Klinz and Woeginger (1995) prove that the minimum cost quickest flow problem is NP-hard. On the other hand, the quickest minimum cost flow problem can be solved efficiently via a straightforward reduction to the quickest flow problem without costs. More generally, we show how the quickest minimum cost transshipment problem can be reduced to the efficiently solvable quickest transshipment problem, thus adding another mosaic tile to the rich complexity landscape of flows over time.

翻译：Klinz和Woeginger(1995年)证明最低成本快速流动问题是NP-硬性的问题。 另一方面,最快速的最低成本流动问题可以通过直截了当地降低到最快速流动问题而无需成本而得到有效解决。 更一般地说,我们展示如何将最快速最低成本的转运问题降低到高效可溶最快的转运问题,从而给长期流动的复杂面貌带来又一团乱麻。