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Two-Stage Fleet Assignment Model Considering Stochastic Passenger Demands

Grado Department of Industrial and Systems Engineering, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061
Grado Department of Industrial and Systems Engineering, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061
hanifs{at}vt.edu
xzhu{at}vt.edu

An airline's fleet typically contains multiple aircraft families, each having a specific cockpit design and crew requirement. Each aircraft family contains multiple aircraft types having different capacities. Given a flight schedule network, the fleet assignment model is concerned with assigning aircraft to flight legs to maximize profits with respect to captured itinerary-based demand. However, because of related yield management and crew-scheduling regulations, in particular, this decision needs to be made well in advance of departures when market demand is still highly uncertain, although subsequently at a later stage, reassignments of aircraft types within a given family can be made when demand forecasts improve, while preserving crew schedules. In this paper, we propose a two-stage stochastic mixed-integer programming approach in which the first stage makes only higher-level family-assignment decisions, while the second stage performs subsequent family-based type-level assignments according to forecasted market demand realizations. By considering demand uncertainty up-front at the initial fleeting stage, we inject additional flexibility in the process that offers more judicious opportunities for later revisions. We conduct a polyhedral analysis of the proposed model and develop suitable solution approaches. Results of some numerical experiments are presented to exhibit the efficacy of using the stochastic model as opposed to the traditional deterministic model that considers only expected demand, and to demonstrate the efficiency of the proposed algorithms as compared with solving the model using its deterministic equivalent.

Subject classifications: industries; transportation; programming; integer; stochastic; large-scale systems.
History: Received February 2006; revision received December 2006; accepted February 2007.