A Subsequence Generation Approach for the Airline Crew Pairing Problem Matias Sevel Rasmussen ∗,1 , Richard M. Lusby 1 , David M. Ryan 2 , and Jesper Larsen 1 1 Department of Management Engineering, Technical University of Denmark, Denmark 2 Department of Engineering Science, The University of Auckland, New Zealand May, 2011 Abstract In this paper we consider an important problem for the airline industry. The widely studied crew pairing problem is typically for- mulated as a set partitioning problem and solved using the branch- and-price methodology. Here we develop a new integer programming framework, based on the concept of subsequence generation, for solv- ing the set partitioning formulation. In subsequence generation one restricts the number of permitted subsequent flights, that a crew mem- ber can turn to after completing any particular flight. By restricting the number of subsequences, the number of pairings in the problem de- creases. The aim is then to dynamically add attractive subsequences to the problem, thereby increasing the number of possible pairings and improving the solution quality. Encouraging results are obtained on 19 real-life instances supplied by Air New Zealand and show that the described methodology is a viable alternative to column generation. Keywords: Airline crew pairing, Crew pairing, Subsequence generation, Column generation, Limited subsequence, Crew scheduling, Real-life appli- cation, Set partitioning, Scheduling * Corresponding author: E-mail: mase@man.dtu.dk. Address: Department of Man- agement Engineering, Technical University of Denmark, Produktionstorvet, Building 424, DK-2800 Kgs. Lyngby, Denmark. Tel.: +45-45254442. Fax: +45-45933435. 1