Given a railway line with n stops and the number of travelers between each pair of stops, we show how to split these stops into k different fare zones in order to maximize the benefit obtained from the sale of tickets to the travelers. We present a method to obtain this solution that is based on finding the longest path in a weighted root tree. This method improves in terms of efficiency the combinatorial method, where all the possible distributions have to be considered for deciding which is the optimal one. The authors would like to thank RENFE for his collaboration and providing us several tables of data of the flow of passengers of the commuter trains of the Valencia region. J. Alberto Conejero is supported by MEC Project MTM2013-47093-P and Esther Sanabria-Codesal is supported by MEC Project MTM2012-33073. Conejero Casares, JA.; Jordan Lluch, C.; Sanabria Codesal, E. (2014). A tree-based model for setting optimal train fare zones. Mathematical Problems in Engineering. 2014:1-11. doi:10.1155/2014/384321 S 1 11 2014
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