Min-Max quickest path problems

In a dynamic network, the quickest path problem asks for a path such that a given amount of flow can be sent from source to sink via this path in minimal time. In practical settings, for example, in evacuation or transportation planning, the problem parameters might not be known exactly a priori. It is therefore of interest to consider robust versions of these problems in which travel times and/or capacities of arcs depend on a certain scenario. In this article, min–max versions of robust quickest path problems are investigated and, depending on their complexity status, exact algorithms or fully polynomialtime approximation schemes are proposed. © 2012 Wiley Periodicals, Inc. NETWORKS, Vol. 000(00), 000–00