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A Genetic Algorithm for Minimizing Completion Time with Non-identical Parallel Machines

이종 병렬설비 공정의 작업완료시간 최소화를 위한 유전 알고리즘

  • 최유준 (동아대학교 경영대학 경영학과) ;
  • 송한식 (동아대학교 경영대학 경영학과) ;
  • 이익선 (동아대학교 경영대학 경영학과)
  • Received : 2013.08.27
  • Accepted : 2013.11.07
  • Published : 2013.11.30

Abstract

This paper considers a parallel-machine scheduling problem with dedicated and common processing machines. Non-identical setup and processing times are assumed for each machine. A genetic algorithm is proposed to minimize the makespan objective measure. In this paper, a lowerbound and some heuristic algorithms are derived and tested through computational experiments.

Keywords

References

  1. 최유준, 유지돈, 송한식, 이익선, "병렬설비를 가지는 열처리공정에서의 배치일정계획 수립 연구", 한국생산관리학회지, 제22권, 제4호(2011), pp.451-467.
  2. 하병현, "자원 제약이 없는 환경에서 부분 우선순위를 고려한 Earliness-Tardiness 최적일정계획 알고리즘", 한국경영과학회지, 제38권, 제2호(2013), pp.141-157.
  3. Agarwal, A., C. Colak, V. Jacob, and H. Pirkul, "Heuristics and augmented neural networks for task scheduling with non-identical machines," European Journal of Operational Research, Vol.175, No.1(2006), pp.296-317. https://doi.org/10.1016/j.ejor.2005.03.045
  4. Baker, K.R., Introduction to sequencing and scheduling, New York : Wiley, Vol.31(1974).
  5. Behnamian, J., M. Zandieh, and S.M.T. Fatemi Ghomi, "Parallel-machine scheduling problems with sequence-dependent setup times using an ACO, SA and VNS hybrid algorithm," Expert Systems with Applications, Vol.36, No.6(2009), pp.9637-9644. https://doi.org/10.1016/j.eswa.2008.10.007
  6. Chen, C.L. and C.L. Chen, "A bottleneckbased heuristic for minimizing makespan in a flexible flow line with unrelated parallel machines," Computers and Operations Research, Vol.36, No.11(2009), pp.3073-3081. https://doi.org/10.1016/j.cor.2009.02.004
  7. Cheng, B., S. Yang, X. Hu, and B. Chen, "Minimizing makespan and total completion time for parallel batch processing machines with non-identical job sizes," Applied Mathematical Modelling, Vol.36, No.7(2011), pp.3161-3167.
  8. Davis, E. and J. M. Jaffe, "Algorithms for scheduling tasks on unrelated processors," Journal of the ACM(JACM), Vol.28, No.4 (1981), pp.721-736.
  9. De, P. and T.E. Morton, "Scheduling to minimize makespan on unequal parallel processors," Decision Sciences, Vol.11, No.4 (1980), pp.586-602. https://doi.org/10.1111/j.1540-5915.1980.tb01163.x
  10. Franca, P.M., M. Gendreau, G. Laporte, and F.M. Muller, "A tabu search heuristic for the multiprocessor scheduling problem with sequence dependent setup times," International Journal of Production Economics, Vol.43, No.2(1996), pp.79-89. https://doi.org/10.1016/0925-5273(96)00031-X
  11. Garey, M.R. and D.S. Johnson, Computer and intractability : A guide to the theory of NP-completeness, San Francisco : W.H. Freeman, 1979.
  12. Gendreau, M., G. Laporte, and E.M. Guimaraes, "A divide and merge heuristic for the multiprocessor scheduling problem with sequence dependent setup times," European Journal of Operational Research, Vol.133, No.1(2001), pp.183-189. https://doi.org/10.1016/S0377-2217(00)00197-1
  13. Ghirardi, M. and C.N. Potts, "Makespan minimization for scheduling unrelated parallel machines : A recovering beam search approach," European Journal of Operational Research, Vol.165, No.2(2005), pp.457-467. https://doi.org/10.1016/j.ejor.2004.04.015
  14. Guinet, A., "Scheduling sequence-dependent jobs on identical parallel machines to minimize completion time criteria," The International Journal of Production Research, Vol.31, No.7(1993), pp.1579-1594. https://doi.org/10.1080/00207549308956810
  15. Hariri, A.M.A. and C.N. Potts, "Heuristics for scheduling unrelated parallel machines," Computers and operations research, Vol.18, No.3(1991), pp.323-331. https://doi.org/10.1016/0305-0548(91)90034-O
  16. Holland, J.H., Adaptation in Natural and Artificial System, University of Michigan Press, Ann Arbor, 1975.
  17. Horowitz, E. and S. Sahni, "Exact and approximate algorithms for scheduling nonidentical processors," Journal of the ACM (JACM), Vol.23, No.2(1976), pp.317-327. https://doi.org/10.1145/321941.321951
  18. Hu, T.C., "Parallel sequencing and assembly line problems," Operations Research, Vol.9 (1961), pp.841-848. https://doi.org/10.1287/opre.9.6.841
  19. Ibarra, O.H. and C.E. Kim, "Heuristic algorithms for scheduling independent tasks on nonidentical processors," Journal of the ACM(JACM), Vol.24, No.2(1977), pp.280-289.
  20. Kim, D.W., K.H. Kim, W. Jang, and C.F. Frank, "Unrelated parallel machine scheduling with setup times using simulated annealing," Robotics and Computer-Integrated Manufacturing, Vol.18, No.3(2002), pp.223-231. https://doi.org/10.1016/S0736-5845(02)00013-3
  21. Kim, J.G., J.S. Kim, and D.H. Lee, "Common Due-Date Assignment and Scheduling with Sequence-Dependedt Setup Times : a Case Study on a Paper Remanufacturing System," Management Science and Financial Engineering, Vol.18, No.1(2012), pp.1-12.
  22. Lenstra, J.K. and A.H.G. Rinnooy Kan, "Complexity of scheduling under precedence constraints," Operations Research, Vol.26 (1978), pp.22-35. https://doi.org/10.1287/opre.26.1.22
  23. Lenstra, J.K., D.B. Shmoys, and E. Tardos, "Approximation algorithms for scheduling unrelated parallel machines," Mathematical programming, Vol.46, No.1(1990), pp.259-271. https://doi.org/10.1007/BF01585745
  24. McNaughton, R., "Scheduling with deadlines and loss functions," Management Science, Vol.6(1959), pp.1-12. https://doi.org/10.1287/mnsc.6.1.1
  25. Min, L. and W. Cheng, "A genetic algorithm for minimizing the makespan in the case of scheduling identical parallel machines," Artificial Intelligence in Engineering, Vol.13 (1999), pp.399-403. https://doi.org/10.1016/S0954-1810(99)00021-7
  26. Palekar, U.S., N. Rama, and K. Toaffe, "Duality based relaxations for makespan minimization for unrelated parallel machines," TIMS/ORSA Bulletin, Vol.31(1991) p.21.
  27. Piersma, N. and W . van Dijk, "A local search heuristic for unrelated parallel machine scheduling with efficient neighborhood search," Mathematical and Computer Modelling, Vol.24, No.9(1996), pp.11-19.
  28. Potts, C.N., "Analysis of a linear programming heuristic for scheduling unrelated parallel machines," Discrete Applied Mathematics, Vol.10, No.2(1985), pp.155-164. https://doi.org/10.1016/0166-218X(85)90009-5
  29. Rinnooy Kan, A.H.G., Machine scheduling problems : Classification, complexity and computations. The Hague : Martinus Nijhoff, 1976.
  30. Sethi, R., "On the complexity of mean flow time scheduling," Mathematics of Operations Research, Vol.2, No.4(1977), pp.320-330. https://doi.org/10.1287/moor.2.4.320
  31. Srivastava, B., "An effective heuristic for minimising makespan on unrelated parallel machines," Journal of the Operational Research Society, Vol.49, No.8(1998), pp.886-894. https://doi.org/10.1057/palgrave.jors.2600547
  32. Van de Velde, S.L., "Duality-based algorithms for scheduling unrelated parallel machines," ORSA Journal on Computing, Vol.5, No.2(1993), pp.192-205. https://doi.org/10.1287/ijoc.5.2.192