The optimality of LEPT in parallel machine scheduling

[[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 of show that LEPT stochastically minimizes the makespan, and that it minimizes the expected cost when the cost function satisfies certain agreeability conditions.[[fileno]]2030162010045[[department]]電機工程學