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Efficient Algorithms for Solving the Shortest Covering Path Problem

Author

Listed:
  • John Current

    (Fisher College of Business Administration, The Ohio State University, Columbus, Ohio 43210)

  • Hasan Pirkul

    (Fisher College of Business Administration, The Ohio State University, Columbus, Ohio 43210)

  • Erik Rolland

    (Graduate School of Management, University of California, Riverside, Riverside, California 92521)

Abstract

The Shortest Covering Path Problem (SCPP) is one of identifying the least cost path from a pre-specified starting node to a pre-specified terminus node. The path is constrained by the condition that it must cover every node in the network. A node is considered to be covered if it is within some pre-specified covering distance of a node on the path. This SCPP has many potential applications, especially in hierarchical network design, and bi-modal routing problems. In this paper we introduce two efficient algorithms for solving the SCPP. The first is a heuristic based upon a Lagrangian relaxation of the problem. The second is an exact algorithm based upon a branch and bound procedure which utilizes the bounds generated by the Lagrangian relaxation scheme. Computational tests indicate that both procedures are very efficient. The heuristic identified and verified the optimal solution for 135 of the 160 test problems solved. The optimal solution to the remaining 25 problems was readily identified by the exact algorithm.

Suggested Citation

  • John Current & Hasan Pirkul & Erik Rolland, 1994. "Efficient Algorithms for Solving the Shortest Covering Path Problem," Transportation Science, INFORMS, vol. 28(4), pages 317-327, November.
    • Handle: RePEc:inm:ortrsc:v:28:y:1994:i:4:p:317-327
    DOI: 10.1287/trsc.28.4.317
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    Citations

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    Cited by:

    1. Timothy J. Niblett & Richard L. Church, 2016. "The Shortest Covering Path Problem," International Regional Science Review, , vol. 39(1), pages 131-151, January.
    2. J. Beasley & E. Nascimento, 1996. "The Vehicle Routing-Allocation Problem: A unifying framework," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 4(1), pages 65-86, June.
    3. Eusebio Angulo & Ricardo García-Ródenas & José Luis Espinosa-Aranda, 2016. "A Lagrangian relaxation approach for expansion of a highway network," Annals of Operations Research, Springer, vol. 246(1), pages 101-126, November.
    4. Russell Halper & S. Raghavan, 2011. "The Mobile Facility Routing Problem," Transportation Science, INFORMS, vol. 45(3), pages 413-434, August.
    5. Su, Jason G. & Winters, Meghan & Nunes, Melissa & Brauer, Michael, 2010. "Designing a route planner to facilitate and promote cycling in Metro Vancouver, Canada," Transportation Research Part A: Policy and Practice, Elsevier, vol. 44(7), pages 495-505, August.
    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. Dominique Feillet & Pierre Dejax & Michel Gendreau, 2005. "Traveling Salesman Problems with Profits," Transportation Science, INFORMS, vol. 39(2), pages 188-205, May.
    8. Emilio Carrizosa & Jonas Harbering & Anita Schöbel, 2016. "Minimizing the passengers’ traveling time in the stop location problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(10), pages 1325-1337, October.
    9. Mesa, Juan A. & Brian Boffey, T., 1996. "A review of extensive facility location in networks," European Journal of Operational Research, Elsevier, vol. 95(3), pages 592-603, December.
    10. Santos, Luis & Coutinho-Rodrigues, João & Current, John R., 2007. "An improved solution algorithm for the constrained shortest path problem," Transportation Research Part B: Methodological, Elsevier, vol. 41(7), pages 756-771, August.
    11. Lei, Chao & Lin, Wei-Hua & Miao, Lixin, 2014. "A multicut L-shaped based algorithm to solve a stochastic programming model for the mobile facility routing and scheduling problem," European Journal of Operational Research, Elsevier, vol. 238(3), pages 699-710.
    12. L Vogt & C A Poojari & J E Beasley, 2007. "A tabu search algorithm for the single vehicle routing allocation problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(4), pages 467-480, April.

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