Considering Competition to Solve a Flight Schedule and Aircraft Routing Problem for Small Airlines

 

J. Díaz-Ramírez*¹, Y. Garzón², J. l. Huertas³

 

¹ Tecnológico de Monterrey Campus Santa Fe, Distrito Federal, México, *jenny.diaz@itesm.mx.

^{2, 3} Tecnológico de Monterrey Campus Toluca, Toluca, Estado de México, México.

 

ABSTRACT

For the case of low-cost airlines, which are characterized by having a single fleet with a small number of airplanes, in a previous work, a heuristic algorithm (AFS-MRA) was developed to simultaneously find the flight schedule and the aircraft routes subject to maintenance constraints. This work advances this algorithm by incorporating competition in the planning process (MAFS-MRA).

Within a time frame with a given demand data, competition is seen as a game with two players (one airline and all its competitors), where the strategies are all the potential origin-destinations that could be included in the flight schedule, and the payment matrix contains the objective function coefficients that depend on the market share and the routes previously selected.

Numerical experimentation was undertaken using real data for the case of two airlines that operate at Toluca International Airport in Mexico. It was found that, by considering competition, the occupation improves to 3% and that the number of flights required to satisfy the demand was reduced to 21%. Besides, the updating process reduces the profit computation error in almost 80%, as compared to the real market behavior for the period under study.

Keywords: Aircraft maintenance routing, flight schedule design, competition, game.

 

RESUMEN

Para el caso de aerolíneas de bajo costo, caracterizadas por tener una flota de aviones, en un trabajo previo los autores desarrollaron un algoritmo heurístico (AFS-MRA) para encontrar el programa de vuelos y las rutas de aviones con restricciones de mantenimiento simultáneamente. Este trabajo mejora este algoritmo incorporando los efectos de la competencia en el proceso de planeación (MAFS-MRA).

En un horizonte de tiempo con información de demanda tomada de datos históricos, la competencia se maneja como un juego con dos jugadores (mi aerolínea y todos las demás aerolíneas competidoras), donde las estrategias son todos los potenciales vuelos (orígenes-destinos) que podrían incluirse en el programa de vuelos, y la matriz de pagos contiene los coeficientes de la función objetivo del problema de optimización, los cuales dependen de la participación en el mercado de la aerolínea y de las rutas previamente seleccionadas.

Se desarrolló una experimentación numérica usando datos reales de dos aerolíneas que operan en el Aeropuerto lnternacional de Toluca en México. Se encontró que, considerando la competencia, la ocupación mejora en 3%, el número de vuelos necesarios para satisfacer demanda disminuye en 21%. El proceso de actualización reduce los errores en casi 80% cuando se comparan con el comportamiento real del mercado en el período bajo estudio.

 

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