# Aircraft routing and crew pairing: updated algorithms at Air France

## TL;DR

This paper presents updated, efficient algorithms for aircraft routing and crew pairing at Air France, enabling quick solutions for large industrial instances and integrating both problems effectively.

## Contribution

It introduces a compact MIP formulation for aircraft routing and a resource constrained shortest path framework for crew pairing, improving solution speed and scalability.

## Key findings

- Routing can be solved in minutes for large instances.
- Crew pairing optimal solutions are achievable for large instances.
- Integrated problem solutions are near optimal using combined algorithms.

## Abstract

Aircraft routing and crew pairing problems aims at building the sequences of flight legs operated respectively by airplanes and by crews of an airline. Given their impact on airlines operating costs, both have been extensively studied for decades. Our goal is to provide reliable and easy to maintain frameworks for both problems at Air France. We propose simple approaches to deal with Air France current setting. For routing, we introduce a compact MIP formulation that can be solved by current MIP solvers in at most a few minutes even on Air France largest instances. Regarding crew pairing, we provide a standard methodology to model the column generation pricing subproblem within a new resource constrained shortest path framework recently introduced by the first author. This new framework, which can be used as a black-box, leverages on bounds on paths' resource to discard partial solutions and speed-up the resolution. The resulting approach enables to solve to optimality Air France largest instances. Recent literature has focused on integrating aircraft routing and crew pairing problems. As a side result, we have been able to solve to near optimality large industrial instances of the integrated problem by combining the aforementioned algorithms within a simple cut generating method.