Managing delay in tail assignment: from minimum turn time to stochastic routing at Air France

Abstract: On-time performance is a critical challenge in the airline industry, leading to large operational and customer dissatisfaction costs. The tail assignment problem builds the sequences of flights or routes followed by individual airplanes. While airlines cannot avoid some sources of delay, choosing routes wisely limits propagation along these. This paper addresses the stochastic tail assignment problem at Air France. We propose a column generation approach for this problem. The key ingredient is the pricing algorithm, which is a stochastic shortest path problem. We use dedicated bounds to discard paths in an enumeration algorithm, and introduce new bounds based on a lattice ordering of the set of piecewise linear convex functions to strike a balance between bounds quality and computational cost. A diving heuristic enables us to retrieve integer solutions. Numerical experiments on real-world Air France instances demonstrate that our algorithms lead to an average 0.28% optimality gap on instances with up to 600 flight legs in a few hours of computing time. The resulting solutions effectively balance operational costs and delay resilience, outperforming previous approaches based on minimum turn time.