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On the use of the Varignon frame for single facility Weber problems in the presence of convex barriers

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  • Canbolat, Mustafa S.
  • Wesolowsky, George O.

Abstract

This paper presents a new experimental approach to the Weber problem in the presence of convex barriers by using the Varignon frame. The Varignon frame is a mechanical system of strings, weights and a board with holes that has been used to identify an optimal location for the classical Weber problem. We show through analytical results that the same analog can also be used for some of the Weber problems in the presence of barriers. Some examples from the literature are revisited through experiments. Findings are compared to those found in the literature. Practical use of the analog is discussed as it provides rapid solutions, allows for flexibility, and enables one to visualize the problem.

Suggested Citation

  • Canbolat, Mustafa S. & Wesolowsky, George O., 2012. "On the use of the Varignon frame for single facility Weber problems in the presence of convex barriers," European Journal of Operational Research, Elsevier, vol. 217(2), pages 241-247.
    • Handle: RePEc:eee:ejores:v:217:y:2012:i:2:p:241-247
    DOI: 10.1016/j.ejor.2011.09.006
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    References listed on IDEAS

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    1. Canbolat, Mustafa S. & Wesolowsky, George O., 2010. "The rectilinear distance Weber problem in the presence of a probabilistic line barrier," European Journal of Operational Research, Elsevier, vol. 202(1), pages 114-121, April.
    2. Klamroth, K., 2001. "A reduction result for location problems with polyhedral barriers," European Journal of Operational Research, Elsevier, vol. 130(3), pages 486-497, May.
    3. Bischoff, M. & Klamroth, K., 2007. "An efficient solution method for Weber problems with barriers based on genetic algorithms," European Journal of Operational Research, Elsevier, vol. 177(1), pages 22-41, February.
    4. Klamroth, K., 2004. "Algebraic properties of location problems with one circular barrier," European Journal of Operational Research, Elsevier, vol. 154(1), pages 20-35, April.
    5. Richard C. Larson & Ghazala Sadiq, 1983. "Facility Locations with the Manhattan Metric in the Presence of Barriers to Travel," Operations Research, INFORMS, vol. 31(4), pages 652-669, August.
    6. Butt, Steven E. & Cavalier, Tom M., 1996. "An efficient algorithm for facility location in the presence of forbidden regions," European Journal of Operational Research, Elsevier, vol. 90(1), pages 56-70, April.
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    Cited by:

    1. S. Nobakhtian & A. Raeisi Dehkordi, 2018. "An algorithm for generalized constrained multi-source Weber problem with demand substations," 4OR, Springer, vol. 16(4), pages 343-377, December.
    2. Murray, Alan T. & Church, Richard L. & Feng, Xin, 2020. "Single facility siting involving allocation decisions," European Journal of Operational Research, Elsevier, vol. 284(3), pages 834-846.
    3. Byrne, Thomas & Kalcsics, Jörg, 2022. "Conditional facility location problems with continuous demand and a polygonal barrier," European Journal of Operational Research, Elsevier, vol. 296(1), pages 22-43.

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