A Scheduling Problem to Minimize Weighted Completion Time in the Two-stage Assembly-type Flowshop

두 단계 조립시스템에서 총 가중완료시간을 최소화하는 일정계획문제

  • Yoon, Sang Hum (School of Management, Yeungnam University) ;
  • Lee, Ik Sun (Department of Industrial Engineering, KAIST) ;
  • Lee, Jong Hyup (Department of Information and Communications Engineering, Inje University)
  • 윤상흠 (영남대학교 경영학부) ;
  • 이익선 (한국과학기술원 산업공학과) ;
  • 이종협 (인제대학교 정보통신공학과)
  • Published : 2007.06.30

Abstract

This paper considers a scheduling problem to minimize the total weighted completion time in the two-stage assembly-type flowshop. The system is composed of multiple fabrication machines in the first stage and a final-assembly machine in the second stage. Each job consists of multiple components, each component is machined on the fabrication machine specified in advance. The manufactured components of each job are subsequently assembled into a final product on the final-assembly machine. The objective of this paper is to find the optimal schedule minimizing the total weighted completion time of jobs. Three lower bounds are derived and tested in a branch-and-bound (B&B) Procedure. Also, three heuristic algorithms are developed based on the greedy strategies. Computational results show that the proposed B&B procedure is more efficient than the previous work which has considered the same problem as this paper.

Keywords

References

  1. Ahmadi, R., Bagchi, D., and Roemer, T. A. (2005), Coordinated Scheduling of Customer Orders for Quick Response, Naval Research Logistics, 52, 493-512 https://doi.org/10.1002/nav.20092
  2. Baker, K. R. (1974), Introduction to Sequencing and Scheduling, John Wiley & Sons
  3. Baker, K. R. and Powell, S. G. (1993), A Predictive Model for the Throughput of Simple Assembly Systems, European Journal of Operational Research, 81, 336-345
  4. Baker, K. R., Powell, S. G., and Pyke, D. F. (1993), Optimal Allocation of Work in Assembly Systems, Management Science, 39, 101-106 https://doi.org/10.1287/mnsc.39.1.101
  5. Bhat, U. N. (1986), Finite Capacity Assembly-like Queues, Queueing Systems, 1, 85-101. https://doi.org/10.1007/BF01149329
  6. Duda, A. and Czachorski, T. (1987), Performance Evaluation of Fork and Join Syschronization Primitives, Acta Informatica, 24, 525-553
  7. Hariri, A. M. A. and Potts, C. N. (1997), A Branch-and-Bound Algorithm for the Two-Stage Assembly Scheduling Problem, European Journal of Operational Research, 103, 547-556 https://doi.org/10.1016/S0377-2217(96)00312-8
  8. He, D. W. and Kusiak, A. (1996), Performance Analysis of Modular Products, International Journal of Production Research, 34, 253-272 https://doi.org/10.1080/00207549608904900
  9. Lee, C. Y., Cheng, T. C. E., and Lin, B. M. T. (1993), Minimizing the Makespan in the 3-Machine Assembly-type Flowshop Scheduling Problem, Management Science, 39, 616-625 https://doi.org/10.1287/mnsc.39.5.616
  10. Leung, J. Y. T., Li, H., and Pinedo, M. (2005a), Order Scheduling in an Environment with Dedicated Resources in Parallel, Journal of Scheduling, 8, 355-386 https://doi.org/10.1007/s10951-005-2860-x
  11. Leung, J. Y. T., Li, H., and Pinedo, M. (2005b), Order Scheduling Models: an Overview, Multidisciplinary Scheduling, 1, 37-56
  12. Leung, J. Y. T., Li, H., and Pinedo, M. (2006a), Approximation Algorithms for Minimizing Total Weighted Completion Time of Orders on Identical Machines in Parallel, Naval Research Logistics, 53, 243-260 https://doi.org/10.1002/nav.20138
  13. Leung, J. Y. T., Li, H., and Pinedo, M. (2006b), Scheduling Orders for Multiple Product Types with Due Date Related Objectives, European Journal of Operational Research, 168, 370-389 https://doi.org/10.1016/j.ejor.2004.03.030
  14. Norahari, Y. and Sundarrajan, P. (1995), Performability Analysis of Fork-Join Queueing Systems, Journal of the Operational Research Society, 46, 1237-1249 https://doi.org/10.1038/sj/jors/0461007
  15. Potts, C. N., Sevast'janov, S. Y., Strusevich, V. A., Wassenhove, L. N., and Zwaneveld, C. M. (1995), The Two-Stage Assembly Scheduling Problem: Complexity and Approximation, Operations Research, 43, 346-355 https://doi.org/10.1287/opre.43.2.346
  16. Sun, X., Morizawa, K., and Nagasawa, H. (2003), Powerful Heuristics to Minimize Makespan in Fixed, 3-Machine, Assembly-type Flowshop Scheduling, European Journal of Operational Research, 146, 499-517
  17. Sung, C. S. and Yoon, S. H. (1998), Minimizing Total Weighted Completion Time at a Pre-assembly Stage Composed of Two Feeding Machines, International Journal of Production Economics, 54, 247-255 https://doi.org/10.1016/S0925-5273(97)00151-5
  18. Tozkapan, A., Kirca, O., and Chung, C. S. (2003), A Branch-andBound Algorithm to Minimize the Total Weighted Flowtime for the Two-stage Assembly Scheduling Problem, Computers & Operations Research, 30, 309-320 https://doi.org/10.1016/S0305-0548(01)00098-3
  19. Wang, G. and Cheng, T. C. E. (2007), Customer Order Scheduling to Minimize Total Weighted Completion Time, to appear in Omega
  20. Yang, J. and Posner, M. E. (2005), Scheduling Parallel Machines for the Customer Order Problem, Journal of Scheduling, 8, 49-74 https://doi.org/10.1007/s10951-005-5315-5
  21. Yoon, S. H. and Sung, C. S. (2005), Fixed Pre-assembly Scheduling on Multiple Fabrication Machines, International Journal of Production Economics, 96, 109-118 https://doi.org/10.1016/j.ijpe.2004.03.005