International Journal of Nonlinear Analysis and Applications
Solving a bi-objective flexible flow shop problem with transporter preventive maintenance planning and limited buffers by NSGA-II and MOPSO
Document Type : Research Paper
Authors
School of Industrial Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran
Abstract
This study deals with a bi-objective flexible flow shop problem (BOFFSP) with transportation times and preventive maintenance (PM) on transporters via considering limited buffers. The PM actions on transporters are a missing part of the literature of the flexible flow shop problem (FFSP) which before the breakdown occurs, each transporter at each stage is stopped and the PM action is performed on it. The capacity of each intermediate buffer is limited and each job has to wait in the intermediate buffers. By including all these features in the proposed BOFFSP, not only processing times affect the objective functions, but also, the transportation times of jobs, the waiting time of jobs in the intermediate buffers, and availability of transporters in the system are considered in the model and make it a sample of a real-world FFSP. The presented BOFFSP has simultaneously minimized the total completion time and the unavailability of the system. As the problem is NP-hard, a non-dominated sorting genetic algorithm II (NSGA-II) and a multi-objective particle swarm optimization (MOPSO) is proposed to solve the model for large size problems. The experimental results show that the proposed MOPSO relatively outperforms the presented NSGA-II in terms of five different metrics considered to compare their performance. Afterwards, two one-way ANOVA tests are performed. It can be observed MOPSO achieves relatively better results than NSGA-II. Finally, sensitivity analysis is conducted to investigate the sensitivity of the objective functions to the number of jobs and their transportation time at each stage.
Keywords
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preventive maintenance planning, J. Manufact. Syst. 37 (2015) 182–192.
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Procedia Engin. 15 (2011) 3978–3983.
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robotic transportation and release time, Appl. Soft Comput. 40 (2016) 319–330.
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sequence-dependent setup times, Appl. Math. Comput. 180(1) (2006) 111–127.
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Pareto approach, IEEE Trans. Evolut. Comput. 3(4) (1999).
[3] S.F. Attar, M. Mohammadi, R. Tavakkoli-Moghaddam and S. Yaghoubi, Solving a new multi-objective hybrid
flexible flow shop problem with limited waiting times and machine-sequence-dependent set-up time constraints,
Int. J. Comput. Integ. Manufact. 27(5) (2014) 450–469.
[4] A. Berrichi, L. Amodeo, F. Yalaoui, E. Chˆatelet and M. Mezghiche, Bi-objective optimization algorithms for joint
production and maintenance scheduling: application to the parallel machine problem, J. Intell. Manufact. 20(4)
(2009) 389.
[5] A. Berrichi, F. Yalaoui, L. Amodeo and M. Mezghiche, Bi-objective ant colony optimization approach to optimize
production and maintenance schedules, Comput. Oper. Res. 37(9) (2010) 1584–1596.
[6] S.H. Choi and K. Wang, Flexible flow shop scheduling with stochastic processing times: A decomposition-based
approach, Comput. Indust. Engin. 63(2) (2012) 362–373.
[7] C.C. Coello and M.S. Lechuga, MOPSO: A proposal for multiple objective particle swarm optimization, Proc.
2002 Cong. Evolut. Comput. CEC′02 (Cat. No. 02TH8600) 2 (2002) 1051–1056.
[8] K. Deb, A. Pratap, S. Agarwal and T. Meyarivan, A fast and elitist multi-objective genetic algorithm: NSGA−
Q
,
IEEE Trans. Evolut. Comput. 6(2) (2002).
[9] R. Eberhart and J. Kennedy, Particle swarm optimization, Proc. IEEE Int. Conf. Neural Networks 4 (1995)
1942–1948.
[10] E. Gheisariha, M. Tavana, F. Jolai and M. Rabiee, A simulation-optimization model for solving flexible flow shop
scheduling problems with rework and transportation, Math. Comput. Simul. 180 (2021) 152–177.
[11] A. Ghodratnama, F. Jolai and R. Tavakkoli-Moghaddam, Solving a new multi-objective multi-route flexible flow
line problem by multi-objective particle swarm optimization and NSGA-II, J. Manufact. Syst. 36 (2015) 189–202.
[12] A. Hasani, S.M.H. Hosseini, A bi-objective flexible flow shop scheduling problem with machine-dependent processing
stages: Trade-off between production costs and energy consumption, Appl. Math. Comput.386 (2020) 125533.
[13] M. Hekmatfar, S.F. Ghomi and B. Karimi, Two-stage reentrant hybrid flow shop with setup times and the criterion
of minimizing the makespan, Appl. Soft Comput. 11(8) (2011) 4530–4539.
[14] F. Jolai, H. Asefi, M. Rabiee and P. Ramezani, Bi-objective simulated annealing approaches for no-wait two-stage
flexible flow shop scheduling problem, Scientia Iranica 20(3) (2013) 861–872.
[15] M. Khalili, R. Tavakkoli-Moghaddam, A multi-objective electromagnetism algorithm for a bi-objective flow shop
scheduling problem, J. Manufact. Syst. 31(2) (2012) 232–239.
[16] M.E. Kurz and R.G. Askin, Scheduling flexible flow lines with sequence-dependent setup times, European J. Oper.
Res. 159(1) (2004) 66–82.
[17] K.S. Moghaddam, Multi-objective preventive maintenance and replacement scheduling in a manufacturing system
using goal programming, Int. J. Prod. Econ. 146(2) (2013) 704–716.
[18] M. Mohammadi, J.Y. Dantan, A. Siadat and R. Tavakkoli-Moghaddam, A bi-objective robust inspection planning
model in a multi-stage serial production system, Int. J. Prod. Econ. 56(4) (2018) 1432–1457.
[19] B. Naderi, R. Tavakkoli-Moghaddam and M. Khalili, Electromagnetism-like mechanism and simulated annealing
algorithms for flow shop scheduling problems minimizing the total weighted tardiness and makespan, KnowledgeBased Syst. 23(2) (2010) 77–85.
[20] B. Naderi, M. Zandieh and V. Roshanaei, Scheduling hybrid flow shops with sequence-dependent setup times to
minimize makespan and maximum tardiness, Int. J. Adv. Manufact. Tech. 41(11–12) (2009) 1186–1198.
[21] M. Naderi-Beni, E. Ghobadian, S. Ebrahimnejad and R. Tavakkoli-Moghaddam, The fuzzy bi-objective formulation for a parallel machine scheduling problem with machine eligibility restrictions and sequence-dependent setup
times, Int. J. Prod. Res. 52(19) (2014) 5799–5822.
[22] S. Noori-Darvish and R. Tavakkoli-Moghaddam, Minimizing the total tardiness and makespan in an open shop
scheduling problem with sequence-dependent setup times, J. Indust. Engin. Int. 8(1) (2012) 25.
[23] K.E. Parsopoulos and M.N. Vrahatis, Particle swarm optimization method in multiobjective problems, Proc. 2002
ACM Symp. Appl. Comput. (2002) 603–607.
[24] S. Raissi, R. Rooeinfar and V.R. Ghezavati, Three hybrid metaheuristic algorithms for stochastic flexible flow shop
scheduling problem with preventive maintenance and budget constraint, J. Opt. Indust. Engin. (2019) 131–147.
[25] M. Reyes-Sierra and A. Carlos, Multi-objective particle swarm optimizers: A survey of the state of the art, Int.
J. Comput. Intel. Res. 2(3) (2006) 287–308.
[26] R. Rooeinfar, R. Raissi and V.R. Ghezavati, Stochastic flexible flow shop scheduling problem with limited buffers
and fixed interval preventive maintenance: a hybrid approach of simulation and metaheuristic algorithms, Simulation (2019) 509–528.
[27] B. Shahidi-Zadeh, R. Tavakkoli-Moghaddam, A. Taheri-Moghadam and I. Rastgar, Solving a bi-objective unrelatedparallel batch processing machines scheduling problem: A comparison study, Comput. Oper. Res. 88 (2017) 71–90.
[28] N. Sriniva and K. Deb, Multi-objective optimization using non-dominated sorting in genetic algorithms, J. Evolut.
Comput. 2(3) (1994) 221–248.
[29] J.U. Sun, A Taguchi approach to parameter setting in a genetic algorithm for a general job shop scheduling
problem, IEMS 6(2) (2007) 119–124.
[30] G. Taguchi, Introduction to Quality Engineering: Designing Quality Into Products and Processes, The Organization, the University of Michigan, 1986.
[31] R. Tavakkoli-Moghaddam, M. Azarkish and A. Sadeghnejad-Barkousaraie, A new hybrid multi-objective Pareto
archive PSO algorithm for a bi-objective job shop scheduling problem, Expert Syst. Appl. 38(9) (2011) 10812–
10821.
[32] R. Tavakkoli-Moghaddam, M. Azarkish and A. Sadeghnejad-Barkousaraie, Solving a multi-objective job shop
scheduling problem with sequence-dependent setup times by a Pareto archive PSO combined with genetic operators
and VNS, Int. J. Adv. Manufact. Tech. 53(5–8) (2011) 733–750.
[33] A. Villemeur, Assessment, Hardware, Software and Human Factors, Volume 2 of Reliability, availability, Maintainability and Safety Assessment, Wiley, 1992.
[34] S. Wang, Bi-objective optimization for integrated scheduling of single machines with setup times and preventive
maintenance planning, Int. J. Prod. Res. 51(12) (2013) 3719–3733.
[35] S. Wang and M. Liu, Multi-objective optimization of parallel machine scheduling integrated with multi-resources
preventive maintenance planning, J. Manufact. Syst. 37 (2015) 182–192.
[36] Y. Yusoff, M.S. Ngadiman and A.M. Zain, Overview of NSGA-II for optimizing machining process parameters,
Procedia Engin. 15 (2011) 3978–3983.
[37] S.S. Zabihzadeh and J. Rezaeian, Two meta-heuristic algorithms for flexible flow shop scheduling problem with
robotic transportation and release time, Appl. Soft Comput. 40 (2016) 319–330.
[38] M. Zandieh, S.F. Ghomi and S.M. Husseini, An immune algorithm approach to hybrid flow shops scheduling with
sequence-dependent setup times, Appl. Math. Comput. 180(1) (2006) 111–127.
[39] M. Zandieh, S.M. Sajadi and R. Behnoud, Integrated production scheduling and maintenance planning in a hybrid
flow shop system: a multi-objective approach, Int. J. Syst. Assur. Engin. Manag.8(2) (2017) 1630–1642.
[40] E. Zitzler and L. Thiele, Multi-objective Evolutionary algorithms: A comparative case study and the strength
Pareto approach, IEEE Trans. Evolut. Comput. 3(4) (1999).
)
Volume 13, Issue 1
March 2022Pages 217-246
- Receive Date: 24 August 2021
- Revise Date: 24 September 2021
- Accept Date: 16 November 2021
- First Publish Date: 16 November 2021