This paper studies a single-machine scheduling problem with a non-renewable resource (NR-SSP) and total weighted completion time criterion. The non-renewable resource is consumed when the machine starts processing a job. We consider the case where each job's weight in the objective function is proportional to its resource consumption amount. The problem is known to be NP-hard in this case. We propose a 3-approximation list scheduling algorithm for this problem. Besides, we show that the approximation ratio 3 is tight for the algorithm.

翻译：本文研究的是不可再生资源(NR-SSP)和总加权完成时间标准的单机排期问题。 当机器开始处理一项工作时, 将消耗不可再生资源。 我们考虑的是每份工作在客观功能中的权重与其资源消耗量成正比的情况。 在此情况下, 这个问题是已知的硬性 NP 问题。 我们为此问题提出了一个三维的排期算法。 此外, 我们显示, 近似比 3 对算法来说是紧凑的 。