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Fixed Job Scheduling with Two Types of Processors

Author

Listed:
  • V. R. Dondeti

    (Norfolk State University, Norfolk, Virginia)

  • Hamilton Emmons

    (Case Western Reserve University, Cleveland, Ohio)

Abstract

We consider a scheduling problem that involves two types of processors, but three types of jobs. Each job has a fixed start time and a fixed completion time, and falls into one of three types. Jobs of type 1 can be done only by type-1 processors, type-2 jobs only by type-2 processors, and type-0 jobs by either type of processors. We present a polynomial algorithm for finding the minimal cost combination of the two types of processors required to complete all jobs. The steps of the algorithm consist of constructing a job schedule network, transforming it into a single-commodity flow problem and finding the maximal flow through it.

Suggested Citation

  • V. R. Dondeti & Hamilton Emmons, 1992. "Fixed Job Scheduling with Two Types of Processors," Operations Research, INFORMS, vol. 40(1-supplem), pages 76-85, February.
    • Handle: RePEc:inm:oropre:v:40:y:1992:i:1-supplement-1:p:s76-s85
    DOI: 10.1287/opre.40.1.S76
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    Citations

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    Cited by:

    1. Antoon W.J. Kolen & Jan Karel Lenstra & Christos H. Papadimitriou & Frits C.R. Spieksma, 2007. "Interval scheduling: A survey," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(5), pages 530-543, August.
    2. Gabrel, Virginie, 1995. "Scheduling jobs within time windows on identical parallel machines: New model and algorithms," European Journal of Operational Research, Elsevier, vol. 83(2), pages 320-329, June.
    3. Borgonjon, Tessa & Maenhout, Broos, 2022. "An exact approach for the personnel task rescheduling problem with task retiming," European Journal of Operational Research, Elsevier, vol. 296(2), pages 465-484.
    4. Kovalyov, Mikhail Y. & Ng, C.T. & Cheng, T.C. Edwin, 2007. "Fixed interval scheduling: Models, applications, computational complexity and algorithms," European Journal of Operational Research, Elsevier, vol. 178(2), pages 331-342, April.
    5. Diego B.C. Faneyte & Frits C.R. Spieksma & Gerhard J. Woeginger, 2002. "A branch‐and‐price algorithm for a hierarchical crew scheduling problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(8), pages 743-759, December.
    6. Kroon, Leo G. & Edwin Romeijn, H. & Zwaneveld, Peter J., 1997. "Routing trains through railway stations: complexity issues," European Journal of Operational Research, Elsevier, vol. 98(3), pages 485-498, May.

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