Branch-and-Price: Column Generation for Solving Huge Integer Programs

We discuss formulations of integer programs with a huge number of variables and their solution by column generation methods i e implicit pricing of nonbasic variables to generate new columns or to prove LP optimality at a node of the branch and bound tree We present classes of models for which this approach decomposes the problem provides tighter LP relaxations and eliminates symmetry We then discuss computational issues and implementation of column generation branch and bound algorithms including special branching rules and e cient ways to solve the LP relaxation February Revised May Revised January