Currently a passenger from the city of Medellin - Colombia to some domestic destinations, has the option of traveling by either of the two airports, Jose Maria Cordova (JMC) or Enrique Olaya Herrera (EOH). This research presents the results of a stated preference survey in a discrete choice experiment, and based on this, a model by destination is obtained; for each one of these models multinomial logit and mixed logit were applied, and evaluated each way multinomial logit was chosen as the best.
Keywords: Discrete choice model, airports, air transport.
La mayoría de los estudios del modo aéreo han tratado individualmente los aspectos de tarifas, demoras y demás variables inherentes a este medio de transporte, así como la elección del modo aéreo frente a otros modos, pero poco se ha hecho por modelar cómo un viajero elige un aeropuerto entre dos opciones disponibles en una gran ciudad.
En la actualidad un pasajero que parte de la ciudad de Medellín - Colombia a algunos destinos nacionales, tiene la opción de viajar por alguno de los dos aeropuertos, el José María Córdova (JMC) o el Enrique Olaya Herrera (EOH); esta investigación presenta los resultados de una encuesta de preferencias declaradas en un experimento de elección discreta, y partiendo de esto se obtiene un modelo por destino; para cada uno de estos se hallaron modelos logit multinomial y logit mixto; en cada trayecto evaluado se eligió el logit multinomial como el mejor.
Palabras clave: Modelo de elección discreta, aeropuertos, transporte aéreo.
During the past few years air passenger transport has experienced a noticeable growth, which indicates the importance of studying the demand for this means of transport.
Many cities in the world have or are serviced by more than one airport (London, Paris, New York, Washington, Medellin, etc.). Even though choice models have been studied between planes and trains, planes and cars, planes and busses, Very few variables are found in the literature which influence the choice of an airport terminal, in these types of city which have two airports, given that a user has already decided to use the air mode. What is addressed in this article are the econometric technique considerations to estimate the demand that would have each of the airports for different journeys on domestic flights.
This research is illustrated with the particular case of Medellin and its metropolitan area, Since this area has two airports, the Enrique Olaya Herrera located in the city of Medellin and the José Maria Córdoba located 40 kilometers from the metropolitan area, both airports have direct competition since airplanes can depart from both airports to common destinations.
This article shows the different applications of economic principles in choosing an airport. Microeconomic theory applies due to the consuming decision-making to maximize utility, given a series of restrictions. This is how an air travelling passenger has the option of travelling to Bogota by any of the two available airports in the city of Medellin, keeping in mind that both terminals offer a variety of rates, besides the time and cost that the user experiences as you reach each one of them.
The article contains 6 sections. In section 2 is an art review status, in which the theory of the discreet choice models is presented and will be used to study the choice between the two closest airports. Among possible models are analyzed the Multinomial Logit models and mixed Logit; through these models the behavior of individuals faced with the two alternatives can be analyzed. At the same time, the subjective value of the time given by each selected model can be determined. The Biogeme program is used for the survey process and for obtaining the model. Section 3 presents the applied methodology for the study and the application case to the city of Medellin. Section 4 presents the different developed models for several common journeys, which are also discussed. In section 5 the most relevant conclusions are extracted and the recommendations to future researches. Finally in the last section, the bibliographic references are presented.
2. Art review status
According to civil aeronautics, passenger transportation in Colombia over the past decade has duplicated the number of travelers, nationwide passenger mobilization figures went from 7.854.000 to 14.627.000 between 2001 and 2011. On international flights , the numbers also duplicated in the same period of time and it went from 3.060.000 to 6.960.000. 2010 is considered to be the year of highest growth in aviation market history, over the previous year, nationwide level increased 30,3%, mobilizing a historic peak of 13.2 million passengers annually; the international market has mobilized about 6.2 million passengers, growing 11.5% compared to 2009 . Of the 21 million passengers that Colombia mobilized in 2011, 6 million did so, through the two airports that are in the metropolitan area. 
2.1 Modeling demand at airports
Within the framework of the air transport company, marketing must perform certain functions designed to analyze and understand the market where the company is moving, identify customer needs and promote and develop a demand for the company's products. The knowledge of the markets, which is consistent with strategic marketing, will allow firms to tailor offerings to the market. 
The aviation industries strategic planning is based on the demand that routes represent, also the prediction of passengers expected to travel, among others. The discreet choice model development applied in airports, gives airlines and airport operators an important understanding in the different factors concerning service which can be modified to increase the participation in the air transport market .
The airport terminal chosen models represent a backup in making decisions, for example; helps analyze new routes, reducing connection times, in price analyzing, in the flight programming and profitability; this is how to improve the ability of the requested models, you get better management revenue a programming and profitability efficiency. An airport terminal choice is an effective tool for planning and decision making for both tactical and strategic levels.
Previews studies have helped greatly in understanding the connection between the attributes and air mode. A multinomial logit model was developed by Algers and Beser  for flights and class reservations, while Proussaloglou and Koppelman  modeled the simultaneous choice of airline, flight, type of ticket taking out the balance between market presence, quality service, frequent flight membership programs, rate categories, flight restrictions and flight programming. Logit models were obtained in previous jobs; the costs for passengers who were willing to pay for a higher class ticket or to travel on a membership airline in the frequent flyer program were estimated.
In Coldren and Koppeman work was estimated that route choice models were measured by the great service impact provided by airlines of each route using an added logit model (MNL); these MNL are suitable to describe the attribute service impact in the chosen airport terminal. However, the implied competition between airport terminals is assumed to be consistent when its function is with MNL, this is shown by a well-known property of the MNL model, the independence of irrelevant alternatives, establishes that the probability of choosing any airport is an independent indication. Proussaglou y Koppelman , y Parker y Walker , formed and evaluated a schedule delay impact, which indicates the difference between the passengers preferred flight time and the flight hours offered. These schedule delay studies indicate a negative impact probability in choosing a particular flight. Proussaglou y Koppelman  also show that delays effect more business travelers than pleasure travelers, just like passengers who take flights that take off before and after their preferred flight time. Parker and Walker  use the non-linear function to evaluate the increasing delay effect between take off time and route usage.
The studies mentioned above are due to two general categories: studies based on official information with a high geographic gathering level or limited to few Origin—Destination pairs, or survey studies implementing both with revealed preferences and stated preferences and information covering a very limited Origen— Destination pair number. IN all cases, studies consider that for on Origen—Destination pair, is from one airport and the Origen choice problem is not studied. The only work found, is from Mendieta and Cantillo  which achieve an airport terminal choice model, but using shown preferences.
2.2. Discrete choice models
The discrete election models are based on the random utility theory, which is informed on the principle that the probability of given option being chosen by an individual is dependent on the socio-economic characteristic and the relative attraction of the option . The utility is formed considering the deterministic component observed by the analyst
, and an unknown random component. In each alternative, the utility function of the deterministic component is represented according to its attributes, such as flight time and cost of the trip, and also the characteristics of the passengers (age, gender, income, occupation, etc.).
The transportation models were initially developed based on added approaches, but the use of disaggregated discreet choice models was to calibrate them. The test shows that the indirect use of alternative j for an individual q, Ujq, is represented by the sum of a known term known by the modeler and a random other , as shown in equation 1:
Viq belongs to a measurable utility part, which is the alternative attribute function and the individual characteristics and εiq a random error which includes all unknown factors or were not taken into account by the modeler.
2.2.1 Multinomial logit model
The random utility theory considers that the individual chooses the maximum utility alternative, which is choosing option i
(see equation 2):
The probability of the alternative is Piq, in this case mode i; chosen by individual q; among all j alternatives; is given by equation 3: 
The model estimation is to find the coefficients θk that more often generate the watched sample; which are most likely to maximize the possibility of an observed event. The parameter β is invaluable and that is why it is incorporated with the coefficient θk in one parameter. Xikq is the vector of k socioeconomic characteristics of the q individual (gender, age, income, etc.) and the alternative attributes i (time, fare, etc.).
2.2.2 Mixed logit model
The mixed logit is presumably a Uin utility function, formed from different components such as; deterministic Vin, a random component εin independently and identically distributed, and one or more additional random terms ηin. Like that, the utility function is defined in equation 4
3. Case study
The most interesting characteristic of this model is that, under certain conditions, any random utility model is likely to choose to be approximately as close as it´s wanted by a mixed logit .
First a region is chosen that has two airports and serves a metropolitan area of a city, with some common destination journeys.
Secondly a survey was designed with basic information revealed about the socioeconomic characteristics of the traveller, also design a Declared Preferences (DP) a survey that permits to capture the sensibility and different variables in a customer’s hypothetical case. Thirdly, the pilot tested was applied and the survey is corrected with changes to be considered.
Fourthly a revealed and declared information survey was carried out. The (DP) consists of questioning about decisions which are eventually made by individuals that determine a low alternative under a series of fictitious aspects, proposed by the investigator according to his objectives. In this case, different situations were investigated to make a trip through any of the two considered airports
; such situations are caused from the different values of attributes that are investigated; such as the ticket cost (CT); the trip to the airport cost (CD), and the traveling time to the airport (TV), which is a new variable to this type of studies, as shown in previous studies above, studies focus on comparing routes that are related to different airlines that serve an airport, discreet choice models are obtained through the development of this investigation, which permits customers to know the differences between costs and travel times to two airports competing from the origin of the trip.
Each of the three variables mentioned (CT, CD and TV) is divided in three levels; high, medium and low. The PD survey design details are in Muñoz . See table 1 and table 2