DOI QR코드

DOI QR Code

작업순서 의존형 준비시간을 갖는 이종병렬기계의 휴리스틱 일정계획

Heuristics for Non-Identical Parallel Machine Scheduling with Sequence Dependent Setup Times

  • 고시근 (부경대학교 시스템경영공학부) ;
  • Koh, Shiegheun (Department of Systems Management and Engineering, Pukyong National University) ;
  • Mahardini, Karunia A. (Department of Systems Management and Engineering, Pukyong National University)
  • 투고 : 2013.09.25
  • 심사 : 2014.02.12
  • 발행 : 2014.06.15

초록

This research deals with a problem that minimizes makespan in a non-identical parallel machine system with sequence and machine dependent setup times and machine dependent processing times. We first present a new mixed integer programming formulation for the problem, and using this formulation, one can easily find optimal solutions for small problems. However, since the problem is NP-hard and the size of a real problem is large, we propose four heuristic algorithms including genetic algorithm based heuristics to solve the practical big-size problems in a reasonable computational time. To assess the performance of the algorithms, we conduct a computational experiment, from which we found the heuristic algorithms show different performances as the problem characteristics are changed and the simple heuristics show better performances than genetic algorithm based heuristics for the case when the numbers of jobs and/or machines are large.

키워드

참고문헌

  1. Agarwal, A., Colak, S., Jacob, V. S., and Pirkul, H. (2006), Heuristics and augmented neural networks for task scheduling with non-identical machines, European Journal of Operational Research, 175(1), 296-317. https://doi.org/10.1016/j.ejor.2005.03.045
  2. Allahverdi, A., Gupta, J. N. D. and Aldowaisan, T. (1999), A review of scheduling research involving setup considerations, OMEGA The International Journal of Management Science, 27(2), 219-239. https://doi.org/10.1016/S0305-0483(98)00042-5
  3. Allahverdi, A., Ng, C. T., Cheng, T. C. E., and Kovalyov, M. Y. (2008), A survey of scheduling problems with setup times or costs, European Journal of Operational Research, 187(3), 985-1032. https://doi.org/10.1016/j.ejor.2006.06.060
  4. Cheng, T. C. E. and Sin, C. C. S. (1990), A state-of-the-art review of parallel-machine scheduling research, European Journal of Operational Research, 47(3), 271-292. https://doi.org/10.1016/0377-2217(90)90215-W
  5. Gharehgozli, A. H., Tavakkoli-Moghaddam, R., and Zaerpour, N. (2009), A fuzzy-mixed integer goal programming model for a parallel-machine scheduling problem with sequence-dependent setup times and release dates, Robotics and Computer-Integrated Manufacturing, 25 (4/5), 853-859. https://doi.org/10.1016/j.rcim.2008.12.005
  6. Guinet, A. (1990), Textile production systems : a succession of non-identical parallel processor shops, Journal of the Operational Research Society, 42(8), 655-671.
  7. Hop, N. V. and Nagaur, N. N. (2004), The scheduling problem of PCBs for multiple non-identical parallel machines, European Journal of Operational Research, 158(3), 577-594. https://doi.org/10.1016/S0377-2217(03)00376-X
  8. Joo, C. M. and Kim, B. S. (2012a), Non-identical parallel machine scheduling with sequence and machine dependent setup times using metaheuristic algorithms, Industrial Engineering and Management Systems, 11(1), 114-122. https://doi.org/10.7232/iems.2012.11.1.114
  9. Joo, C. M. and Kim, B. S. (2012b), Genetic algorithm with an effective dispatching method for unrelated parallel machine scheduling with sequence dependent and machine dependent setup times, IE Interfaces, 25(3), 357-364. https://doi.org/10.7232/IEIF.2012.25.3.357
  10. Kang, Y. H., Lee, H. C. and Kim, S. S. (1998), Scheduling for non-identical parallel machines with different due dates, Journal of the Korean Institute of Industrial Engineers, 24(1), 37-50.
  11. Lee, J. S. and Park, S. H. (1999), Scheduling for two stage mixed flow production system with non-identical parallel machines, Journal of the Korean Institute of Industrial Engineers, 25(2), 254-265.
  12. Li, K. and Yang, S. L. (2009), Non-identical parallel-machine scheduling research with minimizing total weighted completion times : Models, relaxations and algorithms, Applied Mathematical Modelling, 33(4), 2145-2158. https://doi.org/10.1016/j.apm.2008.05.019
  13. Marsh, J. D. and Montgomery, D. C. (1973), Optimal procedure for scheduling jobs with sequence-dependent changeover times on parallel processors, AIIE Technical Papers, 279-286.
  14. Potts, C. N. and Kovalyov, M. Y. (2000), Scheduling with batching : A review, European Journal of Operational Research, 120(2), 228-249. https://doi.org/10.1016/S0377-2217(99)00153-8
  15. Ruiz, R. and Vazquez-Rodriguez, J. A. (2010), The hybrid flow shop scheduling problem, European Journal of Operational Research, 205(1), 1-18. https://doi.org/10.1016/j.ejor.2009.09.024
  16. Tavakkoli-Moghaddam, R., Taheri, F., Bazzazi, F., Izadi, M., and Sassani, F. (2009), Design of a genetic algorithm for bi-objective unrelated parallel machines scheduling with sequence-dependent setup times and precedence constraints, Computers and Operations Research, 36(12), 3224-3230. https://doi.org/10.1016/j.cor.2009.02.012
  17. Vallada, E. and Ruiz, R. (2011), A genetic algorithm for the unrelated parallel machine scheduling problem with sequence dependent setup times, European Journal of Operational Research, 211(3), 612-622. https://doi.org/10.1016/j.ejor.2011.01.011
  18. Weng, M. X., Lu, J. and Ren, H. (2001), Unrelated parallel machine scheduling with setup consideration and a total weighted completion time objective, International Journal of Production Economics, 70(3), 215-226. https://doi.org/10.1016/S0925-5273(00)00066-9
  19. Zhu, Z. and Heady, R. B. (2000), Minimizing the sum of earliness/tardiness in multi-machine scheduling: a mixed integer programming approach, Computers and Industrial Engineering, 38(2), 297-305. https://doi.org/10.1016/S0360-8352(00)00048-6