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. $C_{\max }^A+\theta C_{\max }^B(\theta \ge 1)$, is minimized. For the problem, we propose an online algorithm and show the competitive ratio of the algorithm is $1+\frac{2\theta +{\theta }^2}{2+2\theta +{\theta }^2}$.

中文翻译：

---

在线单机调度以最小化两个代理的makespans的线性组合

本文考虑一个在线双代理调度问题。所有作业都属于两个代理 A 和 B，并且每个作业都是随着时间的推移到达的，这意味着在到达之前没有预先知道作业的信息。目标是在一台机器上调度所有作业，使得两个代理的制造跨度的线性组合，即$C_{\mathrm{最大限度}}^{\mathrm{一种}}+\theta C_{\mathrm{最大限度}}^{乙}(\theta \ge 1)$，最小化。针对该问题，我们提出了一种在线算法，并表明该算法的竞争率为$1+\frac{2\theta +{\theta }^2}{2+2\theta +{\theta }^2}$.