Mathematical analysis and simulation of tax and fare trends on airline routes

This document contains a study of the demand of the ticket sales for each fare within American Airlines for one of their routes, Barcelona to Miami. The project is an approach to the studies carried out by the airlines but without all the tools that the airline has. In the document are detailed simplifications and assumptions that have been considered for the project. The study has been conducted by analysing and modelling historical data from previous years, by clustering methods such as K-means algorithm in addition to modelling the behaviour of the ticket sales and the trending of demand, which has been modelled using logistic regression. Algorithms used for MLE (Maximum Likelihood Estimation) of the logistic model will be analysed in terms of performance as well as accuracy. In addition, the document contains the implementation of a basic genetic algorithm that could be combined as a meta-heuristic method with other deterministic methods to optimize the computational time, or use it as an approximation. The project objective is to find the number of fares that the airline should sell to achieve the most cost effective solution and achieving a balance between supply and demand. The approach followed implies using a good trained logistic model in order to constraint the search space, or possible selling strategies to the real demand. Finally, with the aim of increasing sales and profits of the airline, it has designed a simple and friendly graphical user interface (GUI) to facilitate the work of sales agents. The computer system is a Server-Client architecture type which works with an own implementation of TCP sockets and asynchronous programming. Data might be continuously optimized either by real time algorithms or for long term planning on the server side with logistic models running inside machine learning algorithms, which are also supported