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Simultaneous Resource Scheduling to Minimize Weighted Flow Times

Author

Listed:
  • Gregory Dobson

    (University of Rochester, Rochester, New York)

  • Uday S. Karmarkar

    (University of Rochester, Rochester, New York)

Abstract

Many scheduling problems in manufacturing and service firms involve tasks that require more than one resource to be used simultaneously to execute the task. Two formulations of this scheduling problem are given. We develop a Lagrangian relaxation for the problem that has an intuitive interpretation. The relaxation suggests heuristics and provides a lower bound on the optimal solution. Next a surrogate relaxation is developed that provides a second bound and a heuristic solution. An enumeration procedure to determine the optimal solution is described, and computational results on the effectiveness of the bounds and the heuristics are presented. The Lagrangian relaxation performs better on problems with a low degree of simultaneity, and the surrogate relaxation does better with a high degree of simultaneity.

Suggested Citation

  • Gregory Dobson & Uday S. Karmarkar, 1989. "Simultaneous Resource Scheduling to Minimize Weighted Flow Times," Operations Research, INFORMS, vol. 37(4), pages 592-600, August.
    • Handle: RePEc:inm:oropre:v:37:y:1989:i:4:p:592-600
    DOI: 10.1287/opre.37.4.592
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    Citations

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    Cited by:

    1. Reza Ahmadi & Uttarayan Bagchi & Thomas A. Roemer, 2005. "Coordinated scheduling of customer orders for quick response," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(6), pages 493-512, September.
    2. Itai Gurvich & Jan A. Van Mieghem, 2015. "Collaboration and Multitasking in Networks: Architectures, Bottlenecks, and Capacity," Manufacturing & Service Operations Management, INFORMS, vol. 17(1), pages 16-33, February.
    3. Jingui Huang & Jianer Chen & Songqiao Chen & Jianxin Wang, 2007. "A simple linear time approximation algorithm for multi-processor job scheduling on four processors," Journal of Combinatorial Optimization, Springer, vol. 13(1), pages 33-45, January.
    4. Cha, Young-Ho & Kim, Yeong-Dae, 2010. "Fire scheduling for planned artillery attack operations under time-dependent destruction probabilities," Omega, Elsevier, vol. 38(5), pages 383-392, October.
    5. Jianer Chen & Chung‐Yee Lee, 1999. "General multiprocessor task scheduling," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(1), pages 57-74, February.
    6. Khosla, Inder, 1995. "The scheduling problem where multiple machines compete for a common local buffer," European Journal of Operational Research, Elsevier, vol. 84(2), pages 330-342, July.
    7. Milind Dawande & Zhichao Feng & Ganesh Janakiraman, 2021. "On the Structure of Bottlenecks in Processes," Management Science, INFORMS, vol. 67(6), pages 3853-3870, June.
    8. Fumero, Francesca & Vercellis, Carlo, 1997. "Integrating distribution, machine assignment and lot-sizing via Lagrangean relaxation," International Journal of Production Economics, Elsevier, vol. 49(1), pages 45-54, March.

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