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Mathematical Problems in Engineering
Volume 2015, Article ID 758919, 9 pages
Research Article

Single-Machine Group Scheduling Problems with Variable Job Processing Times

Ping Ji1 and Lin Li2

1Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong
2College of Science, Shenyang Aerospace University, Shenyang, Liaoning, China

Received 2 September 2014; Accepted 16 November 2014

Academic Editor: Yunqiang Yin

Copyright © 2015 Ping Ji and Lin Li. 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.


This paper considers two resource constrained single-machine group scheduling problems. These problems involve variable job processing times (general position-dependent learning effects and deteriorating jobs); that is, the processing time of a job is defined by the function that involves its starting time and position in the group, and groups’ setup time is a positive strictly decreasing continuous function of the amount of consumed resource. Polynomial time algorithms are proposed to optimally solve the makespan minimization problem under the constraint that the total resource consumption does not exceed a given limit and the total resource consumption minimization problem under the constraint that the makespan does not exceed a given limit, respectively.