Stochastic single-machine scheduling problems with both time-dependent deterioration and position-dependent learning effect

With the advancement of the manufacturing industry, scheduling problems with both deterioration and learning effect, under the assumption of constant the actual processing times and due dates of jobs, have emerged as a prominent research focus over the past two decades. Nevertheless, investigations into this category of problems have been significantly overlooked in stochastic environments. Therefore, we study several stochastic scheduling problems on a single machine where the processing times and due dates of the jobs are random variables. Two new models with both deterioration and learning effect are proposed, where deterioration is time-dependent and learning effect is position-dependent. In the two general models, the true processing time of a job is determined by both an increasing function of its starting processing time and a non-increasing function of its scheduled position. Based on the two general models, the following performance measures are studied: the expected total general completion time 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 prove that some optimal schedules are derived to minimize the above performance measures under agreeability conditions.