Generation Approach to Airline Crew Scheduling

The airline crew scheduling problem deals with the construction of crew rotations in order to cover the flights of a given schedule at minimum cost. The problem involves complex rules for the legality and costs of individual pairings and base constraints for the availability of crews at home bases. A typical instance considers a planning horizon of one month and several thousand flights. We propose a column generation approach for solving airline crew scheduling problems that is based on a set partitioning model. We discuss algorithmic aspects such as the use of bundle techniques for the fast, approximate solution of linear programs, a pairing generator that combines Lagrangean shortest path and callback techniques, and a novel “rapid branching” IP heuristic. Computational results for a number of industrial instances are reported. Our approach has been implemented within the commercial crew scheduling system NetLine/Crew of Lufthansa Systems Berlin GmbH. 1 The Airline Crew Scheduling Problem The Airline Crew Scheduling Problem (CSP) plays a prominent role in the operations research literature not only because of its economic significance, but also because of its influence on the development of important mathematical techniques, among them branch-and-cut [7], branch-and-price [1], shortest path algorithms [4], stabilization [5], aggregation [10], and heuristics [11], see also the book of Yu [12] for a general overview. The CSP can be described in terms of a pairing digraph N = (V,A). Its nodes V are called tasks. They can be subdivided into legs L ⊆ V that model flights and have to be assigned to crews, supplementary tasks that model crew activities such as check-in and check-out, deadheading (flying as a passenger), and ground transports, and artificial tasks, among them two tasks s and t that model the beginning and the end of a pairing. The arcs Supported by Lufthansa Systems Berlin.