Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 628254, 8 pages
http://dx.doi.org/10.1155/2015/628254
Research Article

Online Scheduling with Delivery Time on a Bounded Parallel Batch Machine with Limited Restart

1School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, Henan 450001, China
2College of Science, Henan Institute of Engineering, Zhengzhou, Henan 451191, China
3School of Information Technology, Jiangxi University of Finance and Economics, Nanchang 330013, China
4Accounting School, Jiangxi University of Finance and Economics, Nanchang 330013, China

Received 23 August 2014; Accepted 28 September 2014

Academic Editor: Yunqiang Yin

Copyright © 2015 Hailing 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.

Abstract

We consider the online (over time) scheduling of equal length jobs on a bounded parallel batch machine with batch capacity to minimize the time by which all jobs have been delivered with limited restart. Here, “restart” means that a running batch may be interrupted, losing all the work done on it, and jobs in the interrupted batch are then released and become independently unscheduled jobs, called restarted jobs. “Limited restart” means that a running batch which contains some restarted jobs cannot be restarted again. When , we propose a best possible online algorithm with a competitive ratio of , where is the positive solution of . When , we present a best possible online algorithm with a competitive ratio of , where is the positive solution of .