A problem of scheduling n jobs with random processing times on a single machine is considered. The processing times are exponentially distributed. The objective is to minimize an objective function which is a general form of several regular and non-regular objective functions, such as the total expected tardiness and the total expected absolute deviations of the completion times about a common due date, etc. The characters of the optimal schedules, including SEPT (shortest expected processing time) schedule, LEPT (largest expected processing time) schedule and V-shaped schedule with respect to the rates of the processing times, are derived. These characters can be used to establish the optimal solutions.
