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A Non-Numerical Approach to Production Scheduling Problems

Author

Listed:
  • Sheldon B. Akers

    (ACF Electronics, Alexandria, Virginia)

  • Joyce Friedman

    (ACF Electronics, Alexandria, Virginia)

Abstract

In a typical production scheduling problem, n parts must be fabricated using m machines, and each part must be fabricated in a given order on the machines. It is desired to schedule the parts so that the program is optimal with respect to some given criteria. In general, ( n !) m programs must be examined. To obtain the ultimate solution, it is necessary to know for each part its actual time of fabrication on each machine. However, it is shown that without consideration of numerical values, it is possible to eliminate initially a great number of the possible programs by purely non-numerical methods. Operations Research , ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.

Suggested Citation

  • Sheldon B. Akers & Joyce Friedman, 1955. "A Non-Numerical Approach to Production Scheduling Problems," Operations Research, INFORMS, vol. 3(4), pages 429-442, November.
    • Handle: RePEc:inm:oropre:v:3:y:1955:i:4:p:429-442
    DOI: 10.1287/opre.3.4.429
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    Cited by:

    1. 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.
    2. Tao Ren & Yan Zhang & Shuenn-Ren Cheng & Chin-Chia Wu & Meng Zhang & Bo-yu Chang & Xin-yue Wang & Peng Zhao, 2020. "Effective Heuristic Algorithms Solving the Jobshop Scheduling Problem with Release Dates," Mathematics, MDPI, vol. 8(8), pages 1-25, July.
    3. C N Potts & V A Strusevich, 2009. "Fifty years of scheduling: a survey of milestones," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(1), pages 41-68, May.
    4. Zribi, N. & El Kamel, A. & Borne, P., 2008. "Minimizing the makespan for the MPM job-shop with availability constraints," International Journal of Production Economics, Elsevier, vol. 112(1), pages 151-160, March.
    5. Ohashi, Kazumasa, 1999. "Dynamic process planning system for a machining center in an FMS environment," International Journal of Production Economics, Elsevier, vol. 60(1), pages 457-464, April.
    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. Gabriel Mauricio Zambrano-Rey & Eliana María González-Neira & Gabriel Fernando Forero-Ortiz & María José Ocampo-Monsalve & Andrea Rivera-Torres, 2024. "Minimizing the expected maximum lateness for a job shop subject to stochastic machine breakdowns," Annals of Operations Research, Springer, vol. 338(1), pages 801-833, July.
    8. 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.
    9. Rossit, Daniel A. & Vásquez, Óscar C. & Tohmé, Fernando & Frutos, Mariano & Safe, Martín D., 2021. "A combinatorial analysis of the permutation and non-permutation flow shop scheduling problems," European Journal of Operational Research, Elsevier, vol. 289(3), pages 841-854.
    10. Aggoune, Riad & Portmann, Marie-Claude, 2006. "Flow shop scheduling problem with limited machine availability: A heuristic approach," International Journal of Production Economics, Elsevier, vol. 99(1-2), pages 4-15, February.
    11. S. Sevastyanov & D. Chemisova & I. Chernykh, 2014. "On some properties of optimal schedules in the job shop problem with preemption and an arbitrary regular criterion," Annals of Operations Research, Springer, vol. 213(1), pages 253-270, February.
    12. 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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