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

Andrew A. Cunningham and Sujit K. Dutta

Naval Research Logistics Quarterly, 1973, vol. 20, issue 1, 69-81

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.

Date: 1973
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Persistent link: https://EconPapers.repec.org/RePEc:wly:navlog:v:20:y:1973:i:1:p:69-81

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