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

We investigate the problem of scheduling n jobs on a single machine with the following features. The cost functions are general stochastic processes, which can be used to model the effects of stochastic price fluctuations, stochastic due times, etc., and the stochastic processing times follow a class of distributions, which includes exponential, geometric, and other families of distributions. Such a class of distributions is characterized by its characteristic functions. The optimal policies for these scheduling problems, both without precedence constraints, or with precedence in the form of nonpreemptive chains, are discussed, respectively.