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The Shortest Covering Path Problem

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  • Timothy J. Niblett
  • Richard L. Church

Abstract

The shortest covering path (SCP) problem involves finding the shortest path between an origin node and a destination node, where the path traverses the network and passes within a maximal covering distance of all nodes of the network. This problem was originally proposed by Current, ReVelle, and Cohon. Since that time researchers have proposed both heuristic and optimal approaches for this problem as well as have developed more general forms, including the maximal covering shortest path problem. From the outset, it has been assumed that any optimal covering path would never loop or double back on itself. This assumption is examined in detail. We demonstrate that this assumption can lead to longer than necessary covering paths. We also present a new, more general construct, which can be used to generate optimal SCPs and demonstrate its use on an example problem.

Suggested Citation

  • Timothy J. Niblett & Richard L. Church, 2016. "The Shortest Covering Path Problem," International Regional Science Review, , vol. 39(1), pages 131-151, January.
    • Handle: RePEc:sae:inrsre:v:39:y:2016:i:1:p:131-151
    DOI: 10.1177/0160017614550082
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    References listed on IDEAS

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    1. Wright, Jeffrey & Revelle, Charles & Cohon, Jared, 1983. "A multiobjective integer programming model for the land acquisition problem," Regional Science and Urban Economics, Elsevier, vol. 13(1), pages 31-53, February.
    2. Current, J. R. & Re Velle, C. S. & Cohon, J. L., 1985. "The maximum covering/shortest path problem: A multiobjective network design and routing formulation," European Journal of Operational Research, Elsevier, vol. 21(2), pages 189-199, August.
    3. Brian Boffey & Subhash Narula, 1998. "Models for multi-path covering-routing problems," Annals of Operations Research, Springer, vol. 82(0), pages 331-342, August.
    4. Peter J. Slater, 1981. "On Locating a Facility to Service Areas within a Network," Operations Research, INFORMS, vol. 29(3), pages 523-531, June.
    5. Laporte, Gilbert & Mesa, Juan A. & Ortega, Francisco A., 2000. "Optimization methods for the planning of rapid transit systems," European Journal of Operational Research, Elsevier, vol. 122(1), pages 1-10, April.
    6. Kenneth R. Fox & Bezalel Gavish & Stephen C. Graves, 1980. "Technical Note—An n -Constraint Formulation of the (Time-Dependent) Traveling Salesman Problem," Operations Research, INFORMS, vol. 28(4), pages 1018-1021, August.
    7. Matisziw, Timothy C. & Murray, Alan T. & Kim, Changjoo, 2006. "Strategic route extension in transit networks," European Journal of Operational Research, Elsevier, vol. 171(2), pages 661-673, June.
    8. Current, John R. & Schilling, David A., 1994. "The median tour and maximal covering tour problems: Formulations and heuristics," European Journal of Operational Research, Elsevier, vol. 73(1), pages 114-126, February.
    9. G. Dantzig & R. Fulkerson & S. Johnson, 1954. "Solution of a Large-Scale Traveling-Salesman Problem," Operations Research, INFORMS, vol. 2(4), pages 393-410, November.
    10. 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.
    11. Hutson, Vicki Aaronson & ReVelle, Charles, 1993. "Indirect covering tree problems on spanning tree networks," European Journal of Operational Research, Elsevier, vol. 65(1), pages 20-32, February.
    12. John R. Current & David A. Schilling, 1989. "The Covering Salesman Problem," Transportation Science, INFORMS, vol. 23(3), pages 208-213, August.
    13. 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.
    14. Peter J. Slater, 1982. "Locating Central Paths in a Graph," Transportation Science, INFORMS, vol. 16(1), pages 1-18, February.
    15. Vicki Aaronson Hutson & Charles S. ReVelle, 1989. "Maximal Direct Covering Tree Problems," Transportation Science, INFORMS, vol. 23(4), pages 288-299, November.
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