One-parametric analysis of column-oriented linear programs

A linear optimization problem which is amenable to column generation and contains a single parameter in the objective function is considered. We extend and adapt the standard linear programming column generation scheme to effectively and efficiently solve this problem for all values of the parameter. As a potential application we consider bi-objective discrete optimization and describe how the one-parametric column generation scheme can be used to form an outer approximation of the Pareto frontier for such a problem.