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Mathematical Problems in Engineering
Volume 2013, Article ID 972358, 9 pages
Research Article

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

Operations Management Area, DeGroote School of Business, McMaster University, Hamilton, ON, Canada L8S 4L8

Received 2 August 2013; Revised 23 October 2013; Accepted 23 October 2013

Academic Editor: Chin-Chia Wu

Copyright © 2013 Jianbo Qian and George Steiner. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.