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A Graph Coloring Model for a Feasibility Problem in Crew Scheduling

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We consider a crew scheduling problem with preferential bidding in the airline in- dustry. We propose a new methodology based on a graph coloring model and a tabu search algorithm for determining if the problem contains at least one feasible solu-
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  Les Cahiers du GERAD   ISSN: 0711–2440 A Graph Coloring Model for aFeasibility Problem in CrewScheduling M. Gamache, A. Hertz,J. OuelletG–2005–34April 2005 Les textes publi´es dans la s´erie des rapports de recherche HEC n’engagent que la responsabilit´e de leursauteurs. La publication de ces rapports de recherche b´en´eficie d’une subvention du Fonds qu´eb´ecois de larecherche sur la nature et les technologies.  A Graph Coloring Model for a FeasibilityProblem in Crew Scheduling Michel Gamache GERAD and D´epartement des g´enies civil, g´eologique et des mines ´ Ecole Polytechnique de Montr´eal C.P. 6079, Succ. Centre-ville Montr´eal (Qu´ebec) Canada H3C 3A7  michel.gamache@polymtl.ca Alain Hertz, J´erˆome Ouellet GERAD and D´epartement de math´ematiques et de g´enie industriel ´ Ecole Polytechnique de Montr´eal C.P. 6079, Succ. Centre-ville Montr´eal (Qu´ebec) Canada H3C 3A7  { alain.hertz;jerome.ouellet } @polymtl.ca April 2005 Les Cahiers du GERAD  G–2005–34 Copyright c  2005 GERAD  Abstract We consider a crew scheduling problem with preferential bidding in the airline in-dustry. We propose a new methodology based on a graph coloring model and a tabusearch algorithm for determining if the problem contains at least one feasible solu-tion. We then show how to combine the proposed approach with a heuristic sequentialscheduling method that uses column generation and branch-and-bound techniques. Key Words:  Graph coloring, crew scheduling, preferential bidding, tabu search. R´esum´e Nous consid´erons un probl`eme de confection d’horaires d’´equipages en transporta´erien, dans lequel on tient compte des pr´ef´erences des employ´es. Nous proposons unenouvelle m´ethodologie bas´ee sur un mod`ele de coloration de graphe et sur un algorithmede type Recherche avec tabous, le but ´etant de d´eterminer si le probl`eme consid´er´e con-tient au moins une solution qui respecte toutes les contraintes. Nous montrons ensuitecomment combiner l’approche propos´ee avec une heuristique s´equentielle de confec-tion d’horaires qui utilise la g´en´eration de colonnes et une technique de s´eparation-´evaluation (branch-and-bound).
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