Abstract
We consider preemptive scheduling on parallel machines where the number of available machines may be an arbitrary, possibly random, function of time. Processing times of jobs are from a family of DLR (decreasing likelihood ratio) distributions, and jobs may arrive at random agreeable times. We give a constructive coupling proof to show that LEPT stochastically minimizes the makespan, and that it minimizes the expected cost when the cost function satisfies certain agreeability conditions.
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