摘要
In this paper, we consider scheduling problems with m machines in parallel andtwo classes of job. We assume that all jobs are present at time 0 and there are nofurther arrivals. The service times of class 1 (2) jobs are independent andexponentially distributed with mean Fi-1 (M2'1). Each class 1 (2) job incurs a costc1 (c2) per unit of time until it leaves the system. The objective is to minimize theexpected total cost, that is the expected weighted sum of completion times. We showthat the optimal policy among all preemptive policies is of threshold type. Based onthese structural results, we also show that the ratio of the expected weighted sum ofcompletion times under the c/z-rule to that under the optimal rule is less than 1.71.