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Approximating the 2-machine flow shop problem with exact delays taking two values
Journal of Global Optimization ( IF 1.8 ) Pub Date : 2019-04-25 , DOI: 10.1007/s10898-019-00775-0
Alexander Ageev

Abstract

In the 2-Machine Flow Shop problem with exact delays the operations of each job are separated by a given time lag (delay). Leung et al. (Int J Found Comput Sci 18:341–359, 2007) established that the problem is strongly NP-hard when the delays may have at most two different values. We present further results for this case: we prove that the existence of \((1.25-\varepsilon )\)-approximation implies \(\hbox {P}=\hbox {NP}\) and develop a 2-approximation algorithm.



中文翻译:

用精确的延迟近似两个机器的流水车间问题,取两个值

摘要

在具有确切延迟的2机流水车间问题中,每个作业的操作之间都存在给定的时间滞后(延迟)。梁等。(诠释J实测值COMPUT科学18:341-359,2007)建立的问题是强NP难度时的延迟可以具有至多两个不同的值。我们给出这种情况的进一步结果:我们证明\((1.25- \ varepsilon)\) -逼近的存在意味着\(\ hbox {P} = \ hbox {NP} \)并开发了一种2逼近算法。

更新日期:2020-03-20
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