An Introduction to Transshipments Over Time

TL;DR

This paper surveys the computational aspects of transshipments over time in networks, focusing on efficient algorithms for complex multi-source and multi-sink flow problems that incorporate temporal dynamics.

Contribution

It provides a comprehensive overview of the polynomial-time solvable transshipment over time problem with multiple sources and sinks, highlighting recent algorithmic developments.

Findings

Transshipment over time can be solved in polynomial time.

Efficient algorithms exist for networks with multiple sources and sinks.

Flow over time problems are more complex than static flows but still tractable in certain cases.

Abstract

Network flows over time are a fascinating generalization of classical (static) network flows, introducing an element of time. They naturally model problems where travel and transmission are not instantaneous and flow may vary over time. Not surprisingly, flow over time problems turn out to be more challenging to solve than their static counterparts. In this survey, we mainly focus on the efficient computation of transshipments over time in networks with several source and sink nodes with given supplies and demands, which is arguably the most difficult flow over time problem that can still be solved in polynomial time.