Invited Tutorial Airline fleet assignment concepts, models, and algorithms Hanif D. Sherali * , Ebru K. Bish, Xiaomei Zhu Grado Department of Industrial and Systems Engineering (0118), Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, United States Received 5 May 2004; accepted 3 January 2005 Available online 2 April 2005 Abstract The fleet assignment problem (FAP) deals with assigning aircraft types, each having a different capacity, to the sched- uled flights, based on equipment capabilities and availabilities, operational costs, and potential revenues. An airlineÕs fleet- ing decision highly impacts its revenues, and thus, constitutes an essential component of its overall scheduling process. However, due to the large number of flights scheduled each day, and the dependency of the FAP on other airline processes, solving the FAP has always been a challenging task for the airlines. In this paper, we present a tutorial on the basic and enhanced models and approaches that have been developed for the FAP, including: (1) integrating the FAP with other airline decision processes such as schedule design, aircraft maintenance routing, and crew scheduling; (2) proposing solu- tion techniques that include additional considerations into the traditional fleeting models, such as considering itinerary- based demand forecasts and the recapture effect, as well as investigating the effectiveness of alternative approaches such as randomized search procedures; and (3) studying dynamic fleeting mechanisms that update the initial fleeting solution as departures approach and more information on demand patterns is gathered, thus providing a more effective way to match the airlineÕs supply with demand. We also discuss future research directions in the fleet assignment arena. Ó 2005 Elsevier B.V. All rights reserved. Keywords: Airlines; Fleet assignment; Integer programming; Large scale optimization; Transportation 1. Introduction Aircraft seats are an airlineÕs product. Similar to any other product, a larger quantity secures sales, while extra inventory incurs costs. For airlines, providing larger capacities implies higher operating costs. On the other hand, aircraft seats are ‘‘perishable’’, that is, unsold seats at the departure of the flight are wasted. Consequently, the ideal strategy is to provide just the ‘‘right number’’ of seats to passengers at the ‘‘right 0377-2217/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.ejor.2005.01.056 * Corresponding author. Tel.: +1 540 231 5474; fax: +1 540 231 3322. E-mail addresses: hanifs@vt.edu (H.D. Sherali), ebru@vt.edu (E.K. Bish), xzhu@vt.edu (X. Zhu). European Journal of Operational Research 172 (2006) 1–30 www.elsevier.com/locate/ejor