Online scheduling on a single machine with rejection under an agreeable condition to minimize the total completion time plus the total rejection cost

Authors:
Ran Ma;Jinjiang Yuan
Affiliations:
School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China and School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China;School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China
Venue:
Information Processing Letters
Year:
2013

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Abstract

We consider the single-machine online scheduling with job rejection to minimize the total completion time of the scheduled jobs plus the total rejection cost of the rejected jobs under an agreeable condition on the processing times and rejection penalties of the jobs. In the problem, a set of independent jobs arriving online over time has to be scheduled on the machine with the flexibility of rejecting some of the jobs, where preemption is not allowed and the information of each job J"j, including its processing time p"j, release date r"j and rejection penalty e"j, is not known in advance. The agreeable condition means that, for every two jobs J"i and J"j, p"i=e"j, and furthermore, p"i=p"j and r"i=e"j. For this problem, we provide an online algorithm with the best possible competitive ratio of 2. As a consequence, the online algorithm is also best possible when the jobs have identical rejection penalties.