Joint Scheduling of Jobs and Variable Maintenance Activities in the Flowshop Sequencing Problems: Review, Classification and Opportunities

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Much of the scheduling theory assumes that machines are always available to process jobs at any time during the scheduling horizon. However, machines may be unavailable for various reasons in realistic practices, such as unexpected failures or variable maintenance activities. This article discusses in depth the works published in the literature of joint scheduling of jobs and variable maintenance activities in the flowshop sequencing problems. Our literature review focuses first on the basic concepts of scheduling problems, and more specifically, the scheduling strategies of production and maintenance that have been identified in the literature. Subsequently, we focus our attention on the principal methods for solving scheduling problems, while presenting in the following the main published works for the aforementioned systems. Lastly, a comparative analysis is carried out to highlight the fundamental ideas leading to the adoption of an effective approach capable of producing an optimal solution in a reasonable calculation time.

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November 2018

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[1] S. M. Johnson, Optimal two and three-stage production schedules with setup times included, Naval Research Logistics Quarterly. 1 (1) (1954) 61-68.

DOI: 10.1002/nav.3800010110

Google Scholar

[2] I. Adiri, J. Bruno, E. Frostig, A.H.G. Rinnooy Kan, Single machine flow-time scheduling with a single breakdown, Acta Informatica. 26 (1989) 679-696.

DOI: 10.1007/bf00288977

Google Scholar

[3] Weiwei Cui, Zhiqiang Lu, Chen Li, Xiaole Han .A proactive approach to solve integrated production scheduling and maintenance planning problem in flow shops.Computers & Industrial Engineering. 115 (2018) 342–353.

DOI: 10.1016/j.cie.2017.11.020

Google Scholar

[4] Shijin Wang & Ming Liu, Two-machine flow shop scheduling integrated with preventive maintenance planning, International Journal of Systems Science. 900137(2014) 10-1080.

Google Scholar

[5] Emmons, H., Vairaktarakis, G. Flowshop Scheduling: Theory, Algorithms, and Managerial Insights. ISOR (2012)182.

Google Scholar

[6] Ghita Lebbar, Abdellah El Barkany, Abdelouahhab Jabri, Scheduling Problems of Flexible Manufacturing Systems: Review, Classification and Opportunities,, International Journal of Engineering Research in Africa. 1663-4144 (2016) 142-160.

DOI: 10.4028/www.scientific.net/jera.26.142

Google Scholar

[7] R.L. Graham, E.L. Lawler, J.K. Lenstra, A.H. G. Rinnooy Kan, Optimization and approximation in deterministic sequencing and scheduling: a survey. Annals Discrete Math., 5(1979) 287 - 326.

DOI: 10.1016/s0167-5060(08)70356-x

Google Scholar

[8] C. Y. Lee and Z. L. Chen. Scheduling jobs and maintenance activities on parallel machines. Naval Research Logistics, 47: ( 2000) 145–165.

DOI: 10.1002/(sici)1520-6750(200003)47:2<145::aid-nav5>3.0.co;2-3

Google Scholar

[9] M. Bembla. Ordonnancement conjoint production et maintenance : Critère et heuristique de résolution. Mémoire de dea, U.F.R des Sciences et Techniques de l'Université de Franche Comté, (2002).

Google Scholar

[10] Amel Yahyaoui. Élaboration de nouveaux outils non conventionnels intelligents pour l'ordonnancement conjoint de la production et de la maintenance : application au cas d'un job shop. Automatique / Robotique. Université de Tunis - ECOLE SUPERIEURE DES SCIENCES ET TECHNIQUES DE TUNIS(2011).

DOI: 10.3166/jesa.37.621-640

Google Scholar

[11] R. Aggoune, Ordonnancement d'ateliers sous contraintes de disponibilités des machines. Thèse de PhD. Université de Metz, France, (2002).

Google Scholar

[12] T.W. Sloan and J.G. Shanthikumar. Combined production and maintenance scheduling for a multiple product, single machine production system. Production and Operation Management, 9(4): (2000)379–399.

DOI: 10.1111/j.1937-5956.2000.tb00465.x

Google Scholar

[13] M. Brandolese, M. Franci, and A. Pozzetti. Production and maintenance integrated planning. International Journal of production Research, 34(7): (1996)2059–(2075).

DOI: 10.1080/00207549608905013

Google Scholar

[14] S.A. Cook, The Complexity of Theorem Proving Procedures. Proceedings of the Third Annual ACM Symposium on the Theory of Computing, Association of Computing Machinery, New York, (1971)151-158.

DOI: 10.1145/800157.805047

Google Scholar

[15] R.M. Karp, Reducibility Among Combinatorial Problems. in Miller, R.E. and Thatcher, J. W. (eds).Complexity of Computer Computations, Plenum Press, New York, (1972)85-104.

DOI: 10.1007/978-1-4684-2001-2_9

Google Scholar

[16] M.R. Garey, M.R. Johnson, Computers and intractability: A guide to the theory of NP-completeness. San Francisco: Freeman, (1979).

Google Scholar

[17] C. Sriskandarajah and S. K. Goyal. The Journal of the Operational Research Society. 40 (10) (1989) 907-921.

Google Scholar

[18] M.Garey, and D. S. Jonhson. Two-processor scheduling with start times and deadlines, SIAM J. Comput, 6(3) (1977) 416-426.

DOI: 10.1137/0206029

Google Scholar

[19] Ahmed Gara-Ali n, Marie-Laure Espinouse .Erratum to: Simultaneously scheduling n jobs and the preventive maintenance on the two-machine flow shop to minimize the makespan,, Int. J. Production Economics 153 (2014) 361–363.

DOI: 10.1016/j.ijpe.2014.02.018

Google Scholar

[20] A. Gara-Ali et M.-L. Espinouse. A two-machine flow-shop scheduling with a deteriorating maintenance activity on the second machine. In Industrial Engineering and Systems Management (IESM), International Conference, 481– 488 (2015).

DOI: 10.1109/iesm.2015.7380202

Google Scholar

[21] G.B. Dantzig, R. Fulkerson, S. Johnson, Solution of a large-scale travelingsalesman problem. Operational Research 2 (1954) 393-410.

Google Scholar

[22] W. Kubiak, J. Blazewicz, P. Formanowicz, J. Breit, G. Schmidt, Two-machine flow shops with limited machine availability, European Journal of Operational Research,136(2002)528-540.

DOI: 10.1016/s0377-2217(01)00083-2

Google Scholar

[23] J. Kaabi, C. Varnier, and N. Zerhouni. Ordonnancement conjoint de la production et de la maintenance dans un flow shop. In 5ème Conférence Francophone de Modélisation et Simulation, Nantes, France, 1-3 septembre (2004).

DOI: 10.3166/jesa.37.641-660

Google Scholar

[24] Faten Ben Chihaoui, Imed Kacem, Atidel B. Hadj-Alouane, Najoua Dridi, Nidhal Rezg. No-wait Scheduling of a Two-machine Flow-shop to Minimize the Makespan under Non-Availability Constraints and Different Release Dates. International Journal of Production Research, Taylor & Francis, 2011, p.1.

DOI: 10.1080/00207543.2010.531775

Google Scholar

[25] Faicel Hnaien n, Farouk Yalaoui, Ahmed Mhadhbi .Makespan minimization on a two-machine flowshop with an availability constraint on the first machine. Int. J. Production Economics 164 (2015) 95–104.

DOI: 10.1016/j.ijpe.2015.02.025

Google Scholar

[26] M. Gondran, M. Minoux, Graphs and Algorithms. John Wiley and Sons, New York. 21(1984).

Google Scholar

[27] R. Bellman, Dynamic Programming, A Markovian Decision Process ,Princeton University Press. Journal of Mathematics and Mechanics, Vol. 6, No. 5 (1957), pp.679-684.

Google Scholar

[28] C.-Y. Lee, Minimizing the makespan in the two-machine flowshop scheduling problem with an availability constraint, Operations Research Letters, 20(3):129 – 139(1997).

DOI: 10.1016/s0167-6377(96)00041-7

Google Scholar

[29] C.Y. Lee, Two-machine flowshop scheduling with availability constraints, European Journal of Operational Research, 114 (1999) 420-429.

DOI: 10.1016/s0377-2217(97)00452-9

Google Scholar

[30] C.T. Ng, M.Y. Kovalyov, An FPTAS for scheduling a two-machine flowshop with one unavailability interval, Naval Research Logistics, 51, 3(2003) 307-315.

DOI: 10.1002/nav.10107

Google Scholar

[31] H. Allaoui, H. Artiba, F. Riane, Scheduling of two-machine flow-shops with availability constraints. Dans : Proceedings of 18th ORBEL conference. Brussels, Belgium(2003).

Google Scholar

[32] Ng, C.T., & Kovalyov, M.K. ,An FPTAS for scheduling a two-machine flow shop with one unavailability interval, Naval Research Logistics, 51(2004) 307–315.

DOI: 10.1002/nav.10107

Google Scholar

[33] M.A. Kubzin, V.A. Strusevich, Planning Machine Maintenance in Two-Machine Shop Scheduling, Operations Research, 54, 4, (2006) 789-800.

DOI: 10.1287/opre.1060.0301

Google Scholar

[34] H. Allaoui, A. Artiba, S.E. Elmaghraby, F. Riane, Scheduling of a two-machine flow shop with availability constaints on the first machine,International Journal of Production Economics, 99, 1-2, (2006)16-27.

DOI: 10.1016/j.ijpe.2004.12.003

Google Scholar

[35] Rapine, C.,Erratum to Scheduling of a two-machine flowshop with availability constraints on the first machine, [Int. J. Prod. Econ. 99 (2006) 16–27].Int. J. Prod. Econ. 142 (2013)211–212.

DOI: 10.1016/j.ijpe.2012.11.006

Google Scholar

[36] Vahedi Nouri, B., P. Fattahi, and R. Ramezanian. Hybrid Firefly-simulated Annealing Algorithm for the Flow Shop Problem with Learning Effects and Flexible Maintenance Activities., International Journal of Production Research 51 (12) (2013).

DOI: 10.1080/00207543.2012.750771

Google Scholar

[37] Reza Ramezanian , Mohammad Saidi-Mehrabad , Parviz Fattahi .MIP formulation and heuristics for multi-stage capacitated lot-sizing and scheduling problem with availability constraints. Journal of Manufacturing Systems 32 (2013) 392–401.

DOI: 10.1016/j.jmsy.2013.01.002

Google Scholar

[38] N. Kangarloo, J. Rezaeian, X. Khosrawi ,JIT scheduling problem on flexible flow shop with machine break down, machine eligibility and setup times, J. Math. Computer Sci. 16 (2016)50-68.

DOI: 10.22436/jmcs.016.01.06

Google Scholar

[39] J. Erscher, C. Merce, Consistency of the disaggregation process in hierarchical planning. Operation Research, 34(1985) 464-469.

Google Scholar

[40] Choi, B. C., Lee, K., Leung, J. Y. T., & Pinedo, M. L, Flow shops with machine maintenance: Ordered and proportionate cases, European Journal of Operational Research, 207(2010)97–104.

DOI: 10.1016/j.ejor.2010.04.018

Google Scholar

[41] Cheng, C-Y., Ying, K-C., Chen, H-H., Lin, J-X., Optimization algorithms for proportionate flowshop scheduling problems with variable maintenance activities, Computers & Industrial Engineering (2018).

DOI: 10.1016/j.cie.2018.01.027

Google Scholar

[42] M.C. Portmann, Méthodes de décomposition spatiales et temporelles en ordonnancement. RAIRO-APII, 22, 5(1988) 439-451.

Google Scholar

[43] S. Kirkpatrick, C.D. Gellatt, M.P. Vecchi, Optimization by Simulated Annealing.Science, 220 (1983)671-680.

DOI: 10.1126/science.220.4598.671

Google Scholar

[44] M.L. Espinouse, P. Formanowicz, B. Penz, Minimizing the makespan in the two-machine no-wait flow-shop, Computers and Industrial Engineering, 37(1999) 497-500.

DOI: 10.1016/s0360-8352(99)00127-8

Google Scholar

[45] T.C.E. Cheng, G. Wang, Two-machine flow shop scheduling with consecutive availability constraints, Information Processing Letters, 71, 2(1999) 49-54.

DOI: 10.1016/s0020-0190(99)00094-0

Google Scholar

[46] T.C.E. Cheng, G. Wang ,An improved heuristic for two-machine owshop scheduling with an availability constraint ,Operations Research Letters 26 (2000) 223-229.

DOI: 10.1016/s0167-6377(00)00033-x

Google Scholar

[47] Blazewicz, J., Breit, J., Formanowicz, P., Kubiak, W., & Schmidt,G. ,Heuristic algorithms for the two-machine flow shop with limited machine availability, Omega, 29(2001) 599–608.

DOI: 10.1016/s0305-0483(01)00048-2

Google Scholar

[48] G. Wang, T.C.E. Cheng, Heuristics for two-machine no-wait flowshop scheduling with an availability constraint, Information Processing Letters, 80, 6(2001) 305-309.

DOI: 10.1016/s0020-0190(01)00181-8

Google Scholar

[49] O. Braun, G. Schmidt, Y. Sotskov, Stability of Jonson's Schedule with limited Machine availability. Actes de la 3e conférence francophone de Modélisation et de Simulation (MOSIM'01), Troyes, Conception, analyse et gestion des systèmes industriels, SCS European Publishing House, 2(2001).

Google Scholar

[50] M.L. Espinouse, P. Formanowicz, B. Penz, Complexity results and approximation algorithms for the two machine no-wait flow-shop with limited machine availability, Journal of the Operational Research Society, 52, 1(1999) 116-121.

DOI: 10.1057/palgrave.jors.2601025

Google Scholar

[51] R.Aggoune, A.Halim Mahdi and Marie-Claude Portmann, GeneticAlgorithms for the Flow Shop Scheduling Problem with Availability Constraints , 0-7803-7087-2(2001).

Google Scholar

[52] J. Kaabi, C. Varnier, and N. Zerhouni. ordonnancement de la production et de la maintenance: cas d'un atelier de type flow shop à deux machines. APII-JESA, décembre (2003) 37:641–660.

DOI: 10.3166/jesa.37.641-660

Google Scholar

[53] Aggoune, R., & Portmann, M. C., Flow shop scheduling problem with limited machine availability: A heuristic approach, International Journal of Production Economics, 99(1–2), (2006) 4–15.

DOI: 10.1016/j.ijpe.2004.12.002

Google Scholar

[54] X. Wang, T.C.E. Cheng, Heuristics for two-machine flowshop scheduling with setup times and an availability constraint, Computers and Operations Research 34, (2007)152-162.

DOI: 10.1016/j.cor.2005.05.003

Google Scholar

[55] Ruiz, R., García-Díaz, J. C., & Maroto, C.,Considering scheduling and preventive maintenance in the flowshop sequencing problem,Computers & Operations Research,34(2007) 3314–3330.

DOI: 10.1016/j.cor.2005.12.007

Google Scholar

[56] H. Allaoui, S. Lamouri, A. Artiba, E. Aghezzaf . Simultaneously scheduling n jobs and the preventive maintenance on the two-machine flow shop to minimize the makespan Int. J. Production Economics 112 (2008) 161–167.

DOI: 10.1016/j.ijpe.2006.08.017

Google Scholar

[57] Yang, D.L., Hsu, C.J., & Kuo, W.H. ,A two-machine flow shop scheduling problem with a separated maintenance constraint, Computers & Operations Research, 35(2008)876–883.

DOI: 10.1016/j.cor.2006.04.007

Google Scholar

[58] Hamid Allaoui, AbdelHakim Artiba .Johnson's algorithm: A key to solve optimally or approximately flow shop scheduling problems with unavailability periods. Int. J. Production Economics 121 (2009) 81–87.

DOI: 10.1016/j.ijpe.2008.09.018

Google Scholar

[59] Hadda, H., Dridi, N., Hajri-Gabouj, S., An improved heuristic for two-machine flow shop scheduling with an availability constraint and nonresumable jobs.4OR - Q. J. Oper. Res. 8(2010)87–99.

DOI: 10.1007/s10288-009-0102-3

Google Scholar

[60] Vahedi-Nouri, B., Fattahi, P., Tavakkoli-Moghaddam, R., & Ramezanian, R, A general flow shop scheduling problem with consideration of position-based learning effect and multiple availability constraints. International Journal of Advanced Manufacturing Technology, 73(2014).

DOI: 10.1007/s00170-014-5841-4

Google Scholar

[61] Hatem Hadda, A note on Simultaneously scheduling n jobs and the preventive maintenance on the two-machine flow shop to minimize the makespan,, Int. J. Production Economics 159 (2015) 221–222.

DOI: 10.1016/j.ijpe.2014.09.022

Google Scholar

[62] Wei-Wei Cui, Zhiqiang Lu, Binghai Zhou, Chen Li & Xiaole Han ,A hybrid genetic algorithm for non-permutation flow shop scheduling problems with unavailability constraints, International Journal of Computer Integrated Manufacturing, 10.10801130247(2016).

DOI: 10.1080/0951192x.2015.1130247

Google Scholar

[63] Zahedi, Rojalib, Rinto Yusriski .Stepwise Optimization for Model of Integrated Batch Production and Maintenance Scheduling for Single Item Processed on Flow Shop with Two Machines in JIT Environment .Procedia Computer Science 116 (2017) 408–420.

DOI: 10.1016/j.procs.2017.10.081

Google Scholar

[64] Smith, W.E., Various Optimizers for Single-Stage Production,, Naval Research Logistics Quarterly, 3(1956) 59-66.

DOI: 10.1002/nav.3800030106

Google Scholar

[65] F. Glover, Heuristics for Integer Programming Using Surrogate Constraints, Decision Sciences, 8, 1(1977)156-166.

DOI: 10.1111/j.1540-5915.1977.tb01074.x

Google Scholar

[66] Aggoune, R. ,Minimizing the makespan for the flow shop scheduling problem with availability constraints, European Journal of Operational Research, 153(3) (2004) 534–543.

DOI: 10.1016/s0377-2217(03)00261-3

Google Scholar

[67] J. Holland, Adaptive in Natural and Artificial Systems. University of Michigan Press, Ann Arbor(1975).

Google Scholar

[68] T.C.E. Cheng, Z. Liu, 3/2-approximation for two-machine no-wait flowshop scheduling with availability constraints, Information Processing Letters, 88(2003) 161-165.

DOI: 10.1016/j.ipl.2003.08.002

Google Scholar

[69] B. Naderi a, M. Zandieh b, M. Aminnayeri. Incorporating periodic preventive maintenance into flexible flowshop scheduling problems. Applied Soft Computing 11 (2011) 2094–2101.

DOI: 10.1016/j.asoc.2010.07.008

Google Scholar

[70] Faicel Hnaien , Farouk Yalaoui. A Fuzzy Multi-objective algorithm to obtain Trade-off Between Cmax and Availability of Flow-Shop .Proceedings of the 14th IFAC . 978-3-902661-98-2 (2012).

DOI: 10.3182/20120523-3-ro-2023.00258

Google Scholar

[71] Faicel Hnaien ,Farouk Yalaoui .A bi-criteria flow-shop scheduling with preventive maintenance. 7th IFAC. 978-3-902823-35-9 (2013).

DOI: 10.3182/20130619-3-ru-3018.00206

Google Scholar

[72] Lei Xiao, Sanling Song, Xiaohui Chen and David W. Coit,Joint optimization of production scheduling and machine group preventive maintenance , Reliability Engineering and System Safety. 10.1016.(2015).10.013.

DOI: 10.1016/j.ress.2015.10.013

Google Scholar

[73] Andrew Junfang Yu, Javad Seif .Minimizing tardiness and maintenance costs in flow shop scheduling by a lower-bound-based GA. Computers & Industrial Engineering 97(2016)26–40.

DOI: 10.1016/j.cie.2016.03.024

Google Scholar

[74] Sanlaville, E., & Schmidt, G., Machine scheduling with availability constraints, Acta Informatica, 35 (1998) 795–811.

DOI: 10.1007/s002360050143

Google Scholar

[75] Schmidt, G., Scheduling with limited machine availability, European Journal of Operational Research. 121(1) (2000) 1–15.

Google Scholar

[76] Pinedo, M. ,Scheduling: Theory, algorithms, and systems.Upper Saddle River, NJ: Prentice-Hall. (2002).

Google Scholar

[77] O. Braun, T.C. Lai, G. Schmidt, Y.N. Sotskov ,Stability of Johnsons schedule with respect to limited machine availability, International Journal of Production Research,40, 17(2002) 4381 4400.

DOI: 10.1080/00207540210159527

Google Scholar

[78] Kubzin, M.A., Potts, C.N., & Strusevich, V.A. Approximation results for flow shop scheduling problems with machine availability constraints, Computers & Operations Research,36,(2009)379–390.

DOI: 10.1016/j.cor.2007.10.013

Google Scholar

[79] Allahverdi, A., & Mittenthal, J, Dual criteria scheduling on a two-machine flow shop subject to random breakdowns, International Transactions in Operational Research,5(4) (1998) 317–324.

DOI: 10.1016/s0969-6016(97)00042-7

Google Scholar

[80] T.C.E. Cheng, Z. Liu, Approximability of two-machine no-wait flowshop scheduling with availability constraints, Operations Research Letters, 31(2003) 319-322.

DOI: 10.1016/s0167-6377(02)00230-4

Google Scholar

[81] J. Breit, An improved approximation algorithm for two-machine flow shop scheduling with an availability constraint, Information Processing Letters 90 (2004) 273-278.

DOI: 10.1016/j.ipl.2004.03.004

Google Scholar

[82] Breit, J., A polynomial-time approximation scheme for the two-machine flow shop scheduling problem with an availability constraint, Computers and Operations Research, 33(8), (2006)2143–2153.

DOI: 10.1016/j.cor.2005.01.004

Google Scholar

[83] X. Wang, T.C.E. Cheng, An approximation scheme for two-machine flowshop scheduling with setup times and an availability constraint, Computers and Operations Research, 34, 10(2007) 2894-2901.

DOI: 10.1016/j.cor.2005.11.019

Google Scholar

[84] S.L. Khelifati, F. Benbouzid-Sitayeb, A multi-agent scheduling approach for the joint scheduling of jobs and maintenance operations in the flow shop sequencing problem, Comput. Collect. Intell. Technol. Appl. 6923 (2011) 60–69.

DOI: 10.1007/978-3-642-23938-0_7

Google Scholar

[85] Hadda, H. ,A polynomial-time approximation scheme for the two machine flow shop problem with several availability constraints. Optimization Letters, 6 (2012) 559–569.

DOI: 10.1007/s11590-011-0281-7

Google Scholar

[86] Shoaardebili, N., & Fattahi, P. ,Multi-objective meta-heuristics to solve three-stage assembly flow shop scheduling problem with machine availability constraints,International Journal of Production Research, 53, (2015)944–968.

DOI: 10.1080/00207543.2014.948575

Google Scholar

[87] Hany Seidgar, Mostafa Zandieh & Iraj Mahdavi ,Bi-objective optimization for integrating production and preventive maintenance scheduling in twostage assembly flow shop problem, Journal of Industrial and Production Engineering. 10.1080.1173599(2016).

DOI: 10.1080/21681015.2016.1173599

Google Scholar

[88] Asma Ladj, Fatima Benbouzid-Si Tayeba, Christophe Varnierb, Ali Ayoub Dridia, Nacer Selmane .A Hybrid of Variable Neighbor Search and Fuzzy Logic for the permutation flowshop scheduling problem with predictive maintenance. Procedia Computer Science 112 (2017).

DOI: 10.1016/j.procs.2017.08.120

Google Scholar

[89] Cassady, C.R., & Kutanoglu, E,Integrating preventive maintenance planning and production scheduling for a single machine. IEEE Transactions on Reliability, 54(2) (2005) 304–309.

DOI: 10.1109/tr.2005.845967

Google Scholar

[90] J. Kaabi, C. Varnier, and N. Zerhouni. Scheduling with machine availability :An integrated approach. In Proc.of International conference on industrial Engineering and Production Management, IEPM'03, sur CD ROM, 7 pages,Porto, Portugal, mai 26-28 (2003).

Google Scholar

[91] M.A. Kubzin and V.A. Strusevich, Two-machine flow shop no-wait scheduling with machine maintenance, A Quarterly Journal of Operations Research 4OR 3: 303–313 (2005).

DOI: 10.1007/s10288-005-0070-1

Google Scholar

[92] Rong-Hwa Huang and Shun-Chi Yu .Two-stage multiprocessor flow shop scheduling with deteriorating maintenance in cleaner production. Journal of Cleaner Production 135 (2016) 276e283.

DOI: 10.1016/j.jclepro.2016.06.109

Google Scholar

[93] Cassady, C. R., & Kutanoglu, E.Minimizing job tardiness using integrated preventive maintenance planning and production scheduling. IIE Transactions, 35(2003) 503–513.

DOI: 10.1080/07408170304416

Google Scholar

[94] Sortrakul, N., Nachtmann, H. L., & Cassady, C. R.,Genetic algorithms for integrated preventive maintenance planning and production scheduling for a single machine. Computers in Industry, 56(2005)161–168.

DOI: 10.1016/j.compind.2004.06.005

Google Scholar

[95] Jabbarizadeh, F., Zandieh, M., & Talebi, D. ,Hybrid flexible flowshops with sequence-dependent setup times and machine availability constraints,Computers & Industrial Engineering, 57(2009) 949–957.

DOI: 10.1016/j.cie.2009.03.012

Google Scholar

[96] Leon, V. J., Wu, S. D., & Storer, R. H. ,Robust measures and robust scheduling for job shops, IIE Transactions, 26(1994) 32–43.

DOI: 10.1080/07408179408966626

Google Scholar

[97] O'Donovan, R., Uzsoy, R., & McKay, K. N. ,Predictable scheduling on a single machine with breakdowns and sensitive jobs. International Journal of Production Research, 37(1999)4217–4233.

DOI: 10.1080/002075499189745

Google Scholar

[98] Goren, S., & Sabuncuoglu, I., Robustness and stability measures for scheduling:single machine environment, IIE Transactions, 40(2008) 66–83.

DOI: 10.1080/07408170701283198

Google Scholar

[99] Al-Hinai, N., & ElMekkawy, T. Y., Robust and stable flexible job shop scheduling with random machine breakdowns using a hybrid genetic algorithm. International Journal of Production Economics, 132(2011) 279–291.

DOI: 10.1016/j.ijpe.2011.04.020

Google Scholar

[100] Briskorn, D., Leung, J., & Pinedo, M. ,Robust scheduling on a single machine using time buffers. IIE Transactions, 43(2011) 383–398.

DOI: 10.1080/0740817x.2010.505123

Google Scholar

[101] Rahmani, D., Heydari, M., Makui, A., & Zandieh, M. ,A new approach to reducing the effects of stochastic disruptions in flexible flow shop problems with stability and nervousness. International Journal of Management Science and Engineering Management,8(3) (2013).

DOI: 10.1080/17509653.2013.812332

Google Scholar

[102] Rahmani, D., & Ramezanian, R.,A stable reactive approach in dynamic flexible flow shop scheduling with unexpected disruptions: A case study. Computers & Industrial Engineering, 98(2016) 360–372.

DOI: 10.1016/j.cie.2016.06.018

Google Scholar

[103] Rahmani, D., & Heydari, M. ,Robust and stable flow shop scheduling with unexpected arrivals of new jobs and uncertain processing times. Journal of Manufacturing Systems, 33(2014) 84–92.

DOI: 10.1016/j.jmsy.2013.03.004

Google Scholar

[104] Cui, W. W., Lu, Z., & Pan, E. ,Integrated production scheduling and maintenance policy for robustness in a single machine, Computers & Operations Research, 47(2014) 81–91.

DOI: 10.1016/j.cor.2014.02.006

Google Scholar

[105] Lu, Z., Cui, W. W., & Han, X. ,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

Google Scholar

[106] Aguezzoul, A., Third-party logistics selection problem: A literature review on criteria and methods. Omega, 49(2014) 69-78.

DOI: 10.1016/j.omega.2014.05.009

Google Scholar

[107] Merigo,José M.,and Jian-Bo Yang. A Bibliometric Analysis of Operations Research and Management Science .,Omega (2016).

Google Scholar

[108] Gorman,M.F, A"Metasurvey" analysis in operations Research and Management Science:A survey of literature reviews. Surveys in Operations Research and Management Science, 21(1)(2016)18-28.

DOI: 10.1016/j.sorms.2016.05.002

Google Scholar

[109] Ahmed Gara-Ali. Ordonnancement des tâches et de périodes d'indisponibilité de durée variable. Autre. Université Grenoble Alpes, 2016. Fran¸cais. 01492812 (2016).

Google Scholar