Management Science and Financial Engineering

  • 제13권2호
  • /
  • Pages.47-77
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  • 2007
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  • 2287-2043(pISSN)
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  • 2287-2361(eISSN)
한국경영과학회 (The Korean Operations Research and Management Science Society)
권호 표지

Customer Order Scheduling Problem on Parallel Machines with Identical Order Size

  • Yang, Jae-Hwan (School of Business Administration, University of Seoul)
  • 발행 : 2007.11.30
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초록

This paper considers a scheduling problem where a customer orders multiple products(jobs) from a production facility. The objective is to minimize the sum of the order(batch) completion times. While a machine can process only one job at a time, multiple machines can simultaneously process jobs in a batch. Although each job has a unique processing time, we consider the case where batch processing times are identical. This simplification allows us to develop heuristics with improved performance bounds. This problem was motivated by a real world problem encountered by foreign electronics manufacturers. We first establish the complexity of the problem. For the two parallel machine case, we introduce two simple but intuitive heuristics, and find their worst case relative error bounds. One bound is tight and the other bound goes to 1 as the number of orders goes to infinity. However, neither heuristic is superior for all instances. We extend one of the heuristics to an arbitrary number of parallel machines. For a fixed number of parallel machines, we find a worst case bound which goes to 1 as the number of orders goes to infinity. Then, a tighter bound is found for the three parallel machine case. Finally, the heuristics are empirically evaluated.

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참고문헌

  1. Ahmadi, R., U. Bagchi, and T. A. Roemer, "Coordinated Scheduling of Customer Orders for Quick Response," Naval Research Logistics 52 (2005), 493-512 https://doi.org/10.1002/nav.20092
  2. Baker, K. R., "Scheduling the Production of Components at a Common Facility," IIE Transactions 20 (1988), 32-35 https://doi.org/10.1080/07408178808966147
  3. Blocher, J. D. and D. Chhajed, "The Customer Order Lead Time Problem on Parallel Machines," Naval Research Logistics 43 (1996), 629-654 https://doi.org/10.1002/(SICI)1520-6750(199608)43:5<629::AID-NAV3>3.0.CO;2-7
  4. Blocher, J. D., D. Chhajed, and M. Leung, "Customer Order Scheduling in a General Job Shop Environment," Decision Science 29 (1998), 951-981 https://doi.org/10.1111/j.1540-5915.1998.tb00883.x
  5. Bruno, J., E. G. Coffman and R. Sethi, "Scheduling Independent Tasks to Reduce Mean Finishing Time," Communications of the ACM 17 (1974), 382-387 https://doi.org/10.1145/361011.361064
  6. Coffman, E. G., A. Nozari, and M. Yannakakis, "Optimal Scheduling of Products with Two Subassemblies on a Single Machine," Operations Research 37 (1989), 426-436 https://doi.org/10.1287/opre.37.3.426
  7. Ding, F. Y., "A Pairwise Interchange Solution Procedure for a Scheduling Problem with Production of Components at a Single Facility," Computers and Industrial Engineering 18 (1990), 325-331 https://doi.org/10.1016/0360-8352(90)90054-P
  8. Gerodimos, A. E., C. A. Glass, and C. N. Potts, "Scheduling the Production of Two-Component Jobs on a Single Machine," European Journal of Operational Research 120 (2000), 250-259 https://doi.org/10.1016/S0377-2217(99)00154-X
  9. Graham, R. L., "Bounds on Multiprocessing Timing Anomalies," SIAM Journal on Applied Mathematics 17 (1969), 416-429 https://doi.org/10.1137/0117039
  10. Graham, R. L., E. L. Lawler, J. K. Lenstra, and A. H. G. Rinnooy Kan, "Optimization and Approximation in Deterministic Machine Scheduling: A Survey," Annals of Discrete Mathematics 5 (1979), 287-326 https://doi.org/10.1016/S0167-5060(08)70356-X
  11. Gupta, J. N. D., J. C. Ho, and A. A. van der Veen, "Single Machine Hierarchical Scheduling with Customer Orders and Multiple Job Classes," Annals of Operations Research 70 (1997), 127-143 https://doi.org/10.1023/A:1018913902852
  12. Julien, F. M. and M. J. Magazine, "Scheduling Customer Orders: An Alternative Production Scheduling Approach," Journal of Manufacturing and Operations Management 3 (1990), 177-199
  13. Liao, C. J., "Optimal Scheduling of Products with Common and Unique Components," International Journal of Systems Science 27 (1996), 361-366 https://doi.org/10.1080/00207729608929225
  14. Roemer, T. A. and R. Ahmadi, "Complexity of Scheduling Customer Orders," Working Paper, Anderson School at UCLA (1997), USA
  15. Santos, C. and M. Magazine, "Batching in Single Operation Manufacturing Systems," Operations Research Letters 4 (1985), 99-103 https://doi.org/10.1016/0167-6377(85)90011-2
  16. Yang, J., "The Complexity of Customer Order Scheduling Problems on Parallel Machines," Computers and Operations Research 32 (2005), 1921-1939 https://doi.org/10.1016/j.cor.2003.12.008
  17. Yang, J. and M. E. Posner, "Scheduling Parallel Machines for the Customer Order Problem," Journal of Scheduling 8 (2005), 49-74 https://doi.org/10.1007/s10951-005-5315-5