Abstract
m Parallel machines are available for the processing of n jobs. The jobs require random amounts of processing. When processing times are exponentially distributed, SEPT (shortest expected processing time first) minimizes the flowtime, LEPT (longest expected processing time first) minimizes the makespan and maximizes the time to first machine idleness. For m = 2, various other problems can be optimized by different rules. Optimality of preemptive SEPT and LEPT also holds when processing times are drawn from a common MHR (monotone hazard rate) distribution.
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