Abstract
This paper considers a two-agent scheduling problem, in which all jobs belong to two agents A and B, and each job has a release date. The objective is to schedule all jobs non-preemptively on a single machine such that the linear combination of the makespans of the two agents, i.e., CmaxA+θCmaxB(θ≥1), is minimized. It is known that the problem is NP-hard in the ordinary sense. For this case, we provide an approximation algorithm with worst-case ratio 1+θ1+θ+θ2. We also propose a Fully Polynomial Time Approximation Scheme (FPTAS) for the problem under study. Finally, computational experiments are conducted to verify the effectiveness of the approximation algorithm and the FPTAS.
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