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Covering Part of a Planar Network

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  • Zvi Drezner
  • George Wesolowsky

Abstract

The problem of locating facilities in a feasible area covering some parts of network links within a given radius is analyzed. The feasible area can be the interior (convex hull of the nodes) of a planar network or any union of convex polygons. Both minimization and maximization of coverage are considered. The single facility location problem is solved by the global optimization approach “Big Triangle Small Triangle.” The multiple facility maximization problem is solved by a specially designed heuristic algorithm. The idea of the heuristic algorithm may prove to work well on other planar multiple facility location problems. Computational experience with problems of up to 40,000 links demonstrate the effectiveness of the single facility and multiple facilities algorithms. The largest single facility minimal cover problem is solved in about one minute and the largest single facility maximal cover problem is solved in less than 4 minutes. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Zvi Drezner & George Wesolowsky, 2014. "Covering Part of a Planar Network," Networks and Spatial Economics, Springer, vol. 14(3), pages 629-646, December.
    • Handle: RePEc:kap:netspa:v:14:y:2014:i:3:p:629-646
    DOI: 10.1007/s11067-014-9263-5
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    References listed on IDEAS

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    1. Drezner, Tammy & Drezner, Zvi & Salhi, Said, 2002. "Solving the multiple competitive facilities location problem," European Journal of Operational Research, Elsevier, vol. 142(1), pages 138-151, October.
    2. Jack Elzinga & Donald W. Hearn, 1972. "Geometrical Solutions for Some Minimax Location Problems," Transportation Science, INFORMS, vol. 6(4), pages 379-394, November.
    3. Zvi Drezner & Atsuo Suzuki, 2004. "The Big Triangle Small Triangle Method for the Solution of Nonconvex Facility Location Problems," Operations Research, INFORMS, vol. 52(1), pages 128-135, February.
    4. Eiselt, H.A. & Marianov, Vladimir, 2009. "Gradual location set covering with service quality," Socio-Economic Planning Sciences, Elsevier, vol. 43(2), pages 121-130, June.
    5. Paul Berglund & Changhyun Kwon, 2014. "Robust Facility Location Problem for Hazardous Waste Transportation," Networks and Spatial Economics, Springer, vol. 14(1), pages 91-116, March.
    6. Richard E. Wendell & Arthur P. Hurter, 1973. "Location Theory, Dominance, and Convexity," Operations Research, INFORMS, vol. 21(1), pages 314-320, February.
    7. Nimrod Megiddo, 1981. "The Maximum Coverage Location Problem," Discussion Papers 490, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    8. Jiashan Wang & Yingying Kang & Changhyun Kwon & Rajan Batta, 2012. "Dual Toll Pricing for Hazardous Materials Transport with Linear Delay," Networks and Spatial Economics, Springer, vol. 12(1), pages 147-165, March.
    9. Watson-Gandy, C. D. T., 1982. "Heuristic procedures for the m-partial cover problem on a plane," European Journal of Operational Research, Elsevier, vol. 11(2), pages 149-157, October.
    10. Yafeng Yin, 2008. "A Scenario-based Model for Fleet Allocation of Freeway Service Patrols," Networks and Spatial Economics, Springer, vol. 8(4), pages 407-417, December.
    11. 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.
    12. Berman, Oded & Krass, Dmitry & Drezner, Zvi, 2003. "The gradual covering decay location problem on a network," European Journal of Operational Research, Elsevier, vol. 151(3), pages 474-480, December.
    13. Michael Bell, 2006. "Mixed Route Strategies for the Risk-Averse Shipment of Hazardous Materials," Networks and Spatial Economics, Springer, vol. 6(3), pages 253-265, September.
    14. Karkazis, J. & Boffey, T. B., 1995. "Optimal location of routes for vehicles transporting hazardous materials," European Journal of Operational Research, Elsevier, vol. 86(2), pages 201-215, October.
    15. Drezner, Zvi, 1986. "The p-cover problem," European Journal of Operational Research, Elsevier, vol. 26(2), pages 312-313, August.
    16. Lili Du & Srinivas Peeta, 2014. "A Stochastic Optimization Model to Reduce Expected Post-Disaster Response Time Through Pre-Disaster Investment Decisions," Networks and Spatial Economics, Springer, vol. 14(2), pages 271-295, June.
    17. Plastria, Frank, 1992. "GBSSS: The generalized big square small square method for planar single-facility location," European Journal of Operational Research, Elsevier, vol. 62(2), pages 163-174, October.
    18. Kevin Curtin & Karen Hayslett-McCall & Fang Qiu, 2010. "Determining Optimal Police Patrol Areas with Maximal Covering and Backup Covering Location Models," Networks and Spatial Economics, Springer, vol. 10(1), pages 125-145, March.
    19. Yafeng Yin, 2006. "Optimal Fleet Allocation of Freeway Service Patrols," Networks and Spatial Economics, Springer, vol. 6(3), pages 221-234, September.
    20. Suzuki, Atsuo & Drezner, Zvi, 2009. "The minimum equitable radius location problem with continuous demand," European Journal of Operational Research, Elsevier, vol. 195(1), pages 17-30, May.
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    1. Tammy Drezner & Zvi Drezner, 2019. "Cooperative Cover of Uniform Demand," Networks and Spatial Economics, Springer, vol. 19(3), pages 819-831, September.

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