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Mathematical Problems in Engineering
Volume 2015, Article ID 452602, 9 pages
Research Article

Note on a Single-Machine Scheduling Problem with Sum of Processing Times Based Learning and Ready Times

1Department of Business Administration, Fu Jen Catholic University, New Taipei City 24205, Taiwan
2Department of Statistics, Feng Chia University, Taichung 40724, Taiwan

Received 5 September 2014; Accepted 20 January 2015

Academic Editor: Chuangxia Huang

Copyright © 2015 Shang-Chia Liu et al. 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.


In the recent 20 years, scheduling with learning effect has received considerable attention. However, considering the learning effect along with release time is limited. In light of these observations, in this paper, we investigate a single-machine problem with sum of processing times based learning and ready times where the objective is to minimize the makespan. For solving this problem, we build a branch-and-bound algorithm and a heuristic algorithm for the optimal solution and near-optimal solution, respectively. The computational experiments indicate that the branch-and-bound algorithm can perform well the problem instances up to 24 jobs in terms of CPU time and node numbers, and the average error percentage of the proposed heuristic algorithm is less than 0.5%.