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General multiprocessor task scheduling

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  • Jianer Chen
  • Chung‐Yee Lee

Abstract

Most papers in the scheduling field assume that a job can be processed by only one machine at a time. Namely, they use a one‐job‐on‐one‐machine model. In many industry settings, this may not be an adequate model. Motivated by human resource planning, diagnosable microprocessor systems, berth allocation, and manufacturing systems that may require several resources simultaneously to process a job, we study the problem with a one‐job‐on‐multiple‐machine model. In our model, there are several alternatives that can be used to process a job. In each alternative, several machines need to process simultaneously the job assigned. Our purpose is to select an alternative for each job and then to schedule jobs to minimize the completion time of all jobs. In this paper, we provide a pseudopolynomial algorithm to solve optimally the two‐machine problem, and a combination of a fully polynomial scheme and a heuristic to solve the three‐machine problem. We then extend the results to a general m‐machine problem. Our algorithms also provide an effective lower bounding scheme which lays the foundation for solving optimally the general m‐machine problem. Furthermore, our algorithms can also be applied to solve a special case of the three‐machine problem in pseudopolynomial time. Both pseudopolynomial algorithms (for two‐machine and three‐machine problems) are much more efficient than those in the literature. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 57–74, 1999

Suggested Citation

  • Jianer Chen & Chung‐Yee Lee, 1999. "General multiprocessor task scheduling," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(1), pages 57-74, February.
    • Handle: RePEc:wly:navres:v:46:y:1999:i:1:p:57-74
    DOI: 10.1002/(SICI)1520-6750(199902)46:13.0.CO;2-H
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    References listed on IDEAS

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    1. Brucker, Peter & Kramer, Andreas, 1996. "Polynomial algorithms for resource-constrained and multiprocessor task scheduling problems," European Journal of Operational Research, Elsevier, vol. 90(2), pages 214-226, April.
    2. Gregory Dobson & Uday S. Karmarkar, 1989. "Simultaneous Resource Scheduling to Minimize Weighted Flow Times," Operations Research, INFORMS, vol. 37(4), pages 592-600, August.
    3. Chung-Yee Lee & Lei Lei & Michael Pinedo, 1997. "Current trends in deterministic scheduling," Annals of Operations Research, Springer, vol. 70(0), pages 1-41, April.
    4. L. Bianco & J. Blazewicz & P. Dell'Olmo & M. Drozdowski, 1997. "Preemptive multiprocessor task scheduling with release times and time windows," Annals of Operations Research, Springer, vol. 70(0), pages 43-55, April.
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    Cited by:

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    2. Tamás Bányai & Christian Landschützer & Ágota Bányai, 2018. "Markov-Chain Simulation-Based Analysis of Human Resource Structure: How Staff Deployment and Staffing Affect Sustainable Human Resource Strategy," Sustainability, MDPI, vol. 10(10), pages 1-21, October.
    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. Bukchin, Yossi & Raviv, Tal & Zaides, Ilya, 2020. "The consecutive multiprocessor job scheduling problem," European Journal of Operational Research, Elsevier, vol. 284(2), pages 427-438.
    5. Wu, Lingxiao & Wang, Shuaian, 2018. "Exact and heuristic methods to solve the parallel machine scheduling problem with multi-processor tasks," International Journal of Production Economics, Elsevier, vol. 201(C), pages 26-40.
    6. Ferreira, Cristiane & Figueira, Gonçalo & Amorim, Pedro, 2021. "Scheduling Human-Robot Teams in collaborative working cells," International Journal of Production Economics, Elsevier, vol. 235(C).
    7. Arden Baxter & Pinar Keskinocak & Mohit Singh, 2022. "Heterogeneous Multi-resource Allocation with Subset Demand Requests," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2389-2399, September.

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