# American Institute of Mathematical Sciences

January  2009, 5(1): 95-102. doi: 10.3934/jimo.2009.5.95

## Online scheduling of two uniform machines to minimize total completion times

 1 Department of Mathematics, East China University of Science and Technology, Shanghai 200237, China, China

Received  January 2008 Revised  September 2008 Published  December 2008

In this paper, we study the online scheduling problem on two uniform machines with speeds 1 and $s \geq 1$, in which jobs are arriving over time. We consider both the preemptive and the non-preemptive machine environments. We first present a 2.618-competitive algorithm for the non-preemptive setting with the objective to minimize the total completion times. In the preemptive setting with the objective to minimize the total weighted completion times, we give an online algorithm which has a competitive ratio of 2.
Citation: P. Liu, Xiwen Lu. Online scheduling of two uniform machines to minimize total completion times. Journal of Industrial and Management Optimization, 2009, 5 (1) : 95-102. doi: 10.3934/jimo.2009.5.95
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