This paper focuses on the scheduling problem on two parallel machines with delivery coordination. In particular, given a set of n jobs, we aim to find a schedule with a minimal makespan such that all jobs are first executed on two parallel machines then delivered at the destination with a transporter. This problem is known to be NP-hard Chang and Lee (Eur J Oper Res 158(2):470–487, 2004), cannot be solved with an approximation ratio strictly less than 3/2 unless P=NP. We close the gap by proposing a polynomial time algorithm whose approximation ratio is \(3/2+\varepsilon \) with \(\varepsilon >0\), improve the previous best ratio \(14/9 + \epsilon \).

本文着重讨论两台具有交付协调的并行机器上的调度问题。特别是，给定一组n个作业，我们的目标是找到具有最小制造周期的计划，以使所有作业首先在两台并行计算机上执行，然后通过运输机交付到目的地。已知此问题是NP-hard Chang和Lee（Eur J Oper Res 158（2）：470-487，2004），除非P = NP，否则无法用严格小于3/2的近似比率来解决。我们通过提出一种近似时间比为\（3/2 + \ varepsilon \）与\（\ varepsilon> 0 \）的多项式时间算法，提高以前的最佳比例\（14/9 + \ epsilon \）来缩小差距。