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

• Main Authors: Hailing Liu, Long Wan, Zhigang Yan, Jinjiang Yuan
• Format: Article
• Language: English
• Published: Hindawi Limited 2015-01-01
• Series: Mathematical Problems in Engineering
• Online Access: http://dx.doi.org/10.1155/2015/628254

We consider the online (over time) scheduling of equal length jobs on a bounded parallel batch machine with batch capacity b 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 b=2, we propose a best possible online algorithm H(b=2) with a competitive ratio of 1+α, where α is the positive solution of 2α(1+α)=1. When b≥3, we present a best possible online algorithm H(b≥3) with a competitive ratio of 1+β, where β is the positive solution of β(1+β)2=1.