Integer Muticommodity Flow Problems

We present a column generation model and solution approach for large integer multicommodity flow problems. We solve the model using branch-and-bound, with bounds provided by linear programs at each node of the branch-and-bound tree. Since the model contains one variable for each origin-destination path, for every commodity, the linear programming relaxation is solved using column generation, i.e., implicit pricing of nonbasic variables to generate new columns or to prove LP optimality. Methods for speeding up the solution of the linear program are presented. Also, we devise new branching rules that allow columns to be generated efficiently at each node of the branch-and-bound tree. Computational results are presented for a set of test problems arising from a transportation application.