The paper considers two-agent simultaneous optimization problems on an unbounded serial-batching machine, in which the objective function of agent $A$ is either the maximum lateness or the total completion time and that of agent $B$ is makespan. The above two problems have $O(n_B+n_A^4)$-time algorithm and $O(n_A{n}_B+n_A^4)$-time algorithm respectively, where $n_X$ is the number of jobs owned by agent $X(X\in \{A,B\})$. In the paper, the running time of the two algorithms is improved to be $O(n_B+n_A^{2}log{n}_A)$ time.

中文翻译：

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无界串行批处理机上双智能体调度的改进算法

论文考虑了无界串行批处理机上的两个智能体同时优化问题，其中智能体的目标函数为 $\mathrm{一种}$ 是最大延迟时间或总完成时间以及代理的延迟时间 $乙$是完工时间。以上两个问题都有$哦(n_{乙}+n_{\mathrm{一种}}^4)$-时间算法和 $哦(n_{\mathrm{一种}}{n}_{乙}+n_{\mathrm{一种}}^4)$-时间算法分别，其中 $n_X$ 是代理拥有的工作数量 $X(X\in \{\mathrm{一种},乙\})$. 论文中将两种算法的运行时间改进为$哦(n_{乙}+n_{\mathrm{一种}}^2日志n_{\mathrm{一种}})$ 时间。