Abstract
This paper considers an online two-agent scheduling problem. All jobs belong to two agents A and B, and each job is arriving over time, which means that no information of the job is known in advance before its arrival. The objective is to schedule all jobs on a single machine such that the linear combination of the makespans of the two agents, i.e. CmaxA+θCmaxB(θ≥1), is minimized. For the problem, we propose an online algorithm and show the competitive ratio of the algorithm is 1+2θ+θ22+2θ+θ2.
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