Stochastic single machine scheduling with time-dependent deterioration or position-dependent learning effect.

This paper studies several single machine scheduling problems in a stochastic environment where the processing times and due dates of the jobs are assumed to be random. A new time-dependent deterioration model with two deterioration parameters is proposed and a position-dependent learning effect model with a position variable is revisited. In the time-dependent deterioration model, the true processing time of a job is determined by an increasing function of its starting time, and in the position-dependent learning effect model, the true processing time of a job is determined by a nonincreasing function of its scheduled position. Based on the two models, we consider the minimization of the following performance measures: the expected total general completion time costs, the expected total general tardiness costs, the maximum expected general completion time costs, the expected total weighted number of tardy jobs and the expected total weighted number of tardy and early jobs. We further show that several optimal schedules are obtained to minimize the above objectives under certain conditions. [ABSTRACT FROM AUTHOR]