Single machine scheduling with exponential processing times and a general form objective function

A single machine scheduling with exponential processing times is considered, the objective is to minimize an objective function which is a general form of several regular (the objective function is increasing with respect to job completion times) and non-regular objective functions, such as, the expected flow time, the expected total tardiness about a deterministic common due date and the expected derivations of completion time about a deterministic common due date, etc. The characters of the optimal schedulers, such as V-shaped and Λ-shaped characters, are derived.