Management Science and Financial Engineering

  • 제11권2호
  • /
  • Pages.19-43
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  • 2005
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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 Problems with a Fixed Machine-Job Assignment

  • Yang, Jae-Hwan (School of Business Administration, University of Seoul) ;
  • Rho, Yoo-Mi (Department of Mathematics, University of lncheon)
  • 발행 : 2005.11.01
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초록

This paper considers a variation of the customer order scheduling problem, and the variation is the case where the machine-job assignment is fixed. We examine the parallel machine environment, and the objective is to minimize the sum of the completion times of the batches. While a machine can process only one job at a time, different machines can simultaneously process different jobs in a batch. The recognition version of this problem is known to be NP-complete in the strong sense even if there exist only two parallel machines. When there are an arbitrary number of parallel machines, we establish three lower bounds and develop a dynamic programming (DP) algorithm which runs in exponential time on the number of batches. We present two simple but intuitive heuristics, SB and GR, and find some special cases where SB and GR generate an optimal schedule. We also find worst case upper bounds on the relative error. For the case of the two parallel machines, we show that GR generates an optimal schedule when processing times of all batches are equal. Finally, the heuristics and the lower bounds 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,' Working Paper, Anderson School of Management at UCLA, USA 2004
  2. Baker, K. R., 'Scheduling the Production of Components at a Common Facility,' lIE 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 Res. Logist. 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. 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
  6. 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
  7. 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
  8. 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
  9. Gupta, J. N. D., J. C. Ho, and A. A. van der Veen, 'Single Machine Hierarchical Scheduling with Customer Orders and Multiple Job Classes,' Annal of Operations Research 70 (1997), 127-143 https://doi.org/10.1023/A:1018913902852
  10. Jordan, C., Batching and Scheduling: Models and Methods for Several Problem Classes, Springer, New York 1996
  11. 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
  12. 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
  13. Potts, C. N. and L. N. Van Wassenhove, 'Integrating Scheduling with Batching and Lot-sizing: a Review of Algorithm and Complexity,' Journal of Operational Research Society 43 (1992), 395-406 https://doi.org/10.2307/2583559
  14. Roemer, T. A., and R. Ahmadi, 'The Complexity of Scheduling Customer Orders,' Working Paper, Anderson School of Management at UCLA, USA 1997
  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. Webster, C. and K. R. Baker, 'Scheduling Groups of Jobs on a Single Machine,' Operations Research 43 (1995),692-703 https://doi.org/10.1287/opre.43.4.692
  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
  18. Yang, J., 'Scheduling Parallel Machines for the Customer Order Problem with Fixed Bach Sequence,' Journal of the Korean Institute of Industrial Engineers 29 (2003) 304-311
  19. 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
  20. Yoon, S. H., 'Fabrication Scheduling of Products with Common and Unique Components at a Single Facility,' Journal of the Korean Operations Research and Management Science Society 28 (2003), 105-114