A Note on the Quickest Minimum Cost Transshipment Problem

TL;DR

This paper explores the complexity of the quickest minimum cost transshipment problem, showing it can be reduced to a solvable quickest transshipment problem, thereby expanding understanding of flow over time complexities.

Contribution

It demonstrates a reduction from the quickest minimum cost transshipment problem to the efficiently solvable quickest transshipment problem, clarifying its computational complexity.

Findings

Quickest minimum cost transshipment problem can be reduced to quickest transshipment problem

This reduction places the problem within the efficiently solvable class

Enhances the understanding of flow over time complexity landscape

Abstract

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.