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A Mathematical approach applied to train scheduling in Brazilian railways

Thiago Henrique Nogueira (thnogueira.ufv***at***gmail.com)
Carlos R. V. Carvalho (carlos***at***dep.ufmg.br)
Gabriel Pinheiro Alves Santos (gabriel.pinheiro***at***ufv.br)
Larissa Cristina de Camargo (larissaufmg***at***gmail.com)

Abstract: In this paper, a mathematical approach was used to schedule trains in order to minimize the weighted delay time. The single-track railway studied, is composed of a part of two joined railways in Brazil, which belongs to the VALE company and to Centro-Atl\^antica railway (FCA). This single line is shared by these railways (VALE and FCA) and the trains travel in both directions. These railways have a bottleneck caused by a heavy traffic. Therefore, mathematical equations were developed to determine the shortest time interval admissible between two trains, ensuring that they will not overlap. These equations enable us to simplify the mathematical representation of the problem and define it as a single machine scheduling problem. Later, two formulations of mathematical models were developed and analyzed; one based on ``Arc-Time-Indexed" variables and the other, on ``Binary" variables. Each formulation reflects a specific concept on how the variables and parameters are defined and require particular settings and definitions. Extensive computational experiments are performed considering various instances to capture several aspects of practical situations. Based on the results, recommendations are made for the best adaptation of the MIP formulation for the considered problem.

Keywords: Logistic, Railway transportation, Single-track line, Interchange point, Scheduling, Mathematical modeling

Category 1: Applications -- OR and Management Sciences (Production and Logistics )

Category 2: Applications -- OR and Management Sciences (Transportation )

Citation: Departamento de Engenharia de Produção, Universidade Federal de Minas Gerais, Belo Horizonte, Minas Gerais, Brazil, 06/2014.

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Entry Submitted: 07/15/2014
Entry Accepted: 07/15/2014
Entry Last Modified: 10/28/2014

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