| In this paper, we examine various branch and bound algorithms for a minimum congestion origin-destination integer multi-commodity flow problem. The problem consists of finding a routing such that the congestion of the most congested arc is minimum. For our implementation, we assume that all demands are known a priori.;We provide a mixed integer linear programming formulation of our problem and propose various new branching rules to solve the model. For each rule, we provide theoretical and experimental proof of their effectiveness.;In order to solve large instances, that more accurately portray real-world applications, we outline a path formulation model of our problem. We provide two methods for implementing our branching rules using branch and price. |
