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Mathematical Problems in Engineering
Volume 2015, Article ID 206230, 9 pages
Research Article

Single Machine Group Scheduling with Position Dependent Processing Times and Ready Times

College of Mathematics Science, Chongqing Normal University, Chongqing 400047, China

Received 26 January 2015; Revised 11 April 2015; Accepted 12 April 2015

Academic Editor: Chin-Chia Wu

Copyright © 2015 Xingong Zhang and Qiulian Xie. 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 investigate a single machine group scheduling problem with position dependent processing times and ready times. The actual processing time of a job is a function of positive group-dependent job-independent positional factors. The actual setup time of the group is a linear function of the total completion time of the former group. Each job has a release time. The decision should be taken regarding possible sequences of jobs in each group and group sequence to minimize the makespan. We show that jobs in each group are scheduled in nondecreasing order of its release time and the groups are arranged in nondecreasing order of some certain conditions. We also present a polynomial time solution procedure for the special case of the proposed problem.