We consider the Steiner tree packing problem. For a given undirected graph G = (V,E) with positive integer capacities and non-negative weights on its edges, and a list of node sets (nets), the problem is to find a connection of nets which satisfies the edge capacity limits and minimizes the total weights. We focus on the switchbox routing problem in knock-knee model and formulate this problem as an integer programming using Steiner tree variables. The model contains exponential number of variables, but the problem can be solved using a polynomial time column generation procedure. We develop a branch-and-price algorithm based on this polynomial time column generation procedure. We test the algorithm on some standard test instances and compare the performances with the results using cutting plane approach. Computational results show that our algorithm is competitive to the cutting plane algorithm presented by Grötschel et al. and can be used to solve practically sized problems.
