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Bi-Objective Bus Routing: An Application to School Buses in Rural Areas

Author

Listed:
  • Joaquín Pacheco

    (Departamento de Economía Aplicada, Universidad de Burgos, 09001 Burgos, Spain)

  • Rafael Caballero

    (Departamento de Economía Aplicada (Matemáticas), Universidad de Málaga, 29071 Málaga, Spain)

  • Manuel Laguna

    (Leeds School of Business, University of Colorado, Boulder, Colorado 80306)

  • Julián Molina

    (Departamento de Economía Aplicada (Matemáticas), Universidad de Málaga, 29071 Málaga, Spain)

Abstract

The min-max vehicle routing problem (VRP) is a variant of the classical VRP in which the objective is to minimize the duration of the longest route. Examination of the VRP literature indicates that the min-max VRP has received less attention than other variants have over the years. However, the problem has important practical applications, such as those related to routing school buses. In this setting, in addition to the min-max criterion imposed on the time it takes to complete the longest route, school districts are concerned with the minimization of the total distance traveled, which is the objective of the classical VRP. Hence, the problem is formulated as a bi-objective optimization model that trades off service (i.e., the minimization of the longest route) and operational cost (i.e., the minimization of the total distance traveled). We develop a solution procedure for this problem by applying tabu search within the framework of Multiobjective Adaptive Memory Programming and compare it to an implementation of the Non-dominated Sorting Genetic Algorithm---a well-known approach to multiobjective optimization. We also assess the merit of the solution method by comparing our approximations with solution frontiers obtained with an (epsilon) -constraint implementation.

Suggested Citation

  • Joaquín Pacheco & Rafael Caballero & Manuel Laguna & Julián Molina, 2013. "Bi-Objective Bus Routing: An Application to School Buses in Rural Areas," Transportation Science, INFORMS, vol. 47(3), pages 397-411, August.
    • Handle: RePEc:inm:ortrsc:v:47:y:2013:i:3:p:397-411
    DOI: 10.1287/trsc.1120.0437
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