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The Median Shortest Path Problem: A Multiobjective Approach to Analyze Cost vs. Accessibility in the Design of Transportation Networks

Author

Listed:
  • John R. Current

    (The Ohio State University, Columbus, Ohio)

  • Charles S. Revelle

    (The Johns Hopkins University, Baltimore, Maryland)

  • Jared L. Cohon

    (The Johns Hopkins University, Baltimore, Maryland)

Abstract

In this paper the authors introduce the median shortest path problem (MSPP). The MSPP is a bicriterion path problem with the objectives being the minimization of the total path length and the minimization of the total travel time required for demand to reach a node on the path. Potential applications of the MSPP include, among others, the location of new highways, railroad lines and subway lines and the design of airline routes. It is particularly applicable in transportation network design problems where the trade-off between operator costs and user costs is important. An algorithm is presented to identify noninferior solutions to the MSPP. This algorithm incorporates a K shortest path algorithm. The algorithm is demonstrated with a sample problem and the results are compared to those obtained using integer programming.

Suggested Citation

  • John R. Current & Charles S. Revelle & Jared L. Cohon, 1987. "The Median Shortest Path Problem: A Multiobjective Approach to Analyze Cost vs. Accessibility in the Design of Transportation Networks," Transportation Science, INFORMS, vol. 21(3), pages 188-197, August.
    • Handle: RePEc:inm:ortrsc:v:21:y:1987:i:3:p:188-197
    DOI: 10.1287/trsc.21.3.188
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    Citations

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    Cited by:

    1. Soroush, H.M., 2008. "Optimal paths in bi-attribute networks with fractional cost functions," European Journal of Operational Research, Elsevier, vol. 190(3), pages 633-658, November.
    2. Ghoseiri, Keivan & Szidarovszky, Ferenc & Asgharpour, Mohammad Jawad, 2004. "A multi-objective train scheduling model and solution," Transportation Research Part B: Methodological, Elsevier, vol. 38(10), pages 927-952, December.
    3. Pablo A. Miranda-Gonzalez & Javier Maturana-Ross & Carola A. Blazquez & Guillermo Cabrera-Guerrero, 2021. "Exact Formulation and Analysis for the Bi-Objective Insular Traveling Salesman Problem," Mathematics, MDPI, vol. 9(21), pages 1-33, October.
    4. Yannick Kergosien & Antoine Giret & Emmanuel Néron & Gaël Sauvanet, 2022. "An Efficient Label-Correcting Algorithm for the Multiobjective Shortest Path Problem," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 76-92, January.
    5. Miranda, Pablo A. & Blazquez, Carola A. & Obreque, Carlos & Maturana-Ross, Javier & Gutierrez-Jarpa, Gabriel, 2018. "The bi-objective insular traveling salesman problem with maritime and ground transportation costs," European Journal of Operational Research, Elsevier, vol. 271(3), pages 1014-1036.
    6. Curtin, Kevin M. & Biba, Steve, 2011. "The Transit Route Arc-Node Service Maximization problem," European Journal of Operational Research, Elsevier, vol. 208(1), pages 46-56, January.
    7. Dung-Ying Lin & Chi Xie, 2011. "The Pareto-optimal Solution Set of the Equilibrium Network Design Problem with Multiple Commensurate Objectives," Networks and Spatial Economics, Springer, vol. 11(4), pages 727-751, December.
    8. F. Guerriero & R. Musmanno, 2001. "Label Correcting Methods to Solve Multicriteria Shortest Path Problems," Journal of Optimization Theory and Applications, Springer, vol. 111(3), pages 589-613, December.
    9. Labbe, Martine & Laporte, Gilbert & Rodriguez Martin, Inmaculada & Gonzalez, Juan Jose Salazar, 2005. "Locating median cycles in networks," European Journal of Operational Research, Elsevier, vol. 160(2), pages 457-470, January.
    10. Elisangela Martins de Sá & Ivan Contreras & Jean-François Cordeau & Ricardo Saraiva de Camargo & Gilberto de Miranda, 2015. "The Hub Line Location Problem," Transportation Science, INFORMS, vol. 49(3), pages 500-518, August.
    11. Lari, Isabella & Ricca, Federica & Scozzari, Andrea, 2008. "Comparing different metaheuristic approaches for the median path problem with bounded length," European Journal of Operational Research, Elsevier, vol. 190(3), pages 587-597, November.
    12. Bruno, Giuseppe & Ghiani, Gianpaolo & Improta, Gennaro, 1998. "A multi-modal approach to the location of a rapid transit line," European Journal of Operational Research, Elsevier, vol. 104(2), pages 321-332, January.
    13. Chang, Yu-Hern & Yeh, Chung-Hsing & Shen, Ching-Cheng, 2000. "A multiobjective model for passenger train services planning: application to Taiwan's high-speed rail line," Transportation Research Part B: Methodological, Elsevier, vol. 34(2), pages 91-106, February.
    14. Granat, Janusz & Guerriero, Francesca, 2003. "The interactive analysis of the multicriteria shortest path problem by the reference point method," European Journal of Operational Research, Elsevier, vol. 151(1), pages 103-118, November.
    15. Anita Schöbel, 2005. "Locating Stops Along Bus or Railway Lines—A Bicriteria Problem," Annals of Operations Research, Springer, vol. 136(1), pages 211-227, April.
    16. Avella, P. & Benati, S. & Canovas Martinez, L. & Dalby, K. & Di Girolamo, D. & Dimitrijevic, B. & Ghiani, G. & Giannikos, I. & Guttmann, N. & Hultberg, T. H. & Fliege, J. & Marin, A. & Munoz Marquez, , 1998. "Some personal views on the current state and the future of locational analysis," European Journal of Operational Research, Elsevier, vol. 104(2), pages 269-287, January.
    17. de Lima Pinto, Leizer & Bornstein, Cláudio Thomás & Maculan, Nelson, 2009. "The tricriterion shortest path problem with at least two bottleneck objective functions," European Journal of Operational Research, Elsevier, vol. 198(2), pages 387-391, October.

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