Constraint Programming Based Column Generation for Crew Assignment |
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Authors: | Torsten Fahle Ulrich Junker Stefan E Karisch Niklas Kohl Meinolf Sellmann Bo Vaaben |
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Institution: | (1) Department of Mathematics and Computer Science, University of Paderborn, Fürstenallee 11, D-33102 Paderborn, Germany;(2) ILOG S.A., 1681, route des Dolines, F-06560 Valbonne, France;(3) Carmen Systems Ltd., 1800 McGill College Avenue, Suite 2800, Montreal, Quebec, H3A 3J6, Canada;(4) Carmen Consulting, Fruebjergvej 3, 2100 Copenhagen Ø, Denmark |
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Abstract: | Airline crew assignment problems are large-scale optimization problems which can be adequately solved by column generation. The subproblem is typically a so-called constrained shortest path problem and solved by dynamic programming. However, complex airline regulations arising frequently in European airlines cannot be expressed entirely in this framework and limit the use of pure column generation. In this paper, we formulate the subproblem as a constraint satisfaction problem, thus gaining high expressiveness. Each airline regulation is encoded by one or several constraints. An additional constraint which encapsulates a shortest path algorithm for generating columns with negative reduced costs is introduced. This constraint reduces the search space of the subproblem significantly. Resulting domain reductions are propagated to the other constraints which additionally reduces the search space. Numerical results based on data of a large European airline are presented and demonstrate the potential of our approach. |
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Keywords: | airline crew assignment constraint satisfaction column generation shortest path constraint hybrid OR/CP methods |
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