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Duality in the Cent-Dian of a Graph

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  • Jonathan Halpern

    (University of Calgary, Calgary, Canada, and Technion, Israel)

Abstract

Almost all facility location models seek to minimize either the average distance traveled by all customers to the facility (the median problem), or the distance of the furthest customer from the facility (the center problem). In practice the two objectives are usually antagonistic and yet in many cases both criteria are important (called the cent-dian problem). For such cases the paper presents two possible approaches to model formulation. First is to minimize a function which is a (convex) combination of the furthest (center) and the average (median) objective functions. Second is to minimize one of the criteria, subject to an upper bound on the value of the other criterion. For facility location on a network, it is shown that the first approach is a special case of the second. Furthermore, the two different constrained problems, which exist under the second approach, are dual problems in a well defined sense. Finally the paper provides several features of the tradeoff between the two criteria.

Suggested Citation

  • Jonathan Halpern, 1980. "Duality in the Cent-Dian of a Graph," Operations Research, INFORMS, vol. 28(3-part-ii), pages 722-735, June.
    • Handle: RePEc:inm:oropre:v:28:y:1980:i:3-part-ii:p:722-735
    DOI: 10.1287/opre.28.3.722
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    Cited by:

    1. Dieperink, H. & Nijkamp, P., 1987. "A multiple criteria location model for innovative firms in a communication network," Serie Research Memoranda 0072, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    2. Li, Hongmei & Luo, Taibo & Xu, Yinfeng & Xu, Jiuping, 2018. "Minimax regret vertex centdian location problem in general dynamic networks," Omega, Elsevier, vol. 75(C), pages 87-96.
    3. Soudabeh Seyyedi Ghomi & Fahimeh Baroughi, 2024. "Robust vertex centdian facility location problem on tree networks," Annals of Operations Research, Springer, vol. 341(2), pages 1135-1149, October.
    4. Colebrook, Marcos & Sicilia, Joaquin, 2007. "A polynomial algorithm for the multicriteria cent-dian location problem," European Journal of Operational Research, Elsevier, vol. 179(3), pages 1008-1024, June.
    5. Ohsawa, Yoshiaki, 1999. "A geometrical solution for quadratic bicriteria location models," European Journal of Operational Research, Elsevier, vol. 114(2), pages 380-388, April.

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