1016/j.apm.2009.09.002.  Google Scholar

[52]

J. J. Palacios, M. A. González, C. R. Vela, I. González-Rodríguez and J. Puente, Genetic tabu search for the fuzzy flexible job shop problem, Comp. & Ops. Research, 54 (2015), 74-89.  doi: 10.1016/j.cor.2014.08.023.  Google Scholar

[53]

M. Petroviä, J. Petronijeviä, M. Mitiä, N. Vukoviä, Z. Miljkoviä and B. Babiä, The ant lion optimization algorithm for integrated process planning and scheduling, Appl. Mechanics & Materials, 834 (2016), 187-192.   Google Scholar

[54]

R. K. Phanden, A. Jain and R. Verma, Integration of process planning and scheduling: A state-of-the-art review, Int. J. of Comp. Integrated Manufacturing, 24 (2011), 517-534.  doi: 10.1080/0951192X.2011.562543.  Google Scholar

[55]

L. Qiao and S. Lv, An improved genetic algorithm for integrated process planning and scheduling, The Int. J. of Adv. Manufacturing Tech., 58 (2012), 727-740.  doi: 10.1007/s00170-011-3409-0.  Google Scholar

[56]

A. Rajabinasab and S. Mansour, Dynamic flexible job shop scheduling with alternative process plans: An agent-based approach, The Int. J. of Adv. Manufacturing Tech., 54 (2011), 1091-1107.  doi: 10.1007/s00170-010-2986-7.  Google Scholar

[57]

C. Saygin and S. E. Kilic, Integrating flexible process plans with scheduling in flexible manufacturing systems, The Int. J. of Adv. Manufacturing Tech., 15 (1999), 268-280.  doi: 10.1007/s001700050066.  Google Scholar

[58]

X. Y. Shao, X. Y. Li, L. Gao and C. Y. Zhang, Integration of process planning and scheduling-a modified genetic algorithm-based approach, Comp. & Ops. Research, 36 (2009), 2082-2096.  doi: 10.1016/j.cor.2008.07.006.  Google Scholar

[59]

O. Sobeyko and L. Mã¶Nch, Integrated process planning and scheduling for large-scale flexible job shops using metaheuristics, Int. J. of Prod. Research, 55 (2017), 392-409.  doi: 10.1080/00207543.2016.1182227.  Google Scholar

[60]

D. Sreeramulu, Y. Sagar, P. Suman and A. S. Kumar, Integration of process planning and scheduling of a manufacturing systems using petri nets and genetic algorithm, Indian J. of Science & Tech., 9 (2016), 2-8.  doi: 10.17485/ijst/2016/v9i41/100874.  Google Scholar

[61]

G. Syswerda, Uniform Crossover in Genetic Algorithms, International Conference on Genetic Algorithms, (1989), 2–9. Google Scholar

[62]

Z. Wang and T. Ju, The research about integration of process planning and production scheduling based on genetic algorithm, International Conference on Computer Science and Software Engineering, (2008), 9–12. doi: 10.1109/CSSE.2008.845.  Google Scholar

[63]

T. N. Wong, C. W. Leung, K. L. Mak and R. Y. K. Fung, An agent-based negotiation approach to integrate process planning and scheduling, Int. J. of Prod. Research, 44 (2006), 1331-1351.  doi: 10.1080/00207540500409723.  Google Scholar

[64]

T. N. Wong, C. W. Leung, K. L. Mak and R. Y. K. Fung, Integrated process planning and scheduling/rescheduling-an agent-based approach, Int. J. of Prod. Research, 44 (2006), 3627-3655.  doi: 10.1080/00207540600675801.  Google Scholar

[65]

T. N. Wong, S. C. Zhang, G. Wang and L. P. Zhang, Integrated process planning and scheduling – multi-agent system with two-stage ant colony optimisation algorithm, Int. J. of Prod. Research, 50 (2012), 6188-6201.  doi: 10.1080/00207543.2012.720393.  Google Scholar

[66]

H. Xia, X. Li and L. Gao, A hybrid genetic algorithm with variable neighborhood search for dynamic integrated process planning and scheduling, Comp. & Indust. Engineering, 102 (2016), 99-112.  doi: 10.1016/j.cie.2016.10.015.  Google Scholar

[67]

L. Yin, L. Gao, X. Li and H. Xia, An improved genetic algorithm with rolling window technology for dynamic integrated process planning and scheduling problem, IEEE International Conference on Computer Supported Cooperative Work in Design, (2017), 414–419. doi: 10.1109/CSCWD.2017.8066730.  Google Scholar

[68]

Y. Yuan and H. Xu, Multiobjective flexible job shop scheduling using memetic algorithms, IEEE Transactions on Automation Science and Engineering, 12 (2015), 336-353.  doi: 10.1109/TASE.2013.2274517.  Google Scholar

[69]

G. Zhang, L. Zhang, X. Song, Y. Wang and C. Zhou, A variable neighborhood search based genetic algorithm for flexible job shop scheduling problem, Cluster Computing, (2018), 1–12. doi: 10.1007/s10586-017-1420-4.  Google Scholar

[70]

S. Zhang and T. N. Wong, Integrated process planning and scheduling: An enhanced ant colony optimization heuristic with parameter tuning, J. of Intell. Manufacturing, 29 (2018), 585-601.  doi: 10.1007/s10845-014-1023-3.  Google Scholar

[71]

L. Zhang and T. N. Wong, An object-coding genetic algorithm for integrated process planning and scheduling, European J. of Oper. Research, 244 (2015), 434-444.  doi: 10.1016/j.ejor.2015.01.032.  Google Scholar

[72]

S. Zhang, Z. Yu, W. Zhang, D. Yu and Y. Xu, An extended genetic algorithm for distributed integration of fuzzy process planning and scheduling, Math. Problems in Engineering, 3 (2016), 1-13.  doi: 10.1155/2016/3763512.  Google Scholar

Figure 1.  Alternative process plans networks
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 2.  An illustrative chromosome applying the hierarchical encoding approach
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 3.  Illustrative chromosomes applying the integrated encoding approach
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 4.  Algorithm GENERATE-PROCESS-PLAN
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 5.  A chromosome of the FJSP-OP
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 6.  Algorithm GENERATE-SCHEDULING
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 7.  Decoding a chromosome
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 8.  Crossover operations
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 9.  Mutation operations
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 10.  The Gantt chart of Experiment 1
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 11.  The Gantt chart of Experiment 3
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 12.  The Gantt chart of Experiment 4
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 13.  The Gantt chart of problem mk06 in Experiment 5
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 14.  The Gantt chart of Experiment 6(b)
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 15.  Performance curve of Experiment 4
Figure Options

Download full-size image

Download as PowerPoint slide

Figure A1.  The data of Experiment 3
Figure Options

Download full-size image

Download as PowerPoint slide

Table 1.  Comparison of results for Experiment 1
Solution approach EA Modified GA PBHA GA-OP
Makespan 16 14 14 14
Mean CPU time (ms) N/A N/A N/A 191
1 N/A means the result was not given by the author.
Table Options

Download as excel

Solution approach EA Modified GA PBHA GA-OP
Makespan 16 14 14 14
Mean CPU time (ms) N/A N/A N/A 191
1 N/A means the result was not given by the author.
Table 2.  Parameters and comparison of results on Experiment 3
Solution approach ALO Modified GA GA-OP
Parameters N/A $ PopSize=500 $ $ PopSize=50 $
$ P_c=0.8,P_m=0.1,IterNo=100 $
Makespan 161 162 145
Mean CPU time (ms) N/A N/A 309
Table Options

Download as excel

Solution approach ALO Modified GA GA-OP
Parameters N/A $ PopSize=500 $ $ PopSize=50 $
$ P_c=0.8,P_m=0.1,IterNo=100 $
Makespan 161 162 145
Mean CPU time (ms) N/A N/A 309
Table 3.  Parameters and comparison of results on Experiment 4
Solution approach ALGA GA-OP
Parameters $ PopSize=400 $ $ PopSize=200 $
$ P_c=0.8 $, $ P_m=0.1 $, $ IterNo=100 $
Makespan 188 181
Mean CPU time (ms) N/A 2,907
Table Options

Download as excel

Solution approach ALGA GA-OP
Parameters $ PopSize=400 $ $ PopSize=200 $
$ P_c=0.8 $, $ P_m=0.1 $, $ IterNo=100 $
Makespan 188 181
Mean CPU time (ms) N/A 2,907
Table 4.  Comparison of results for Experiment 5
Problem $ n \times m $ TABC HGTS MA2 HA PSO VNSGA GA-OP
mk01 10x6 40 40 40 40 41 40 40
mk02 10x6 26 26 26 26 26 26 26
mk03 15x8 204 204 204 204 207 204 204
mk04 15x8 60 60 60 60 65 60 60
mk05 15x4 173 172 172 172 171 173 172
mk06 10x15 60 57 59 57 61 58 57
mk07 20x5 139 139 139 139 173 144 139
mk08 20x10 523 523 523 523 523 523 523
mk09 20x10 307 307 307 307 307 307 307
mk10 20x15 202 198 202 197 312 198 198
Table Options

Download as excel

Problem $ n \times m $ TABC HGTS MA2 HA PSO VNSGA GA-OP
mk01 10x6 40 40 40 40 41 40 40
mk02 10x6 26 26 26 26 26 26 26
mk03 15x8 204 204 204 204 207 204 204
mk04 15x8 60 60 60 60 65 60 60
mk05 15x4 173 172 172 172 171 173 172
mk06 10x15 60 57 59 57 61 58 57
mk07 20x5 139 139 139 139 173 144 139
mk08 20x10 523 523 523 523 523 523 523
mk09 20x10 307 307 307 307 307 307 307
mk10 20x15 202 198 202 197 312 198 198
Table 5.  The experimental results (computational time in terms of seconds) of experiment 5
Problem n x m TABC HGTS MA2 HA PSO VNSGA GA-OP
mk01 10x6 3.36 5 20.16 0.06 N/A N/A 0.27
mk02 10x6 3.72 15 28.21 0.59 N/A N/A 3.75
mk03 15x8 1.56 2 53.76 0.16 N/A N/A 0.12
mk04 15x8 66.58 10 30.53 0.49 N/A N/A 3.41
mk05 15x4 78.45 18 36.36 4.57 N/A N/A 6.23
mk06 10x15 173.98 63 80.61 53.82 N/A N/A 65.14
mk07 20x5 66.19 33 37.74 20.01 N/A N/A 25.4
mk08 20x10 2.15 3 77.71 0.02 N/A N/A 0.2
mk09 20x10 304.43 24 75.23 0.86 N/A N/A 4.1
mk10 20x15 418.19 104 90.75 33.21 N/A N/A 73.12
Table Options

Download as excel

Problem n x m TABC HGTS MA2 HA PSO VNSGA GA-OP
mk01 10x6 3.36 5 20.16 0.06 N/A N/A 0.27
mk02 10x6 3.72 15 28.21 0.59 N/A N/A 3.75
mk03 15x8 1.56 2 53.76 0.16 N/A N/A 0.12
mk04 15x8 66.58 10 30.53 0.49 N/A N/A 3.41
mk05 15x4 78.45 18 36.36 4.57 N/A N/A 6.23
mk06 10x15 173.98 63 80.61 53.82 N/A N/A 65.14
mk07 20x5 66.19 33 37.74 20.01 N/A N/A 25.4
mk08 20x10 2.15 3 77.71 0.02 N/A N/A 0.2
mk09 20x10 304.43 24 75.23 0.86 N/A N/A 4.1
mk10 20x15 418.19 104 90.75 33.21 N/A N/A 73.12
Table 6.  Comparison of results on Experiment 6
Solution approach Experiment 6(a) Experiment 6(b)
ACO GA-OP Enhanced ACO GA-OP
Makespan 589 522 484 482
Mean CPU time (ms) 128,700 12,056 120534 12063
Table Options

Download as excel

Solution approach Experiment 6(a) Experiment 6(b)
ACO GA-OP Enhanced ACO GA-OP
Makespan 589 522 484 482
Mean CPU time (ms) 128,700 12,056 120534 12063
Table A1.  Alternative machines of each operation performed for each job
Operation Job
1 2 3 4 5 6
1 2, 4 2, 4 3, 5 3, 5 2, 4 2, 4
2 7, 8 7, 8 4, 6 4, 6 3, 5 3, 5
3 1, 2 1, 2 2, 3, 5 2, 3, 5 1, 2, 6 1, 2, 6
4 8, 6 8, 6 6, 7 6, 7 6, 8 6, 8
5 3, 5 3, 5 1, 8 1, 8 1, 7 1, 7
6 1, 2, 4 1, 2, 4 1, 4 1, 4 1, 3 1, 3
7 5, 6 5, 6 6, 7 6, 7 6, 7 6, 7
8 1, 7 1, 7 5, 8 5, 8 5, 8 5, 8
9 3, 8 3, 8 4, 2 4, 2 4, 3 4, 3
Table Options

Download as excel

Operation Job
1 2 3 4 5 6
1 2, 4 2, 4 3, 5 3, 5 2, 4 2, 4
2 7, 8 7, 8 4, 6 4, 6 3, 5 3, 5
3 1, 2 1, 2 2, 3, 5 2, 3, 5 1, 2, 6 1, 2, 6
4 8, 6 8, 6 6, 7 6, 7 6, 8 6, 8
5 3, 5 3, 5 1, 8 1, 8 1, 7 1, 7
6 1, 2, 4 1, 2, 4 1, 4 1, 4 1, 3 1, 3
7 5, 6 5, 6 6, 7 6, 7 6, 7 6, 7
8 1, 7 1, 7 5, 8 5, 8 5, 8 5, 8
9 3, 8 3, 8 4, 2 4, 2 4, 3 4, 3
Table A2.  Processing times on the alternative machines of each operation
Operation Job
1 2 3 4 5 6
1 18, 22 18, 22 12, 15 12, 15 18, 22 18, 22
2 39, 36 39, 36 24, 23 24, 23 12, 15 12, 15
3 11, 10 37, 39 30, 31, 29 30, 31, 29 50, 52, 54 50, 52, 54
4 31, 34 20, 21 21, 22 21, 22 19, 21 53, 51
5 21, 23 21, 23 32, 30 32, 30 32, 31 22, 24
6 10, 12, 15 10, 12, 15 22, 25 22, 25 22, 25 22, 25
7 32, 30 36, 38 24, 22 42, 44 24, 22 24, 22
8 45, 44 45, 44 20, 19 41, 43 20, 18 20, 18
9 26, 24 26, 24 27, 22 27, 22 27, 22 27, 22
Table Options

Download as excel

Operation Job
1 2 3 4 5 6
1 18, 22 18, 22 12, 15 12, 15 18, 22 18, 22
2 39, 36 39, 36 24, 23 24, 23 12, 15 12, 15
3 11, 10 37, 39 30, 31, 29 30, 31, 29 50, 52, 54 50, 52, 54
4 31, 34 20, 21 21, 22 21, 22 19, 21 53, 51
5 21, 23 21, 23 32, 30 32, 30 32, 31 22, 24
6 10, 12, 15 10, 12, 15 22, 25 22, 25 22, 25 22, 25
7 32, 30 36, 38 24, 22 42, 44 24, 22 24, 22
8 45, 44 45, 44 20, 19 41, 43 20, 18 20, 18
9 26, 24 26, 24 27, 22 27, 22 27, 22 27, 22
Table A3.  Transportation times between the machines
Machine number 1 2 3 4 5 6 7 8
1 0 3 7 10 3 5 8 12
2 3 0 4 7 5 3 5 8
3 7 4 0 3 8 5 3 5
4 10 7 3 0 10 8 5 3
5 3 5 8 10 0 3 7 10
6 5 3 5 8 3 0 4 7
7 8 5 3 5 7 4 0 3
8 12 8 5 3 10 7 3 0
Table Options

Download as excel

Machine number 1 2 3 4 5 6 7 8
1 0 3 7 10 3 5 8 12
2 3 0 4 7 5 3 5 8
3 7 4 0 3 8 5 3 5
4 10 7 3 0 10 8 5 3
5 3 5 8 10 0 3 7 10
6 5 3 5 8 3 0 4 7
7 8 5 3 5 7 4 0 3
8 12 8 5 3 10 7 3 0
[1]

Didem Cinar, José António Oliveira, Y. Ilker Topcu, Panos M. Pardalos. A priority-based genetic algorithm for a flexible job shop scheduling problem. Journal of Industrial & Management Optimization, 2016, 12 (4) : 1391-1415. doi: 10.3934/jimo.2016.12.1391
[2]

Guo Zhou, Yongquan Zhou, Ruxin Zhao. Hybrid social spider optimization algorithm with differential mutation operator for the job-shop scheduling problem. Journal of Industrial & Management Optimization, 2021, 17 (2) : 533-548. doi: 10.3934/jimo.2019122
[3]

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
[4]

Behrad Erfani, Sadoullah Ebrahimnejad, Amirhossein Moosavi. An integrated dynamic facility layout and job shop scheduling problem: A hybrid NSGA-II and local search algorithm. Journal of Industrial & Management Optimization, 2020, 16 (4) : 1801-1834. doi: 10.3934/jimo.2019030
[5]

Adel Dabah, Ahcene Bendjoudi, Abdelhakim AitZai. An efficient Tabu Search neighborhood based on reconstruction strategy to solve the blocking job shop scheduling problem. Journal of Industrial & Management Optimization, 2017, 13 (4) : 2015-2031. doi: 10.3934/jimo.2017029
[6]

Alena Erchenko. Flexibility of Lyapunov exponents for expanding circle maps. Discrete & Continuous Dynamical Systems, 2019, 39 (5) : 2325-2342. doi: 10.3934/dcds.2019098
[7]

Ji-Bo Wang, Mengqi Liu, Na Yin, Ping Ji. Scheduling jobs with controllable processing time, truncated job-dependent learning and deterioration effects. Journal of Industrial & Management Optimization, 2017, 13 (2) : 1025-1039. doi: 10.3934/jimo.2016060
[8]

Jingwen Zhang, Wanjun Liu, Wanlin Liu. An efficient genetic algorithm for decentralized multi-project scheduling with resource transfers. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020140
[9]

F. Zeyenp Sargut, H. Edwin Romeijn. Capacitated requirements planning with pricing flexibility and general cost and revenue functions. Journal of Industrial & Management Optimization, 2007, 3 (1) : 87-98. doi: 10.3934/jimo.2007.3.87
[10]

Jiping Tao, Zhijun Chao, Yugeng Xi. A semi-online algorithm and its competitive analysis for a single machine scheduling problem with bounded processing times. Journal of Industrial & Management Optimization, 2010, 6 (2) : 269-282. doi: 10.3934/jimo.2010.6.269
[11]

Ethel Mokotoff. Algorithms for bicriteria minimization in the permutation flow shop scheduling problem. Journal of Industrial & Management Optimization, 2011, 7 (1) : 253-282. doi: 10.3934/jimo.2011.7.253
[12]

Ji-Bo Wang, Bo Zhang, Hongyu He. A unified analysis for scheduling problems with variable processing times. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021008
[13]

M. Ramasubramaniam, M. Mathirajan. A solution framework for scheduling a BPM with non-identical job dimensions. Journal of Industrial & Management Optimization, 2007, 3 (3) : 445-456. doi: 10.3934/jimo.2007.3.445
[14]

Min-Fan He, Li-Ning Xing, Wen Li, Shang Xiang, Xu Tan. Double layer programming model to the scheduling of remote sensing data processing tasks. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1515-1526. doi: 10.3934/dcdss.2019104
[15]

Yaw Chang, Lin Chen. Solve the vehicle routing problem with time windows via a genetic algorithm. Conference Publications, 2007, 2007 (Special) : 240-249. doi: 10.3934/proc.2007.2007.240
[16]

Abdel-Rahman Hedar, Alaa Fahim. Filter-based genetic algorithm for mixed variable programming. Numerical Algebra, Control & Optimization, 2011, 1 (1) : 99-116. doi: 10.3934/naco.2011.1.99
[17]

Ashkan Ayough, Farbod Farhadi, Mostafa Zandieh, Parisa Rastkhadiv. Genetic algorithm for obstacle location-allocation problems with customer priorities. Journal of Industrial & Management Optimization, 2021, 17 (4) : 1753-1769. doi: 10.3934/jimo.2020044
[18]

Mostafa Abouei Ardakan, A. Kourank Beheshti, S. Hamid Mirmohammadi, Hamed Davari Ardakani. A hybrid meta-heuristic algorithm to minimize the number of tardy jobs in a dynamic two-machine flow shop problem. Numerical Algebra, Control & Optimization, 2017, 7 (4) : 465-480. doi: 10.3934/naco.2017029
[19]

Jiping Tao, Ronghuan Huang, Tundong Liu. A $2.28$-competitive algorithm for online scheduling on identical machines. Journal of Industrial & Management Optimization, 2015, 11 (1) : 185-198. doi: 10.3934/jimo.2015.11.185
[20]

Yuanjia Ma. The optimization algorithm for blind processing of high frequency signal of capacitive sensor. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1399-1412. doi: 10.3934/dcdss.2019096

2020 Impact Factor: 1.801

Tools

Metrics

  • PDF downloads (488)
  • HTML views (854)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences