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A Geometric Model and a Graphical Algorithm for a Sequencing Problem

Author

Listed:
  • William W. Hardgrave

    (Bell Telephone Laboratories, Inc., Holmdel, New Jersey)

  • George L. Nemhauser

    (The Johns Hopkins University, Baltimore, Maryland)

Abstract

A geometric model is given for the problem of scheduling N jobs on M machines so that the total time needed to complete the processing of all jobs is minimized. This model leads to a graphical algorithm, the essence of which is the determination of a shortest path between two nodes in a finite network. Particular attention is given to the case of 2 jobs for which the algorithm developed is simple and efficient. The theoretical analysis is then extended to the general case. Computational problems arise in the general case primarily because of the difficulty of constructing the network.

Suggested Citation

  • William W. Hardgrave & George L. Nemhauser, 1963. "A Geometric Model and a Graphical Algorithm for a Sequencing Problem," Operations Research, INFORMS, vol. 11(6), pages 889-900, December.
    • Handle: RePEc:inm:oropre:v:11:y:1963:i:6:p:889-900
    DOI: 10.1287/opre.11.6.889
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    Citations

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    Cited by:

    1. Peter Brucker & Yu Sotskov & Frank Werner, 2007. "Complexity of shop-scheduling problems with fixed number of jobs: a survey," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(3), pages 461-481, June.
    2. Agnetis, Alessandro & Kellerer, Hans & Nicosia, Gaia & Pacifici, Andrea, 2012. "Parallel dedicated machines scheduling with chain precedence constraints," European Journal of Operational Research, Elsevier, vol. 221(2), pages 296-305.
    3. Mati, Yazid & Xie, Xiaolan, 2004. "The complexity of two-job shop problems with multi-purpose unrelated machines," European Journal of Operational Research, Elsevier, vol. 152(1), pages 159-169, January.
    4. Yuri N. Sotskov, 2020. "Mixed Graph Colorings: A Historical Review," Mathematics, MDPI, vol. 8(3), pages 1-24, March.
    5. Jain, A. S. & Meeran, S., 1999. "Deterministic job-shop scheduling: Past, present and future," European Journal of Operational Research, Elsevier, vol. 113(2), pages 390-434, March.
    6. A. Agnetis & P.B. Mirchandani & D. Pacciarelli & A. Pacifici, 2000. "Nondominated Schedules for a Job-Shop with Two Competing Users," Computational and Mathematical Organization Theory, Springer, vol. 6(2), pages 191-217, July.
    7. Shakhlevich, Natalia V. & Sotskov, Yuri N. & Werner, Frank, 2000. "Complexity of mixed shop scheduling problems: A survey," European Journal of Operational Research, Elsevier, vol. 120(2), pages 343-351, January.
    8. Souren, Rainer & Gerlach, Kurt, 2007. "Graphische Verfahren zur Maschinenbelegungsplanung: Lösungsansätze für Probleme mit zwei Aufträgen und mehrdimensionale Erweiterungen," Ilmenauer Schriften zur Betriebswirtschaftslehre, Technische Universität Ilmenau, Institut für Betriebswirtschaftslehre, volume 1, number 12007.
    9. Peter Damaschke, 2019. "Parameterized Mixed Graph Coloring," Journal of Combinatorial Optimization, Springer, vol. 38(2), pages 362-374, August.
    10. Y N Sotskov & A Allahverdi & T-C Lai, 2004. "Flowshop scheduling problem to minimize total completion time with random and bounded processing times," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(3), pages 277-286, March.

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