Single machine scheduling with generalized due-dates, learning effect, and job-rejection

We study single-machine scheduling problems with Generalized due-dates (GDD), learning effect, and optional job rejection. For the GDD setting, the due dates are assigned to the jobs according to their position in the sequence rather than their identity. Thus, assuming that due dates are numbered in non-decreasing order, the jth due date refers to the job assigned to the jth position. The learning effect is a model where completing former jobs decreases the completion time of latter jobs. The processing time is still part of the input, depending on how many jobs have already been scheduled. Allowing the option of job rejection means that not all jobs must be processed. In this case, the scheduler is penalized for each rejected job, and an input parameter bounds the total rejection cost. Two objective functions are considered with the above-mentioned settings: minimizing total tardiness and minimizing maximal tardiness. The problems are polynomially solvable when there is no option for job rejection. Otherwise, both are shown to be NP-hard, pseudo-polynomial dynamic programming solutions are proposed, and numerical experiments are provided.