Single-machine scheduling CON/SLK due window assignment problems with sum-of-processed times based learning effect

This paper studies systems that can be modeled by single-machine scheduling problems with due date assignment. The actual job processing time is a function of the sum of the processing times of the jobs already processed. The due date assignment methods include the common due date (CON) and the slack due date (SLK). The problem is to determine optimal due date values that minimize objective functions which includes the cost of changing the due dates, a possible penalty for the total earliness of the scheduled jobs and the total penalty for discarding jobs. For the common due date and slack due date, we give polynomial-time dynamic programming algorithms to find the optimal jobs sequence, respectively.