The robust crew pairing problem: model and solution methodology

We present a new robust formulation for the crew pairing problem where flight and connection times are random and vary within an interval. The model protects against infeasibility with a specified level of uncertainty and minimizes crew cost in the worst case. The resulting robust terms in the objective function and in the resource constraints are nonlinear. We apply Lagrangian relaxation to separate the nonlinear terms in the subproblem leading to a new robust formulation of the shortest path problem with resource constraints. We show that the nonlinear subproblem can be solved as a series of linear auxiliary problems. The proposed solution methodology was successful to solve industry instances in very competitive times and led to more robust crew pairing solutions as shown by simulation experiments.