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Combinatorial Benders Cuts for the Minimum Tollbooth Problem

Author

Listed:
  • Lihui Bai

    (College of Business Administration, Valparaiso University, Valparaiso, Indiana 46383)

  • Paul A. Rubin

    (The Eli Broad Graduate School of Management, Michigan State University, East Lansing, Michigan 48824)

Abstract

We address a toll pricing problem in which the objective is to minimize the number of required toll facilities in a transportation network while inducing drivers to make the most efficient collective use of the network. We formulate the problem as a mixed-integer programming model and propose a solution method using combinatorial Benders cuts. Computational study of real networks as well as randomly generated networks indicates that our proposed method is efficient in obtaining provably optimal solutions for networks with small to medium sizes.

Suggested Citation

  • Lihui Bai & Paul A. Rubin, 2009. "Combinatorial Benders Cuts for the Minimum Tollbooth Problem," Operations Research, INFORMS, vol. 57(6), pages 1510-1522, December.
    • Handle: RePEc:inm:oropre:v:57:y:2009:i:6:p:1510-1522
    DOI: 10.1287/opre.1090.0694
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    References listed on IDEAS

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    1. John Gleeson & Jennifer Ryan, 1990. "Identifying Minimally Infeasible Subsystems of Inequalities," INFORMS Journal on Computing, INFORMS, vol. 2(1), pages 61-63, February.
    2. Verhoef, Erik T., 2002. "Second-best congestion pricing in general networks. Heuristic algorithms for finding second-best optimal toll levels and toll points," Transportation Research Part B: Methodological, Elsevier, vol. 36(8), pages 707-729, September.
    3. Gianni Codato & Matteo Fischetti, 2006. "Combinatorial Benders' Cuts for Mixed-Integer Linear Programming," Operations Research, INFORMS, vol. 54(4), pages 756-766, August.
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    Cited by:

    1. Vatsa, Amit Kumar & Jayaswal, Sachin, 2016. "A new formulation and Benders decomposition for the multi-period maximal covering facility location problem with server uncertainty," European Journal of Operational Research, Elsevier, vol. 251(2), pages 404-418.
    2. Jyotirmoy Dalal & Halit Üster, 2021. "Robust Emergency Relief Supply Planning for Foreseen Disasters Under Evacuation-Side Uncertainty," Transportation Science, INFORMS, vol. 55(3), pages 791-813, May.
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    4. Fragkos, Ioannis & Cordeau, Jean-François & Jans, Raf, 2021. "Decomposition methods for large-scale network expansion problems," Transportation Research Part B: Methodological, Elsevier, vol. 144(C), pages 60-80.
    5. Zhang, Qihuan & Wang, Ziteng & Huang, Min & Yu, Yang & Fang, Shu-Cherng, 2022. "Heterogeneous multi-depot collaborative vehicle routing problem," Transportation Research Part B: Methodological, Elsevier, vol. 160(C), pages 1-20.
    6. Vatsa, Amit Kumar & Jayaswal, Sachin, 2015. "A New Formulation and Benders' Decomposition for Multi-period facility Location Problem with Server Uncertainty," IIMA Working Papers WP2015-02-07, Indian Institute of Management Ahmedabad, Research and Publication Department.
    7. Lihui Bai & Donald Hearn & Siriphong Lawphongpanich, 2010. "A heuristic method for the minimum toll booth problem," Journal of Global Optimization, Springer, vol. 48(4), pages 533-548, December.
    8. Chinmay Maheshwari & Kshitij Kulkarni & Druv Pai & Jiarui Yang & Manxi Wu & Shankar Sastry, 2024. "Congestion Pricing for Efficiency and Equity: Theory and Applications to the San Francisco Bay Area," Papers 2401.16844, arXiv.org, revised Sep 2024.
    9. Mustafa C. Camur & Thomas Sharkey & Chrysafis Vogiatzis, 2022. "The Star Degree Centrality Problem: A Decomposition Approach," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 93-112, January.
    10. Christian Va Karsten & Stefan Ropke & David Pisinger, 2018. "Simultaneous Optimization of Container Ship Sailing Speed and Container Routing with Transit Time Restrictions," Transportation Science, INFORMS, vol. 52(4), pages 769-787, August.
    11. Gelareh, Shahin & Nickel, Stefan, 2011. "Hub location problems in transportation networks," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 47(6), pages 1092-1111.
    12. Vatsa, Amit Kumar & Jayaswal, Sachin, 2021. "Capacitated multi-period maximal covering location problem with server uncertainty," European Journal of Operational Research, Elsevier, vol. 289(3), pages 1107-1126.
    13. Jyotirmoy Dalal & Halit Üster, 2018. "Combining Worst Case and Average Case Considerations in an Integrated Emergency Response Network Design Problem," Transportation Science, INFORMS, vol. 52(1), pages 171-188, January.
    14. Quentin Botton & Bernard Fortz & Luis Gouveia & Michael Poss, 2013. "Benders Decomposition for the Hop-Constrained Survivable Network Design Problem," INFORMS Journal on Computing, INFORMS, vol. 25(1), pages 13-26, February.
    15. Jose L. Andrade-Pineda & David Canca & Pedro L. Gonzalez-R, 2017. "On modelling non-linear quantity discounts in a supplier selection problem by mixed linear integer optimization," Annals of Operations Research, Springer, vol. 258(2), pages 301-346, November.
    16. Gelareh, Shahin & Pisinger, David, 2011. "Fleet deployment, network design and hub location of liner shipping companies," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 47(6), pages 947-964.
    17. Mancini, Simona & Ciavotta, Michele & Meloni, Carlo, 2021. "The Multiple Multidimensional Knapsack with Family-Split Penalties," European Journal of Operational Research, Elsevier, vol. 289(3), pages 987-998.

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