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We consider single machine scheduling problems with learning/deterioration effects and time-dependent processing times, with due date assignment consideration, and our objective is to minimize the weighted number of tardy jobs. By reducing all versions of the problem to an assignment problem, we solve them in O(n4) time. For some important special cases, the time complexity can be improved to be O(n2) using dynamic programming techniques

Scheduling with Learning Effects and/or Time-Dependent Processing Times to Minimize the Weighted Number of Tardy Jobs on a Single Machine