A Note on Stochastic Shop Models in Which Jobs have the Same Processing Requirements on Each Machine

Michael Pinedo
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Michael Pinedo: Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027

Management Science, 1985, vol. 31, issue 7, 840-846

Abstract: We consider stochastic models for flow shops, job shops and open shops in which the work required by job j is the same at each machine, being a random variable W j . Because machines operate at different speeds, S i , the processing time of job j at machine i is W j /S i ,. It is the main result of this note that in a flow shop where the machine speeds increase (decrease) from the first to last machine and the workload distributions are ordered by a likelihood ratio criterion, then the makespan of the jobs is stochastically minimized by processing the jobs in the order of least to greatest (greatest to least) workload.

Keywords: job shop; makespan; flow time; monotone likelihood ratio ordering (search for similar items in EconPapers)
Date: 1985
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