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On Johnson's Two-Machine Flow Shop with Random Processing Times

Author

Listed:
  • Peng-Sheng Ku

    (The University of Texas at Dallas, Richardson, Texas)

  • Shun-Chen Niu

    (The University of Texas at Dallas, Richardson, Texas)

Abstract

A set of n jobs is to be processed by two machines in series that are separated by an infinite waiting room; each job requires a (known) fixed amount of processing from each machine. In a classic paper, Johnson gave a simple rule for ordering of the set of jobs to minimize the time until the system becomes empty, i.e., the makespan. This paper studies a stochastic generalization of this problem in which job processing times are independent random variables. Our main result is a sufficient condition on the processing time distributions that implies that the makespan becomes stochastically smaller when two adjacent jobs in a given job sequence are interchanged. We also give an extension of the main result to job shops.

Suggested Citation

  • Peng-Sheng Ku & Shun-Chen Niu, 1986. "On Johnson's Two-Machine Flow Shop with Random Processing Times," Operations Research, INFORMS, vol. 34(1), pages 130-136, February.
    • Handle: RePEc:inm:oropre:v:34:y:1986:i:1:p:130-136
    DOI: 10.1287/opre.34.1.130
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    Cited by:

    1. Yuri N. Sotskov & Natalja M. Matsveichuk & Vadzim D. Hatsura, 2020. "Schedule Execution for Two-Machine Job-Shop to Minimize Makespan with Uncertain Processing Times," Mathematics, MDPI, vol. 8(8), pages 1-51, August.
    2. P J Kalczynski & J Kamburowski, 2004. "Generalization of Johnson's and Talwar's scheduling rules in two-machine stochastic flow shops," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(12), pages 1358-1362, December.
    3. 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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