We consider the $$\mathscr {NP}$$ NP -hard twin robot scheduling problem, which was introduced by Erdoğan et al. (Naval Res Logist (NRL) 61(2):119–130, 2014). Here, two moving robots positioned at the opposite ends of a rail have to perform automated storage and retrieval jobs at given positions along the gantry rail with a non-crossing constraint. The objective is to minimize the makespan. We extend the original problem by considering pickup and delivery times and present exact and approximation algorithms with a performance ratio of $$\approx \,1.1716$$ ≈ 1.1716 for large instances. Further, we compare the presented algorithms in a comprehensive numerical study.

中文翻译：

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双机器人调度问题的近似算法

我们考虑 $$\mathscr {NP}$$ NP -hard 双机器人调度问题，它是由 Erdoğan 等人提出的。（Naval Res Logist (NRL) 61(2):119–130, 2014）。在这里，位于轨道两端的两个移动机器人必须在沿龙门轨道的给定位置执行自动存储和检索工作，且不受交叉约束。目标是最小化完工时间。我们通过考虑取货和交货时间扩展了原始问题，并提出了精确和近似算法，对于大型实例，性能比为 $$\approx \,1.1716$$ ≈ 1.1716。此外，我们在综合数值研究中比较了所提出的算法。