The authors consider a discrete time model of m identical machines operating in parallel to complete a collection of jobs. The processing times of the jobs are independent, identically distributed discrete random variables having increasing hazard rate. The jobs may have received different amounts of prior processing. A reward βt,0<β<1, is acquired when a job is finished at time t. The authors show that a non-preemptive SEPT (Shortest Expected Processing Time) strategy maximizes the expected total reward among all possible policies. They show that SEPT strategy is still optimal for several generalizations of this problem scenario.
