A Heuristic Approach to Column Generation for Airline Crew Scheduling

Airline crew scheduling gives rise to many diicult and interesting optimisation problems. With straightforward approaches to the crew pairing problem one speciically needs to solve very large set-covering problems. One suggested approach to these problems is column generation. In column generation, the choice of master solver can have a signiicant impact on performance, both with respect to speed and quality. We have investigated the possibility of using a heuristic integer optimiser for the master problem, and make a comparison with a simplex based algorithm. We have also tried to direct the generation process by using dual information from a network relaxation of the pairing problem. Finally, the combination of the integer optimiser and a simple subgradient algorithm gives a very competitive master solver which for most problems speeds up the complete solution process many times. Computational results are provided on several production instances from diierent airlines. i Preface This licentate thesis is the conclusion to the ve semester ECMI postgraduate program (European Consortium for Mathematics in Industry). The program consists of number of core and specialised courses in the eld of applied mathemathics, and an important part is the nal project which should treat a speciic industry application. My application has been airline crew scheduling. The work has been performed within the ESPRIT-project PAROS (Parallel large scale automatic scheduling), which mainly aims at improving existing solution techniques through parallelisation and new algorithms. It has also to some extent been sponsored by the Swedish network of applied mathemathics (NTM), as part of their university-industry exchange program. Much of the work has been performed on location at Carmen Systems, who provides a commercial software used by most larger European airlines. I would like to thank my two supervisors Dag Wedelin at Chalmers and Curt Hjorring at Carmen Systems, for help, support and many inspiring ideas. I also wish to thank Federico Hernandez, Olle Liljenzin and Tuomo Takkula as well as many others in the PAROS project, and at Carmen Systems. I would like to thank you all for your inspiration and time.