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

摘要

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 b = 2, we propose a best possible online algorithm H(b = 2) with a competitive ratio of 1 + alpha, where alpha is the positive solution of 2 alpha(1 + alpha) = 1. When.. = 3, we present a best possible online algorithm H(b >= 3) with a competitive ratio of 1 +beta , where beta is the positive solution of beta(1 + beta) 2 = 1.