Abstract

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 branchand-bound tree. We present classes of models for which this approach decomposes the problem, provides tighter LP relaxations, and eliminates symmetry. Wethen discuss computational issues and implementation of column generation, branch-andbound algorithms, including special branching rules and e cient ways to solve the LP relaxation. We also discuss the relationship with Lagrangian duality. 1

Citations