Makespan distribution of permutation flowshop schedules

Authors:
Feng Jin;Jatinder N. Gupta;Shi-Ji Song;Cheng Wu
Affiliations:
Department of Automation, Tsinghua University, Beijing, China 100084;College of Business Administration, University of Alabama in Huntsville, Huntsville, USA 35899;Department of Automation, Tsinghua University, Beijing, China 100084;Department of Automation, Tsinghua University, Beijing, China 100084
Venue:
Journal of Scheduling
Year:
2008

Citing 3
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Abstract

The makespan distribution of permutation flowshop schedules has been a topic of debate for almost fifty years. Many researchers have confirmed or doubted the famous claim that the makespan distribution of permutation flowshop schedules is asymptotically normal if the number of jobs is sufficiently large. This paper theoretically and empirically investigates the makespan distribution of permutation flowshop schedules and shows that the normality claim is not valid for the job-dominated and machine-dominated flowshops. Errors in the proof of normality of the makespan distribution of permutation flowshop schedules are pointed out. It is shown that the makespan distribution of a permutation flowshop scheduling problem depends on the number of jobs as well as the number of machines.