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Scheduling jobs, with exponentially distributed processing times, on two machines of a flow shop

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  • Andrew A. Cunningham
  • Sujit K. Dutta

Abstract

This paper treats the problem of sequencing n jobs on two machines in a “flow shop.” (That is, each job in the shop is required to flow through the same sequence of the machines.) The processing time of a given job on a given machine is assumed to be distributed exponentially, with a known mean. The objective is to minimize the expected job completion time. This paper proves an optimal ordering rule, previously conjectured by Talwar [10]. A formula is also derived through Markov Chain analysis, which evaluates the expected job completion time for any given sequence of the jobs. In addition, the performance of a heuristic rule is discussed in the light of the optimal solution.

Suggested Citation

  • Andrew A. Cunningham & Sujit K. Dutta, 1973. "Scheduling jobs, with exponentially distributed processing times, on two machines of a flow shop," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 20(1), pages 69-81, March.
    • Handle: RePEc:wly:navlog:v:20:y:1973:i:1:p:69-81
    DOI: 10.1002/nav.3800200107
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    Cited by:

    1. Rhonda Righter, 1997. "A generalized Johnson's rule for stochastic assembly systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 44(2), pages 211-220, March.
    2. Lei Liu & Marcello Urgo, 2024. "Robust scheduling in a two-machine re-entrant flow shop to minimise the value-at-risk of the makespan: branch-and-bound and heuristic algorithms based on Markovian activity networks and phase-type dis," Annals of Operations Research, Springer, vol. 338(1), pages 741-764, July.

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