Abstract
In order to deal with uncertainties, a robust schedule for M-machine permutation flowshop is proposed. The presented robust schedule is aimed to maximize the probability of ensuring that makespan will not exceed the expected completion time. An improved genetic algorithm (GA) with a new generation scheme is developed, which can preserve good characteristics of parents in the new generation. Experiments are performed to get robust schedules for well-known Car and Rec permutation flowshop problems, taken from OR library. The schedules obtained from the improved GA are compared with the schedules formed by well-known heuristic in literature. Computational results show that the permutation flowshop schedules obtained from improved GA are robust to produce an affirmative percentage increase in the probability of getting makespan less than expected completion time.
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Aytug H, Lawley MA, McKay K, Mohan S, Uzsoy R (2005) Executing production schedules in the face of uncertainties: a review and some future directions. Eur J Oper Res 161:86–110
Pierreval H, Durieux-Paris S (2007) Robust simulation with a base environmental scenario. Eur J Oper Res 182:783–793
Goren S, Sabuncuoglu I (2008) Robustness and stability measures for scheduling: single-machine environment. IIE Trans 40:66–83
Li Z, Ierapetritou M (2008) Process scheduling under uncertainty: review and challenges. Comput Chem Eng 32:715–727
Herroeleny W, Leus R (2004) Robust and reactive project scheduling: a review and classification of procedures. Int J Prod Res 42(8):1599–1620
Lan S, Clarke J, Barnhart C (2006) Planning for robust airline operations optimizing aircraft routings and flight departure times to minimize passenger disruptions. Transp Sci 40(1):15–28
Tang L, Wang X (2008) A predictive reactive scheduling method for color-coating production in steel industry. Int J Adv Manuf Technol 35:633–645
Feiza G, Henri P, Hajri-Gabouj S (2010) Analysis of robustness in proactive scheduling: a graphical approach. Comput Ind Eng 58:193–198
Sabuncuoglu I, Goren S (2009) Hedging production schedules against uncertainty in manufacturing environment with a review of robustness and stability research. Int J Computer Integr Manuf 22(2):138–157
Kouvelis P, Daniels RL, Vairaktarakis G (2000) Robust scheduling of a two-machine flowshop with uncertain processing times. IIE Trans 32(5):421–432
Kuo CY, Lin FJ (2002) Relative robustness for single-machine scheduling problem with processing time uncertainty. J Chin Inst Ind Eng 19(5):59–67
Kouvelis P, Yu G (1997) Robust discrete optimization and its applications. Kluwer Academic Publishers, Boston
Daniels RL, Kouvelis P (1995) Robust scheduling to hedge against processing time uncertainty in single-stage production. Manage Sci 41:363–376
Kaperski A (2005) Minimizing maximal regret in the single machine sequencing problem with maximum lateness criterion. Oper Res Lett 33:431–436
Yang J, Yu G (2002) On the robust single machine scheduling problem. J Comb Optim 6:17–33
Liu L, Gu HY, ** YG (2007) Robust and stable scheduling of a single machine with random machine breakdowns. Int J Adv Manuf Technol 31:645–654
Daniels RL, Carrillo JE (1997) β-Robust scheduling for single-machine systems with uncertain processing times. IIE Trans 29:977–985
Wu CW, Brown KN, Beck JC (2009) Scheduling with uncertain durations: modeling β-robust scheduling with constraints. Comput Oper Res 36:2348–2356
Teixidor AB (2006) Proactive management of uncertainty to improve scheduling robustness in process industries. PhD thesis, Universitat Politμecnica de Catalunya Barcelona
Hapke M, Jaskievicz A, Slowinski R (1999) Fuzzy multimode resource-constrained project scheduling with multiple objectives. In: Weglarz J (ed) Project scheduling recent models, algorithms and applications. Kluwer Academic Publishers, Dordrecht, pp 355–382
Allen E (2007) Modeling with Itô stochastic differential equation. Springer, Dordrecht
Hayter AJ (1996) Probability and statistics for engineers and scientists. PWB Publishing, Duxbury
Chen CL, Vempati VS, Aljaber N (1995) An application of genetic algorithms for flow shop problems. Eur J Oper Res 80:389–396
Reeves CR (1995) A genetic algorithm for flow shop sequencing. Comput Oper Res 22(1):5–13
Murata T, Ishibuchi H, Tanaka H (1996) Genetic algorithms for flowshop scheduling problems. Comput Ind Eng 30:1061–1071
Etiler O, Toklu B, Atak M, Wilson J (2004) A genetic algorithm for flow shop scheduling problems. J Oper Res Soc 55:830–835
Ruiz R, Maroto C, Alcaraz J (2006) Two new robust genetic algorithms for the flowshop scheduling problem. Omega–Int J Manage S 34:461–476
Zhang BT, Kim JJ (2000) Comparison of selection methods for evolutionary optimization. Evolutionary Optimization an International Journal 2(1):55–70
Sivanandam SN, Deepa SN (2008) Introduction to genetic algorithms. Springer, Berlin
Nawaz M, Enscore E, Ham I (1983) A heuristic algorithm for the m-machine, n-machine flow shop sequencing problem. Omega 11:91–95
Turner S, Booth D (1987) Comparison of heuristics for flow shop sequencing. Int J Manag Sci 15:75–85
Ruiz R, Maroto C (2005) A comprehensive review and evaluation of permutation flowshop heuristics. Eur J Oper Res 165:479–494
Gupta JND, Koulamas C, Kyparisis GJ (2006) Perfomance guarantees for flowshop heuristics to minimize makespan. Eur J Oper Res 169:865–872
Kalczynski PJ, Kamburowski J (2007) On the NEH heuristic for minimizing the makespan in permutation flowshops. Omega–Int J Manage S 35(1):53–60
Carlier J (1978) Ordonnancements a contraintes disjunctives, RAIRO Recherche operations Elle. Oper Res 12:333–351
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Liu, Q., Ullah, S. & Zhang, C. An improved genetic algorithm for robust permutation flowshop scheduling. Int J Adv Manuf Technol 56, 345–354 (2011). https://doi.org/10.1007/s00170-010-3149-6
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DOI: https://doi.org/10.1007/s00170-010-3149-6