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Generalization of Johnson's and Talwar's scheduling rules in two-machine stochastic flow shops

Author

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  • P J Kalczynski

    (The University of Toledo)

  • J Kamburowski

    (The University of Toledo)

Abstract

The paper deals with the classical problem of minimizing the makespan in a two-machine flow shop. When the job processing times are deterministic, the optimal job sequence can be determined by applying Johnson's rule. When they are independent and exponential random variables, Talwar's rule yields a job sequence that minimizes the makespan stochastically. Assuming that the random job processing times are independent and Gompertz distributed, we propose a new scheduling rule that is a generalization of both Johnson's and Talwar's rules. We prove that our rule yields a job sequence that minimizes the makespan stochastically. Extensions to m-machine proportionate stochastic flow shops, two-machine stochastic job shops, and stochastic assembly systems are indicated.

Suggested Citation

  • 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.
    • Handle: RePEc:pal:jorsoc:v:55:y:2004:i:12:d:10.1057_palgrave.jors.2601802
    DOI: 10.1057/palgrave.jors.2601802
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    References listed on IDEAS

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    1. Kamburowski, Jerzy, 1999. "Stochastically minimizing the makespan in two-machine flow shops without blocking," European Journal of Operational Research, Elsevier, vol. 112(2), pages 304-309, January.
    2. 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.
    3. M. R. Garey & D. S. Johnson & Ravi Sethi, 1976. "The Complexity of Flowshop and Jobshop Scheduling," Mathematics of Operations Research, INFORMS, vol. 1(2), pages 117-129, May.
    4. Kenneth N. McKay & Frank R. Safayeni & John A. Buzacott, 1988. "Job-Shop Scheduling Theory: What Is Relevant?," Interfaces, INFORMS, vol. 18(4), pages 84-90, August.
    5. R. A. Dudek & S. S. Panwalkar & M. L. Smith, 1992. "The Lessons of Flowshop Scheduling Research," Operations Research, INFORMS, vol. 40(1), pages 7-13, February.
    6. Kamburowski, Jerzy, 2000. "On three-machine flow shops with random job processing times," European Journal of Operational Research, Elsevier, vol. 125(2), pages 440-448, September.
    7. Michael Pinedo, 1982. "Minimizing the Expected Makespan in Stochastic Flow Shops," Operations Research, INFORMS, vol. 30(1), pages 148-162, February.
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