Abstract
In a proportionate flow shop problem, jobs have to be processed through a fixed sequence of machines, and processing time for each job is equal on all machines. Such a problem has seldom been tackled. Proportionate flexible flow shop (PFFS) scheduling problems combine the properties of proportionate flow shop scheduling problems and parallel machine scheduling problems. This study presents a combined approach based on column generation (CG) for a PFFS problem with the criterion to minimize the objective of the total weighted completion time (TWCT). Minimizing TWCT in a PFFS problem significantly differs from the parallel-identical-machine scheduling problem, an optimal schedule in which jobs on each machine are in the weighted shortest processing time (WSPT) order. This combined approach adopts a CG approach to effectively handle job assignments to machines, and a constructive heuristic to obtain an optimal sequence for a single machine. Experimental results show the effectiveness of the combined approach in obtaining excellent quality solutions in a reasonable time, especially for large-scale problems.
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References
Shakhlevich NV, Hoogeveen H, Pinedo ML (1998) Minimizing total weighted completion time in a proportionate flow shop. J Sched 1:157–168
Pinedo ML (2002) Scheduling: theory, algorithms, and systems, 2nd edn. Prentice-Hall, Englewood Cliffs, NJ
Chan FTS (1996) Exploring the scheduling problems in a flow shop environment via simulation. Int J Mater Prod Technol 11(1–2):108–132
Wang H (2005) Flexible flow shop scheduling: optimum, heuristics and artificial intelligence solutions. Expert Syst 22(2):78–85
Linn R, Zhang W (1999) Hybrid flow shop scheduling: a survey. Comput Ind Eng 37:57–61
Edwin Cheng TC, Shakhlevich N (1999) Proportionate flow shop with controllable processing times. J Sched 2:253–265
Panwalkar SS, Dudek RA, Smith ML (1973) Sequence research and the industrial scheduling problem. In: Elmaghraby SE (ed) Proc. Symp. on the theory of scheduling and its applications. Springer, Berlin Heidelberg New York, pp 29–37
Hou S, Hoogeveen H (2003) The three-machine proportionate flow shop problem with unequal machine speeds. Oper Res Lett 31(3):225–231
Estevez-Fernandez A, Mosquera MA, Borm P, Hamers H (2006) Proportionate flow shop games. Tilburg University, Center for Economic Research
Garey M, Johnson D, Sethi R (1976) The complexity of flow shop and job shop scheduling. Math Oper Res 1:117–129
Pan YP, Shi LY (2005) Dual constrained single machine sequencing to minimize total weighted completion Time. IEEE Trans Autom Sci Eng 2(4):344–357
Smith WE (1956) Various optimizers for single-stage production. Nav Res Log Quart 3:59–66
Shiau DF, Cheng SC, Huang YM (2007) Proportionate flexible flow shop scheduling via a hybrid constructive genetic algorithm. Expert syst appl, In Press
Ow PS (1985) Focused scheduling in proportionate flow shops. Manage Sci 31:852–869
Pinedo ML (1985) A note on stochastic shop models in which jobs have the same processing requirements on each machine. Manage Sci 31:840–845
Allahverdi A (1996) Two-machine proportionate flowshop scheduling with breakdowns to minimize maximum lateness. Comput Oper Res 23(10):909–916
Allahverdi A, Savsar M (2001) Stochastic proportionate flowshop scheduling with setups. Comput Ind Eng 39(3):357–369
Choi BC, Yoon SH, Chung SJ (2006) Minimizing the total weighted completion time in a two-machne proportionate flow shop with different machine speeds. Int J Prod Res 44(4):715–728
Choi BC, Yoon SH, Chung SJ (2007) Minimizing maximum completion time in a proportionate flow shop with one machine of different speed. Eur J Oper Res 176(2):964–974
Tang LX, Xuan H, Liu J (2006) A new Lagrangian relaxation algorithm for hybrid flowshop scheduling to minimize total weighted completion time. Comput Oper Res 33:3344–3359
Tozkapan A, Kırca Ö, Chung CS (2003) A branch and bound algorithm to minimize the total weighted flowtime for the two-stage assembly scheduling problem. Comput Oper Res 30(2):309–320
Moursli O, Pochet Y (2000) A branch-and-bound algorithm for the hybrid flow shop. Int J Prod Econ 64:113–125
Gupta JND, Hariri AMA, Potts CN (1997) Scheduling a two-stage hybrid flow shop with parallel machines at the first stage. Ann Oper Res 69:171–191
Oğuz C, Fikret Ercan M, Edwin Cheng TC, Fung YF (2003) Heuristic algorithms for multiprocessor task scheduling in a two-stage hybrid flow-shop. Eur J Oper Res 149:390–403
Kyparisis G, Koulamas C (2005) A note on makespan minimization in two-stage flexible flow shops with uniform machines. Eur J Oper Res, In Press
Gupta JND, Kruger K, Lauff V, Werner F, Sotskov YN (2002) Heuristics for hybrid flow shops with controllable processing times and assignable due dates. Comput Oper Res 29(10):1417–1439
Yang Y, Kreipl S, Pinedo M (2000) Heuristics for minimizing total weighted tardiness in flexible flow shops. J Sched 3:71–88
Şerifoğlu FS, Ulusoy G (2004) Multiprocessor task scheduling in multistage hybrid flow-shops: a genetic algorithm approach. J Oper Res Soc 55(5):504–512
Oğuz C, Ercan M (2005) A genetic algorithm for hybrid flow-shop scheduling with multiprocessor tasks. J Sched 8(4):323–351
Noorul Hag A, Ravindran D, Aruna V, Nithiya S (2004) A hybridization of metaheuristics for flow shop scheduling. Int J Adv Manufact Technol 24:376–380
Wang L, Zheng DZ (2003) An effective hybrid heuristic for flow shop scheduling. Int J Adv Manufact Technol 21(1):38–44
Van den Akker JM, Hoogeveen JA, Van De Velde SL (1999) Parallel machine scheduling by column generation. Oper Res 47:862–872
Chen ZL, Powell WB (1999) Solving parallel machine scheduling problems by column generation. INFORMS J Comput 11(1):78–94
Lee CY, Chen ZL (2000) Scheduling jobs and maintenance activities on parallel machines. Nav Res Log 47(2):145–165
Van den Akker JM, Hoogeveen JA, Van De Velde SL (2002) Combining column generation and Lagrangean relaxation to solve a single-machine common due date problem. INFORMS J Comput 14(1):37–51
Lübbecke ME, Desrosiers J (2005) Selected topics in column generation. Oper Res 53(6):1007–1023
Glover F (1989) Tabu search - Part I. ORSA J Comput 1:190–206
Barnes JW, Laguna M (1993) Solving the multiple-machine weighted flow time problem using tabu search. IIE Trans 25:121–128
Ben-Daya M, Al-Fawzan M (1998) A tabu search approach for the flow shop scheduling problem. Eur J Oper Res 109:88–95
Bilge Ü, Kiraç F, Kurtulan M, Pekgün P (2004) A tabu search algorithm for parallel machine total tardiness problem. Comput Oper Res 31:397–414
Kim CO, Shin HJ (2003) Scheduling jobs on parallel machines: a restricted tabu search approach. Int J Adv Manufact Technol 22:278–287
Dorn J, Girsh M, Skele G, Slany W (1996) Comparison of iterative improvement techniques for schedule optimization. Eur J Oper Res 94:349–361
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Huang, YM., Shiau, DF. Combined column generation and constructive heuristic for a proportionate flexible flow shop scheduling. Int J Adv Manuf Technol 38, 691–704 (2008). https://doi.org/10.1007/s00170-007-1130-9
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DOI: https://doi.org/10.1007/s00170-007-1130-9