Online scheduling on two parallel-batching machines with limited restarts to minimize the makespan

Authors:
Ruyan Fu;T. C. E. Cheng;C. T. Ng;Jinjiang Yuan
Affiliations:
School of Sciences, China University of Mining and Technology, Xuzhou, Jiangsu 221116, People's Republic of China;Department of Logistics and Maritime Studies, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong SAR, People's Republic of China;Department of Logistics and Maritime Studies, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong SAR, People's Republic of China;Department of Mathematics, Zhengzhou University, Zhengzhou, Henan 450052, People's Republic of China
Venue:
Information Processing Letters
Year:
2010

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Abstract

We study online scheduling on two unbounded parallel-batching machines with limited restarts to minimize the makespan. In this system jobs arrive over time and a batch can be restarted if and only if all the jobs in it have never been restarted. To tackle this difficult problem, we make the second-restart assumption whereby we can only interrupt a running batch B at time t if both machines are busy at time t and batch B has a later starting time than the other running batch. For this case, we provide a best online algorithm with a competitive ratio 3+12~1.366. For the general problem, we show that no online algorithms can have a competitive ratio less than 1.298, leaving a gap from 1.298 to 1.366.