A typical problem in traffic control is the steering over a network of vehicles with different origins and destinations. In this report this scenario is formulated as a multi-commodity network flow problem, a linear programming problem whose objective is to transport, with minimum cost, different commodities from their respective sources to their sinks through a network, while respecting the capacity constraints of the roads. The dynamic network flow formulation of the problem is also presented, extending the network over time to incorporate the temporal dimension. Different algorithms for solving the multi-commodity network flow problem are examined. First, the simplex method, more precisely its revised version, is considered, and then the Dantzig-Wolfe decomposition is illustrated, an optimization algorithm which exploits specific block structures in the constraints. These methods are applied using state-of-the-art linear programming solvers and evaluated with a simulation based on the road network in central Stockholm. The results show that both methods allow for solving the traffic flow problem, with limitations given by the specifics of the solvers and by the space and time discretization of the problem. In particular, the revised simplex algorithm results the faster method.