Single-machine scheduling with general costs under compound-type distributions

We investigate in this paper the problem of scheduling n jobs on a single machine with general stochastic cost functions, which involves the effects of stochastic due times, and with the stochastic processing times in a class of distributions, which covers the family of exponential distributions, the family of geometrical distributions and some other important distribution families as its special cases. Such a class of distributions is characterized by their characteristic functions. The optimal policies for these scheduling problems, without precedence constraints or with precedence constraints of nonpreemptive chains, are discussed respectively.