Abstract: This paper considers stochastic scheduling on a single machine with jobs having a common due date and exponential processing times. The performance measure to be optimized is the expected incompletion cost. Preemptions are not allowed and the machine could not be idle. The results of the paper show that the optimal policy is the sequence the jobs in the nonincrearsing order of ICiλj. Besides the properties of tire incompletion cost (ICj)are evaluated and used to obtain some useful results.