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Coordinated optimization of production scheduling and maintenance activities with machine reliability deterioration
1. | School of Management, Hefei University of Technology, 193 Tunxi Road, Hefei City, Anhui Province, China |
2. | Center for Applied Optimization, Department of Industrial and Systems Engineering, University of Florida, Gainesville, USA |
In this paper, we investigate a coordinated optimization problem of production and maintenance where the machine reliability decreases with the use of the machine. Lower reliability means the machine is more likely to fail during the production stage. In the event of a machine failure, corrective maintenance (CM) of the machine is required, and the CM of the machine will cause a certain cost. Preventive maintenance (PM) can improve machine reliability and reduce machine failures during the production stage, but it will also cause a certain cost. To minimize the total maintenance cost, we must determine an appropriate PM plan to balance these two types of maintenance. In addition, the tardiness cost of jobs is also considered, which is affected not only by the processing sequence of jobs but also by the PM decision. The objective is to find the optimal job processing sequence and the optimal PM plan to minimize the total expected cost. To solve the proposed problem, an improved grey wolf optimizer (IGWO) algorithm is proposed. Experimental results show that the IGWO algorithm outperforms GA, VNS, TS, and standard GWO in optimization and computational stability.
References:
[1] |
J. Jaturonnatee, D. N. P. Murthy and R. Boondiskulchok,
Optimal preventive maintenance of leased equipment with corrective minimal repairs, European Journal of Operational Research, 174 (2006), 201-215.
doi: 10.1016/j.ejor.2005.01.049. |
[2] |
K. Das, R. S. Lashkari and S. Sengupta,
Machine reliability and preventive maintenance planning for cellular manufacturing systems, European Journal of Operational Research, 183 (2007), 162-180.
doi: 10.1016/j.ejor.2006.09.079. |
[3] |
H. Peng, Q. Feng and D. W. Coit,
Reliability and maintenance modeling for systems subject to multiple dependent competing failure processes, IIE transactions, 43 (2010), 12-22.
doi: 10.1080/0740817X.2010.491502. |
[4] |
C.-Y. Lee,
Machine scheduling with an availability constraint, Optimization Applications in Scheduling Theory. J. Global Optim., 9 (1996), 395-416.
doi: 10.1007/BF00121681. |
[5] |
C. Low, M. Ji, C. -J.g Hsu and C.-T. Su,
Minimizing the makespan in a single machine scheduling problems with flexible and periodic maintenance, Appl. Math. Model., 34 (2010), 334-342.
doi: 10.1016/j.apm.2009.04.014. |
[6] |
Y. Mati,
Minimizing the makespan in the non-preemptive job-shop scheduling with limited machine availability, Computers & Industrial Engineering, 59 (2010), 537-543.
doi: 10.1016/j.cie.2010.06.010. |
[7] |
T. C. E. Cheng and Z. Liu,
Approximability of two-machine no-wait flowshop scheduling with availability constraints, Oper. Res. Lett., 31 (2003), 319-322.
doi: 10.1016/S0167-6377(02)00230-4. |
[8] |
G. Li, M. Liu, S. P. Sethi and D. Xu,
Parallel-machine scheduling with machine-dependent maintenance periodic recycles, International Journal of Production Economics, 186 (2017), 1-7.
doi: 10.1016/j.ijpe.2017.01.014. |
[9] |
M. Liu, S. Wang, C. Chu and F. Chu,
An improved exact algorithm for single-machine scheduling to minimise the number of tardy jobs with periodic maintenance, International Journal of Production Research, 54 (2016), 3591-3602.
doi: 10.1080/00207543.2015.1108535. |
[10] |
M. Kong, X. Liu, J. Pei, H. Cheng and P. M. Pardalos,
A BRKGA-DE algorithm for parallel-batching scheduling with deterioration and learning effects on parallel machines under preventive maintenance consideration, Ann. Math. Artif. Intell., 88 (2020), 237-267.
doi: 10.1007/s10472-018-9602-1. |
[11] |
P. Perez-Gonzalez, V. Fernandez-Viagas and J. M. Framinan, Permutation flowshop scheduling with periodic maintenance and makespan objective, Computers & Industrial Engineering, 143 (2020), 106369.
doi: 10.1016/j.cie.2020.106369. |
[12] |
A. Berrichi, F. Yalaoui, L. Amodeo and M. Mezghiche,
Bi-objective ant colony optimization approach to optimize production and maintenance scheduling, Comput. Oper. Res., 37 (2010), 1584-1596.
doi: 10.1016/j.cor.2009.11.017. |
[13] |
H. Mokhtari, A. Mozdgir and I. N. Kamal Abadi,
A reliability/availability approach to joint production and maintenance scheduling with multiple preventive maintenance services, International Journal of Production Research, 50 (2012), 5906-5925.
doi: 10.1080/00207543.2011.637092. |
[14] |
Z. Lu, W. Cui and X. Han,
Integrated production and preventive maintenance scheduling for a single machine with failure uncertainty, Computers & Industrial Engineering, 80 (2015), 236-244.
doi: 10.1016/j.cie.2014.12.017. |
[15] |
R. Renmansour, H. Allaoui, A. Artiba, S. Iassinovski and R. Pellerin, Simulation-based approach to joint production and preventive maintenance scheduling on a failure-prone machine, Journal of Quality in Maintenance Engineering, 17 (2011).
doi: 10.1108/13552511111157371. |
[16] |
Q. Liu, M. Dong and F. F. Chen,
Single-machine-based joint optimization of predictive maintenance planning and production scheduling, Robotics and Computer-Integrated Manufacturing, 51 (2018), 238-247.
doi: 10.1016/j.rcim.2018.01.002. |
[17] |
Y. An, X. Chen, J. Zhang and Y. Li, A hybrid multi-objective evolutionary algorithm to integrate optimization of the production scheduling and imperfect cutting tool maintenance considering total energy consumption, Journal of Cleaner Production, 268 (2020), 121540.
doi: 10.1016/j.jclepro.2020.121540. |
[18] |
H. Feng, L. Xi, L. Xiao, T. Xia and E. Pan,
Imperfect preventive maintenance optimization for flexible flowshop manufacturing cells considering sequence-dependent group scheduling, Reliability Engineering & System Safety, 176 (2018), 218-229.
doi: 10.1016/j.ress.2018.04.004. |
[19] |
J. Hu and Z. Jiang, Job scheduling integrated with imperfect preventive maintenance considering time-varying operating condition, IEEE International Conference on Industrial Engineering and Engineering Management (IEEM), (2017), 578–582.
doi: 10.1109/IEEM.2017.8289957. |
[20] |
C. S. Wong, F. T. S. Chan and S. H. Chung,
A joint production scheduling approach considering multiple resources and preventive maintenance tasks, International Journal of Production Research, 51 (2013), 883-896.
doi: 10.1080/00207543.2012.677070. |
[21] |
S. Kumar and B. K. Lad,
Integrated production and maintenance planning for parallel machine system considering cost of rejection, Journal of the Operational Research Society, 68 (2017), 834-846.
doi: 10.1057/jors.2016.46. |
[22] |
S. Lu, X. Liu, J. Pei, M. T. Thai and P. M. Pardalos,
A hybrid ABC-TS algorithm for the unrelated parallel-batching machines scheduling problem with deteriorating jobs and maintenance activity, Applied Soft Computing, 66 (2018), 168-182.
doi: 10.1016/j.asoc.2018.02.018. |
[23] |
D. Lin, M. J. Zuo and R. C. M. Yam,
General sequential imperfect preventive maintenance models, International Journal of Reliability, Quality and Safety Engineering, 7 (2000), 253-266.
doi: 10.1142/S0218539300000213. |
[24] |
M.-C. Fitouhi and M. Nourelfath,
Integrating noncyclical preventive maintenance scheduling and production planning for a single machine, International Journal of Production Economics, 136 (2012), 344-351.
doi: 10.1016/j.ijpe.2011.12.021. |
[25] |
S. Laohanan and D. Banjerdpongchai, Dynamic programming approach to optimal maintenance scheduling of substation equipment considering life cycle cost and reliability, International Conference on Electrical Engineering/Electronics, Computer, Telecommunications and Information Technology (ECTI-CON). IEEE, (2018), 388–391.
doi: 10.1109/ECTICon.2018.8619884. |
[26] |
P. L. Ramos, D. C. Nascimento, C. Cocolo, et al., Reliability-centered maintenance: Analyzing failure in harvest sugarcane machine using some generalizations of the Weibull distribution, Modelling and Simulation in Engineering, (2018), 2018.
doi: 10.1155/2018/1241856. |
[27] |
D. C. Idoniboyeobu, B. A. Wokoma and V. C. Ibanibo,
Preventive maintenance for substation with aging equipment using weibull distribution, American Journal of Engineering Research, 7 (2018), 95-101.
|
[28] |
J. K. Lenstra, A. H. G. R. Kan and P. Brucker,
Complexity of machine scheduling problems, Ann. of Discrete Math., North-Holland, Amsterdam, 1 (1977), 343-362.
|
[29] |
S. Mirjalili, S. M. Mirjalili and A. Lewis,
Grey wolf optimizer, Advances in Engineering Software, 69 (2014), 46-61.
doi: 10.1016/j.advengsoft.2013.12.007. |
[30] |
G. M. Komaki and V. Kayvanfar,
Grey Wolf Optimizer algorithm for the two-stage assembly flow shop scheduling problem with release time, Journal of Computational Science, 8 (2015), 109-120.
doi: 10.1016/j.jocs.2015.03.011. |
[31] |
C. Lu, L. Gao, X. Li and S. Xiao,
A hybrid multi-objective grey wolf optimizer for dynamic scheduling in a real-world welding industry, Engineering Applications of Artificial Intelligence, 57 (2017), 61-79.
doi: 10.1016/j.engappai.2016.10.013. |
[32] |
M. K. Sattar, A. Ahmad, S. Fayyaz and et al.,
Ramp rate handling strategies in dynamic economic load dispatch (DELD) problem using grey wolf optimizer (GWO), Journal of the Chinese Institute of Engineers, 43 (2020), 200-213.
doi: 10.1080/02533839.2019.1694446. |
[33] |
A.-M. Golmohammadi, H. Bani-Asadi, H. J. Zanjani and H. Tikani,
A genetic algorithm for preemptive scheduling of a single machine, Journal of the Chinese Institute of Engineers, 7 (2016), 607-614.
doi: 10.5267/j.ijiec.2016.3.004. |
[34] |
R. Logendran and A. Sonthinen,
A Tabu search-based approach for scheduling job-shop type flexible manufacturing systems, Journal of the Operational Research Society, 48 (1997), 264-277.
doi: 10.1057/palgrave.jors.2600373. |
[35] |
D. Lei,
Variable neighborhood search for two-agent flow shop scheduling problem, Computers & Industrial Engineering, 80 (2015), 125-131.
doi: 10.1016/j.cie.2014.11.024. |
[36] |
M. Zandieh, A. R. Khatami and S. H. A. Rahmati,
Flexible job shop scheduling under condition-based maintenance: Improved version of imperialist competitive algorithm, Applied Soft Computing, 58 (2017), 449-464.
doi: 10.1016/j.asoc.2017.04.060. |
show all references
References:
[1] |
J. Jaturonnatee, D. N. P. Murthy and R. Boondiskulchok,
Optimal preventive maintenance of leased equipment with corrective minimal repairs, European Journal of Operational Research, 174 (2006), 201-215.
doi: 10.1016/j.ejor.2005.01.049. |
[2] |
K. Das, R. S. Lashkari and S. Sengupta,
Machine reliability and preventive maintenance planning for cellular manufacturing systems, European Journal of Operational Research, 183 (2007), 162-180.
doi: 10.1016/j.ejor.2006.09.079. |
[3] |
H. Peng, Q. Feng and D. W. Coit,
Reliability and maintenance modeling for systems subject to multiple dependent competing failure processes, IIE transactions, 43 (2010), 12-22.
doi: 10.1080/0740817X.2010.491502. |
[4] |
C.-Y. Lee,
Machine scheduling with an availability constraint, Optimization Applications in Scheduling Theory. J. Global Optim., 9 (1996), 395-416.
doi: 10.1007/BF00121681. |
[5] |
C. Low, M. Ji, C. -J.g Hsu and C.-T. Su,
Minimizing the makespan in a single machine scheduling problems with flexible and periodic maintenance, Appl. Math. Model., 34 (2010), 334-342.
doi: 10.1016/j.apm.2009.04.014. |
[6] |
Y. Mati,
Minimizing the makespan in the non-preemptive job-shop scheduling with limited machine availability, Computers & Industrial Engineering, 59 (2010), 537-543.
doi: 10.1016/j.cie.2010.06.010. |
[7] |
T. C. E. Cheng and Z. Liu,
Approximability of two-machine no-wait flowshop scheduling with availability constraints, Oper. Res. Lett., 31 (2003), 319-322.
doi: 10.1016/S0167-6377(02)00230-4. |
[8] |
G. Li, M. Liu, S. P. Sethi and D. Xu,
Parallel-machine scheduling with machine-dependent maintenance periodic recycles, International Journal of Production Economics, 186 (2017), 1-7.
doi: 10.1016/j.ijpe.2017.01.014. |
[9] |
M. Liu, S. Wang, C. Chu and F. Chu,
An improved exact algorithm for single-machine scheduling to minimise the number of tardy jobs with periodic maintenance, International Journal of Production Research, 54 (2016), 3591-3602.
doi: 10.1080/00207543.2015.1108535. |
[10] |
M. Kong, X. Liu, J. Pei, H. Cheng and P. M. Pardalos,
A BRKGA-DE algorithm for parallel-batching scheduling with deterioration and learning effects on parallel machines under preventive maintenance consideration, Ann. Math. Artif. Intell., 88 (2020), 237-267.
doi: 10.1007/s10472-018-9602-1. |
[11] |
P. Perez-Gonzalez, V. Fernandez-Viagas and J. M. Framinan, Permutation flowshop scheduling with periodic maintenance and makespan objective, Computers & Industrial Engineering, 143 (2020), 106369.
doi: 10.1016/j.cie.2020.106369. |
[12] |
A. Berrichi, F. Yalaoui, L. Amodeo and M. Mezghiche,
Bi-objective ant colony optimization approach to optimize production and maintenance scheduling, Comput. Oper. Res., 37 (2010), 1584-1596.
doi: 10.1016/j.cor.2009.11.017. |
[13] |
H. Mokhtari, A. Mozdgir and I. N. Kamal Abadi,
A reliability/availability approach to joint production and maintenance scheduling with multiple preventive maintenance services, International Journal of Production Research, 50 (2012), 5906-5925.
doi: 10.1080/00207543.2011.637092. |
[14] |
Z. Lu, W. Cui and X. Han,
Integrated production and preventive maintenance scheduling for a single machine with failure uncertainty, Computers & Industrial Engineering, 80 (2015), 236-244.
doi: 10.1016/j.cie.2014.12.017. |
[15] |
R. Renmansour, H. Allaoui, A. Artiba, S. Iassinovski and R. Pellerin, Simulation-based approach to joint production and preventive maintenance scheduling on a failure-prone machine, Journal of Quality in Maintenance Engineering, 17 (2011).
doi: 10.1108/13552511111157371. |
[16] |
Q. Liu, M. Dong and F. F. Chen,
Single-machine-based joint optimization of predictive maintenance planning and production scheduling, Robotics and Computer-Integrated Manufacturing, 51 (2018), 238-247.
doi: 10.1016/j.rcim.2018.01.002. |
[17] |
Y. An, X. Chen, J. Zhang and Y. Li, A hybrid multi-objective evolutionary algorithm to integrate optimization of the production scheduling and imperfect cutting tool maintenance considering total energy consumption, Journal of Cleaner Production, 268 (2020), 121540.
doi: 10.1016/j.jclepro.2020.121540. |
[18] |
H. Feng, L. Xi, L. Xiao, T. Xia and E. Pan,
Imperfect preventive maintenance optimization for flexible flowshop manufacturing cells considering sequence-dependent group scheduling, Reliability Engineering & System Safety, 176 (2018), 218-229.
doi: 10.1016/j.ress.2018.04.004. |
[19] |
J. Hu and Z. Jiang, Job scheduling integrated with imperfect preventive maintenance considering time-varying operating condition, IEEE International Conference on Industrial Engineering and Engineering Management (IEEM), (2017), 578–582.
doi: 10.1109/IEEM.2017.8289957. |
[20] |
C. S. Wong, F. T. S. Chan and S. H. Chung,
A joint production scheduling approach considering multiple resources and preventive maintenance tasks, International Journal of Production Research, 51 (2013), 883-896.
doi: 10.1080/00207543.2012.677070. |
[21] |
S. Kumar and B. K. Lad,
Integrated production and maintenance planning for parallel machine system considering cost of rejection, Journal of the Operational Research Society, 68 (2017), 834-846.
doi: 10.1057/jors.2016.46. |
[22] |
S. Lu, X. Liu, J. Pei, M. T. Thai and P. M. Pardalos,
A hybrid ABC-TS algorithm for the unrelated parallel-batching machines scheduling problem with deteriorating jobs and maintenance activity, Applied Soft Computing, 66 (2018), 168-182.
doi: 10.1016/j.asoc.2018.02.018. |
[23] |
D. Lin, M. J. Zuo and R. C. M. Yam,
General sequential imperfect preventive maintenance models, International Journal of Reliability, Quality and Safety Engineering, 7 (2000), 253-266.
doi: 10.1142/S0218539300000213. |
[24] |
M.-C. Fitouhi and M. Nourelfath,
Integrating noncyclical preventive maintenance scheduling and production planning for a single machine, International Journal of Production Economics, 136 (2012), 344-351.
doi: 10.1016/j.ijpe.2011.12.021. |
[25] |
S. Laohanan and D. Banjerdpongchai, Dynamic programming approach to optimal maintenance scheduling of substation equipment considering life cycle cost and reliability, International Conference on Electrical Engineering/Electronics, Computer, Telecommunications and Information Technology (ECTI-CON). IEEE, (2018), 388–391.
doi: 10.1109/ECTICon.2018.8619884. |
[26] |
P. L. Ramos, D. C. Nascimento, C. Cocolo, et al., Reliability-centered maintenance: Analyzing failure in harvest sugarcane machine using some generalizations of the Weibull distribution, Modelling and Simulation in Engineering, (2018), 2018.
doi: 10.1155/2018/1241856. |
[27] |
D. C. Idoniboyeobu, B. A. Wokoma and V. C. Ibanibo,
Preventive maintenance for substation with aging equipment using weibull distribution, American Journal of Engineering Research, 7 (2018), 95-101.
|
[28] |
J. K. Lenstra, A. H. G. R. Kan and P. Brucker,
Complexity of machine scheduling problems, Ann. of Discrete Math., North-Holland, Amsterdam, 1 (1977), 343-362.
|
[29] |
S. Mirjalili, S. M. Mirjalili and A. Lewis,
Grey wolf optimizer, Advances in Engineering Software, 69 (2014), 46-61.
doi: 10.1016/j.advengsoft.2013.12.007. |
[30] |
G. M. Komaki and V. Kayvanfar,
Grey Wolf Optimizer algorithm for the two-stage assembly flow shop scheduling problem with release time, Journal of Computational Science, 8 (2015), 109-120.
doi: 10.1016/j.jocs.2015.03.011. |
[31] |
C. Lu, L. Gao, X. Li and S. Xiao,
A hybrid multi-objective grey wolf optimizer for dynamic scheduling in a real-world welding industry, Engineering Applications of Artificial Intelligence, 57 (2017), 61-79.
doi: 10.1016/j.engappai.2016.10.013. |
[32] |
M. K. Sattar, A. Ahmad, S. Fayyaz and et al.,
Ramp rate handling strategies in dynamic economic load dispatch (DELD) problem using grey wolf optimizer (GWO), Journal of the Chinese Institute of Engineers, 43 (2020), 200-213.
doi: 10.1080/02533839.2019.1694446. |
[33] |
A.-M. Golmohammadi, H. Bani-Asadi, H. J. Zanjani and H. Tikani,
A genetic algorithm for preemptive scheduling of a single machine, Journal of the Chinese Institute of Engineers, 7 (2016), 607-614.
doi: 10.5267/j.ijiec.2016.3.004. |
[34] |
R. Logendran and A. Sonthinen,
A Tabu search-based approach for scheduling job-shop type flexible manufacturing systems, Journal of the Operational Research Society, 48 (1997), 264-277.
doi: 10.1057/palgrave.jors.2600373. |
[35] |
D. Lei,
Variable neighborhood search for two-agent flow shop scheduling problem, Computers & Industrial Engineering, 80 (2015), 125-131.
doi: 10.1016/j.cie.2014.11.024. |
[36] |
M. Zandieh, A. R. Khatami and S. H. A. Rahmati,
Flexible job shop scheduling under condition-based maintenance: Improved version of imperialist competitive algorithm, Applied Soft Computing, 58 (2017), 449-464.
doi: 10.1016/j.asoc.2017.04.060. |








Authors | Production system | Unexpected failures | PM | Objectives | Solutions |
Berrichi et al. (2010) | Parallel machine | - | Perfect | Minimize |
Multi-Objective Ant Colony Optimization approach |
Mokhtari et al. (2012) | Parallel machine | - | Multiple-level | Minimize the total system unavailability | Population-based variable neighborhood search |
Liu et al.(2018) | Single machine | - | Multiple-level | Minimize total cost | Genetic algorithm |
Hu et al.(2017) | Single machine | - | Imperfect | Minimize the total cost | Enumeration method |
Lu et al. (2018) | Parallel machine | - | Perfect | Minimize makespan | A hybrid ABC-TS algorithm |
Wong et al.(2013) | Parallel machine | - | Multiple-level | Minimize the makespan | Genetic algorithm |
Kumar et al.(2017) | Parallel machine | - | Perfect | Minimize overall operations cost | Simulation-based Genetic Algorithm |
Feng et al.(2018) | Flexible flowshop | ✓ | Imperfect | Minimize the total cost | Simulated annealing embedded genetic algorithm |
Lu et al. (2015) | Single machine | ✓ | Perfect | System robustness and stability | Genetic algorithm |
Benmansour et al.(2011) | Single machine | ✓ | Perfect | Minimize the cost related to production and maintenance | Heuristic algorithm |
An et al.(2020) | Flexible job-shop | - | Imperfect | Minimize the makespan and total cost | Evolutionary algorithm |
This paper | Single machine | ✓ | Imperfect | Minimize the total expected cost | Improved grey wolf optimizer algorithm |
Authors | Production system | Unexpected failures | PM | Objectives | Solutions |
Berrichi et al. (2010) | Parallel machine | - | Perfect | Minimize |
Multi-Objective Ant Colony Optimization approach |
Mokhtari et al. (2012) | Parallel machine | - | Multiple-level | Minimize the total system unavailability | Population-based variable neighborhood search |
Liu et al.(2018) | Single machine | - | Multiple-level | Minimize total cost | Genetic algorithm |
Hu et al.(2017) | Single machine | - | Imperfect | Minimize the total cost | Enumeration method |
Lu et al. (2018) | Parallel machine | - | Perfect | Minimize makespan | A hybrid ABC-TS algorithm |
Wong et al.(2013) | Parallel machine | - | Multiple-level | Minimize the makespan | Genetic algorithm |
Kumar et al.(2017) | Parallel machine | - | Perfect | Minimize overall operations cost | Simulation-based Genetic Algorithm |
Feng et al.(2018) | Flexible flowshop | ✓ | Imperfect | Minimize the total cost | Simulated annealing embedded genetic algorithm |
Lu et al. (2015) | Single machine | ✓ | Perfect | System robustness and stability | Genetic algorithm |
Benmansour et al.(2011) | Single machine | ✓ | Perfect | Minimize the cost related to production and maintenance | Heuristic algorithm |
An et al.(2020) | Flexible job-shop | - | Imperfect | Minimize the makespan and total cost | Evolutionary algorithm |
This paper | Single machine | ✓ | Imperfect | Minimize the total expected cost | Improved grey wolf optimizer algorithm |
Number of jobs | |
The processing time of job |
|
The due date of job |
|
Tardiness cost per unit of time of job |
|
The unit basic cost of the factory. | |
The time required for performing corrective maintenance (CM). | |
The cost of a CM activity. | |
The time required for performing preventive maintenance (PM). | |
The cost of a PM activity. | |
Job sequencing decision variable, and it is a zero and one variable | |
PM decision variable, and it is a zero and one variable | |
The processing time of the |
|
The failure rate function during the processing of the |
|
The number of PMs performed on the machine before time 0. | |
The machine age at time 0. | |
The machine age when starting the processing of the |
|
The machine age when finishing the processing of the |
|
The expected number of failures during the processing of the |
|
The expected completion time of the |
|
The expected tardiness time of the |
|
The expected total cost. |
Number of jobs | |
The processing time of job |
|
The due date of job |
|
Tardiness cost per unit of time of job |
|
The unit basic cost of the factory. | |
The time required for performing corrective maintenance (CM). | |
The cost of a CM activity. | |
The time required for performing preventive maintenance (PM). | |
The cost of a PM activity. | |
Job sequencing decision variable, and it is a zero and one variable | |
PM decision variable, and it is a zero and one variable | |
The processing time of the |
|
The failure rate function during the processing of the |
|
The number of PMs performed on the machine before time 0. | |
The machine age at time 0. | |
The machine age when starting the processing of the |
|
The machine age when finishing the processing of the |
|
The expected number of failures during the processing of the |
|
The expected completion time of the |
|
The expected tardiness time of the |
|
The expected total cost. |
Step 1 | Set the maximum number of searches |
Step 2 | Randomly generate three unequal integer |
Step 3 | Let |
Step 4 | Calculate the fitness of |
Step 5 | Judge whether |
Step 6 | Judge whether |
Step 1 | Set the maximum number of searches |
Step 2 | Randomly generate three unequal integer |
Step 3 | Let |
Step 4 | Calculate the fitness of |
Step 5 | Judge whether |
Step 6 | Judge whether |
1 | Initializes the grey wolf population |
2 | Initializes the max number of iterations |
3 | Calculate the fitness of all individuals |
4 | Set the three individuals with the best fitness as |
5 | while( |
6 | for each search agent |
7 | generate a random probability |
8 | if |
9 | generate two random numbers |
10 | calculate the coefficients |
11 | update the position of the current search agent by formula (4.5)-(4.7) |
12 | else if |
13 | update the position of the current search agent by Local search strategy |
14 | end if |
15 | update the population |
16 | calculate the fitness of all individuals |
17 | update |
18 | update |
19 | |
20 | end while |
21 | rerurn |
1 | Initializes the grey wolf population |
2 | Initializes the max number of iterations |
3 | Calculate the fitness of all individuals |
4 | Set the three individuals with the best fitness as |
5 | while( |
6 | for each search agent |
7 | generate a random probability |
8 | if |
9 | generate two random numbers |
10 | calculate the coefficients |
11 | update the position of the current search agent by formula (4.5)-(4.7) |
12 | else if |
13 | update the position of the current search agent by Local search strategy |
14 | end if |
15 | update the population |
16 | calculate the fitness of all individuals |
17 | update |
18 | update |
19 | |
20 | end while |
21 | rerurn |
The total number of jobs, |
10, 20, 30, …, 180,190,200 |
The failure rate adjustment parameter, |
1.05 |
The failure rate parameter, |
2 |
The failure rate parameter, |
50 |
The processing time of job |
Uniform |
The due date of job |
Uniform |
The tardiness cost per unit of time cost of job |
Uniform |
The unit production cost, |
1 |
The time required for performing corrective maintenance, |
1 |
The cost of a corrective maintenance activity, |
1 |
The time required for performing preventive maintenance, |
2 |
The cost of a preventive maintenance activity, |
2 |
The total number of jobs, |
10, 20, 30, …, 180,190,200 |
The failure rate adjustment parameter, |
1.05 |
The failure rate parameter, |
2 |
The failure rate parameter, |
50 |
The processing time of job |
Uniform |
The due date of job |
Uniform |
The tardiness cost per unit of time cost of job |
Uniform |
The unit production cost, |
1 |
The time required for performing corrective maintenance, |
1 |
The cost of a corrective maintenance activity, |
1 |
The time required for performing preventive maintenance, |
2 |
The cost of a preventive maintenance activity, |
2 |
GWO | IGWO | |||||||
Instance | MIN | MAX | AVE | VAR | MIN | MAX | AVE | VAR |
N = 10 | 72 | 78 | 76 | 0.87 | 65 | 67 | 66 | 0.28 |
N = 20 | 315 | 355 | 338 | 124 | 244 | 262 | 253 | 28 |
N = 30 | 595 | 641 | 615 | 263 | 420 | 479 | 442 | 198 |
N = 40 | 1595 | 1680 | 1649 | 3668 | 1330 | 1489 | 1424 | 11075 |
N = 50 | 2462 | 2683 | 2610 | 2375 | 2311 | 2518 | 2405 | 2231 |
N = 60 | 3608 | 4046 | 3849 | 14612 | 3171 | 3336 | 3266 | 2206 |
N = 70 | 4888 | 5268 | 5057 | 17758 | 4481 | 4722 | 4583 | 5833 |
N = 80 | 6760 | 7107 | 6929 | 20810 | 5909 | 6339 | 6089 | 9859 |
N = 90 | 7037 | 7328 | 7174 | 13697 | 6179 | 6544 | 6357 | 9622 |
N = 100 | 10781 | 11429 | 11147 | 35652 | 9768 | 10393 | 10101 | 33610 |
N = 110 | 13256 | 14317 | 13811 | 103514 | 12511 | 13184 | 12788 | 53694 |
N = 120 | 17281 | 18388 | 17783 | 106493 | 15711 | 16953 | 16331 | 104363 |
N = 130 | 20102 | 21580 | 20758 | 214099 | 18108 | 19249 | 18573 | 63512 |
N = 140 | 20919 | 22114 | 21594 | 112116 | 18600 | 19460 | 19020 | 20809 |
N = 150 | 23002 | 24554 | 23793 | 246926 | 19369 | 20752 | 19891 | 56352 |
N = 160 | 29341 | 30523 | 29801 | 157775 | 25098 | 25768 | 25436 | 61450 |
N = 170 | 34321 | 36133 | 35142 | 420426 | 28998 | 30418 | 29632 | 134003 |
N = 180 | 38393 | 40478 | 39255 | 390366 | 32914 | 34377 | 33557 | 177787 |
N = 190 | 49190 | 51420 | 50013 | 395090 | 42772 | 44139 | 43557 | 177696 |
N = 200 | 50416 | 52568 | 51498 | 575500 | 43267 | 44589 | 44003 | 102377 |
GWO | IGWO | |||||||
Instance | MIN | MAX | AVE | VAR | MIN | MAX | AVE | VAR |
N = 10 | 72 | 78 | 76 | 0.87 | 65 | 67 | 66 | 0.28 |
N = 20 | 315 | 355 | 338 | 124 | 244 | 262 | 253 | 28 |
N = 30 | 595 | 641 | 615 | 263 | 420 | 479 | 442 | 198 |
N = 40 | 1595 | 1680 | 1649 | 3668 | 1330 | 1489 | 1424 | 11075 |
N = 50 | 2462 | 2683 | 2610 | 2375 | 2311 | 2518 | 2405 | 2231 |
N = 60 | 3608 | 4046 | 3849 | 14612 | 3171 | 3336 | 3266 | 2206 |
N = 70 | 4888 | 5268 | 5057 | 17758 | 4481 | 4722 | 4583 | 5833 |
N = 80 | 6760 | 7107 | 6929 | 20810 | 5909 | 6339 | 6089 | 9859 |
N = 90 | 7037 | 7328 | 7174 | 13697 | 6179 | 6544 | 6357 | 9622 |
N = 100 | 10781 | 11429 | 11147 | 35652 | 9768 | 10393 | 10101 | 33610 |
N = 110 | 13256 | 14317 | 13811 | 103514 | 12511 | 13184 | 12788 | 53694 |
N = 120 | 17281 | 18388 | 17783 | 106493 | 15711 | 16953 | 16331 | 104363 |
N = 130 | 20102 | 21580 | 20758 | 214099 | 18108 | 19249 | 18573 | 63512 |
N = 140 | 20919 | 22114 | 21594 | 112116 | 18600 | 19460 | 19020 | 20809 |
N = 150 | 23002 | 24554 | 23793 | 246926 | 19369 | 20752 | 19891 | 56352 |
N = 160 | 29341 | 30523 | 29801 | 157775 | 25098 | 25768 | 25436 | 61450 |
N = 170 | 34321 | 36133 | 35142 | 420426 | 28998 | 30418 | 29632 | 134003 |
N = 180 | 38393 | 40478 | 39255 | 390366 | 32914 | 34377 | 33557 | 177787 |
N = 190 | 49190 | 51420 | 50013 | 395090 | 42772 | 44139 | 43557 | 177696 |
N = 200 | 50416 | 52568 | 51498 | 575500 | 43267 | 44589 | 44003 | 102377 |
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