Quickest cluster flow problems on tree networks

Abstract

In this publication we examine a dynamic network flow problem, called the quickest cluster flow problem. This problem is motivated by evacuation planning and yields improved lower bounds on evacuation times. Our approach models people moving in groups rather than individually which can be observed even in the situation of an emergency. To the best of our knowledge, this fact has received little attention in dynamic network flow literature. Interrelations of this new model to existing network flow models like multicommodity flows are pointed out. The quickest cluster flow problem is proven to be NP-hard even on tree networks. We restrict the cluster sizes to pairwise divisible values and obtain an exact greedy-based algorithm. © 2011 Springer-Verlag.