DOI QR코드

DOI QR Code

단일 복구조정활동 하에 단계적 퇴화를 가지는 단일기계 생산일정계획

Single Machine Scheduling Problem with Step-deterioration under A Rate-modifying Activity

  • 김병수 (인천대학교 산업경영공학과)
  • Kim, Byung Soo (Department of Industrial and Management, Incheon National University)
  • 투고 : 2014.08.05
  • 심사 : 2014.08.29
  • 발행 : 2014.09.30

초록

In this paper, we deal with a single machine scheduling problems integrating with step deterioration effect and a rate-modifying activity (RMA). The scheduling problem assumes that the machine may have a single RMA and each job has the processing time of a job with deterioration is a step function of the gap between recent RMA and starting time of the job and a deteriorating date that is individual to all jobs. Based on the two scheduling phenomena, we simultaneously determine the schedule of step deteriorating jobs and the position of the RMA to minimize the makespan. To solve the problem, we propose a hybrid typed genetic algorithm compared with conventional GAs.

키워드

참고문헌

  1. Alidaee, B. and Womer, N.K., Scheduling with time dependent processing times : review and extensions. Journal of the Operational Research Society, 1999, Vol. 50, No. 7, p 711-721. https://doi.org/10.1057/palgrave.jors.2600740
  2. Bachman, A., Janiak, A., and Kovalyov, M.Y., Minimizing the total weighted completion time of deteriorating jobs. Information Processing Letters, 2002, Vol. 81, No. 2, p 81-84. https://doi.org/10.1016/S0020-0190(01)00196-X
  3. Bahalke, U., Yolmeh, A.M., and Shahanaghi, K. Metaheuristics to solve single-machine scheduling problem with sequence-dependent setup time and deteriorating jobs. International Journal of Advanced Manufacturing Technology, 2010, Vol. 50, No. 5-8, p 749-759. https://doi.org/10.1007/s00170-010-2526-5
  4. Bank, M., Fatemi Ghomi, S.M.T., Jolai, F., and Behnamian, J., Application of particle swarm optimization and simulated annealing algorithms in flow shop scheduling problem under linear deterioration. Advances in Engineering Software, 2012, Vol. 47, No. 1, p 1-6. https://doi.org/10.1016/j.advengsoft.2011.12.001
  5. Browne, S. and Yechiali, U., Scheduling deteriorating jobs on a single processor. Operations Research, 1999, Vol. 38, p 495-498.
  6. Cheng, T.C.E. and Ding, Q., Single machine scheduling with deadlines and increasing rates of processing times. Acta Informatica, 2000, Vol. 36, p 673-692. https://doi.org/10.1007/s002360050170
  7. Cheng, T.C.E. and Ding, Q., Single machine scheduling with step-deteriorating processing times. European Journal of Operational Research, 2001, Vol. 134, No. 3, p 623-630. https://doi.org/10.1016/S0377-2217(00)00284-8
  8. Cheng, T.C.E., Ding, Q., and Lin, B.M.T., A concise survey of scheduling with time-dependent processing times. European Journal of Operational Research, 2004, Vol. 152, p 1-13. https://doi.org/10.1016/S0377-2217(02)00909-8
  9. Cheng, T.C.E., Hsu, C. J., Huang, Y.C., and Lee, W.C., Single-machine scheduling with deteriorating jobs and setup times to minimize the maximum tardiness. Computers and Operations Research, 2011, Vol. 38, No. 12, p 1760-1765. https://doi.org/10.1016/j.cor.2010.11.014
  10. Gen, M. and Cheng, R., Genetic Algorithms and Engineering Optimization. New York : Wiley, 2000.
  11. Gupta, J.N.D. and Gupta, S.K., Single facility scheduling with nonlinear processing times. Computers and Industrial Engineering, 1988, Vol. 14, p 387-393. https://doi.org/10.1016/0360-8352(88)90041-1
  12. Huang, X. and Wang, M.Z., Parallel identical machines scheduling with deteriorating jobs and total absolute differences penalties. Applied Mathematical Modelling, 2011, Vol. 35, No. 3, p 1349-1353. https://doi.org/10.1016/j.apm.2010.09.013
  13. Iranpoor, M., Ghomi, S.M.T., and Zandieh, M., Machine scheduling in the presence of sequence-dependent setup times and a rate-modifying activity. International Journal of Production Research, 2012, Vol. 50, No. 24 p 7401-7414. https://doi.org/10.1080/00207543.2011.649801
  14. Jafari, A. and Moslehi, G., Scheduling linear deteriorating jobs to minimize the number of tardy jobs. Journal of Global Optimization, 2012, Vol. 54, No. 2, p 389- 404. https://doi.org/10.1007/s10898-011-9767-1
  15. Kim, B.S. and Joo, C.M., Single-machine total completion time scheduling with position-based deterioration and multiple rate-modifying activities. Industrial Engineering and Management Systems, 2011, Vol. 10, No. 4, p 247-254. https://doi.org/10.7232/iems.2011.10.4.247
  16. Kovalyov, M.Y. and Kubiak, W., A fully polynomial approximation scheme for minimizing makespan of deteriorating jobs. Journal of Heuristics, 1988, Vol. 3, No. 4, p 287-297.
  17. Kubiak, W. and van de Velde, S., Scheduling deteriorating jobs to minimize makespan. Naval Research Logistics, 1998, Vol. 45, No. 5, p 511-523. https://doi.org/10.1002/(SICI)1520-6750(199808)45:5<511::AID-NAV5>3.0.CO;2-6
  18. Kunnathur, A.S. and Gupta, S.K., Minimizing the makespan with late start penalties added to processing times in a single facility scheduling problem, European Journal of Operational Research, 1990, Vol. 47, No. 1, p 56-64. https://doi.org/10.1016/0377-2217(90)90089-T
  19. Lee, C.Y and Lin, C.S., Single-machine scheduling with maintenance and repair rate-modifying activities, European Journal of Operational Research, 2001, Vol. 135, p 493-513. https://doi.org/10.1016/S0377-2217(00)00322-2
  20. Lee, C.Y. and Chen, Z.L., Scheduling of jobs and maintenance activities on parallel machines, Naval Research Logistics, 2000, Vol. 47, p 61-67.
  21. Lee, C.Y. and Leon, V.J., Machine scheduling with a rate-modifying activity. European Journal of Operational Research, 2001, Vol. 128, p 119-128. https://doi.org/10.1016/S0377-2217(99)00066-1
  22. Lodree, E.J. and Geiger, C.D., A note on the optimal sequence position for a rate-modifying activity under simple linear deterioration, European Journal of Operational Research, 2010, Vol. 201, No. 2, p 644-648. https://doi.org/10.1016/j.ejor.2009.03.027
  23. Mosheiov, G. and Sarig, A., Scheduling a maintenance activity and due-window assignment on a single machine, Computers and Operations Research, 2009, Vol. 36, No. 9, p 2541-2545. https://doi.org/10.1016/j.cor.2008.10.007
  24. Mosheiov, G., Scheduling jobs with step-deterioration; Minimizing makespan on a single- and multi-machine. Computers and Industrial Engineering, 1995, Vol. 28, No. 4, p 869-879. https://doi.org/10.1016/0360-8352(95)00006-M
  25. Mosheiov, G., V-Shaped polices to scheduling deteriorating jobs. Operation Research, 1991, Vol. 39, p 979- 991. https://doi.org/10.1287/opre.39.6.979
  26. Moslehi, G. and Jafari, A., Minimizing the number of tardy jobs under piecewise-linear deterioration, Computers and Industrial Engineering, 2010, Vol. 59, No. 4, p 573-584. https://doi.org/10.1016/j.cie.2010.06.017
  27. Qi, X., Chen, T., and Tu, F., Scheduling the maintenance on a single machine. Journal of the Operational Research Society, 1990, Vol. 50, p 1071-1078.
  28. Ruiz-Torres, A-J., Paletta, G., and Perez, E., Parallel machine scheduling to minimize the makespan with sequence dependent deteriorating effects. Computers and Operations Research, 2013, Vol. 40, p 2051-2061. https://doi.org/10.1016/j.cor.2013.02.018
  29. Sundararaghavan, P.S. and Kunnathur, A.S., Single machine scheduling with start time dependent processing times : some solvable cases, European Journal of Operational Research, 1994, Vol. 78, No. 3, p 394-403. https://doi.org/10.1016/0377-2217(94)90048-5
  30. Wang, J.L., Sun, L., and Sun, L., Single-machine total completion time scheduling with a time-dependent deterioration. Applied Mathematical Modelling, 2011, Vol. 35, p 1506-1511. https://doi.org/10.1016/j.apm.2010.09.028
  31. Yang, D.-L. and Yang, S-J., Unrelated parallel-machine scheduling problems with multiple rate-modifying activities. Information Science, 2013, Vol. 235, p 280-286. https://doi.org/10.1016/j.ins.2013.02.013
  32. Yang, D.-L., Cheng, T.C.E., Yang, S.-J., and Hsu, C.-J., Unrelated parallel-machine scheduling with aging effects and multi-maintenance activities. Computers and Operations Research, 2012, Vol. 39, p 1458-1464. https://doi.org/10.1016/j.cor.2011.08.017
  33. Yang, D.-L., Cheng, T.C.E., and Yang, S-J., Parallelmachine scheduling with controllable processing times and rate-modifying activities to minimise total cost involving total completion time and job compressions. International Journal of Production Research, 2013, Vol. 52, No. 4, p 1133-1141.
  34. Zhao, C. and Tang, H., A note to due-window assignment and single machine scheduling with deteriorating jobs and a rate-modifying activity, Computers and Operations Research, 2012, Vol. 39, No. 6, p 1300-1303. https://doi.org/10.1016/j.cor.2010.04.006