Management Science and Financial Engineering

  • 제17권1호
  • /
  • Pages.95-116
  • /
  • 2011
  • /
  • 2287-2043(pISSN)
  • /
  • 2287-2361(eISSN)
한국경영과학회 (The Korean Operations Research and Management Science Society)
권호 표지

Customer Order Scheduling in a Two Machine Flowshop

  • Yang, Jae-Hwan (College of Business Administration, University of Seoul)
  • 투고 : 2010.09.16
  • 심사 : 2011.05.03
  • 발행 : 2011.05.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

This paper considers a flowshop scheduling problem where a customer orders multiple products (jobs) from a production facility. The objectives are to minimize makespan and to minimize the sum of order (batch) completion times. The order cannot be shipped unless all the products in the order are manufactured. This problem was motivated by numerous real world problems encountered by a variety of manufacturers. For the makespan objective, we develop an optimal solution procedure which runs in polynomial time. For the sum of order completion time objective, we establish the complexity of the problem including several special cases. Then, we introduce a simple heuristic and find an asymptotically tight worst case bound on relative error. Finally, we conclude the paper with some implications.

키워드

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. Blocher, J. D. and D. Chhajed, "Minimizing Customer Order Lead‐iime in a Two‐stage Assembly Supply Chain," Decision Science 29 (1998), 951-981. https://doi.org/10.1111/j.1540-5915.1998.tb00883.x
  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. Garey, M. R., D. S. Johnson, and R. Sethi, "The Complexity of Flowshop and Jobshop Scheduling," Mathematics of Operations Research 1 (1976), 117-129. https://doi.org/10.1287/moor.1.2.117
  9. 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
  10. Gonzalez, T. and S. Sahni, "Flowshop and job shop schedules: Complexity and approximation," Operations Research 26 (1978), 36-52. https://doi.org/10.1287/opre.26.1.36
  11. 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.
  12. 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
  13. Hoogeveen, J. A. and T. Kawaguchi, "Minimizing total completion time in a two‐machine flowshop: analysis of special cases," Mathematics of Operations Research 24 (1999), 887-910. https://doi.org/10.1287/moor.24.4.887
  14. Johnson, S. M., "Optimal Two‐ and Three‐Stage Production with Setup Times Included," Naval Research Quarterly 1 (1954), 61-68. https://doi.org/10.1002/nav.3800010110
  15. 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.
  16. 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
  17. Roemer, T. A. and R. Ahmadi, "Complexity of Scheduling Customer Orders," Working Paper, Anderson School at UCLA (1997), USA.
  18. 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
  19. 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