A new pricing scheme for airline crew scheduling

Solving LP relaxations of airline crew scheduling models is computationally challenging due to the presence of a large number of variables, complex feasibility rules to generate columns, and nonlinear cost. We perform computational experiments with a nonlinear pricing strategy. We develop a column generation scheme that uses several pruning rules to fathom column enumeration. The pruning rules are categorized into approximate and exact, where the approximate rules might prune columns that would yield an improved objective value. The pruning rules use the fact that columns are paths in a network, and we use shortest path algorithms and their extensions to obtain bounds.