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The minimum equitable radius location problem with continuous demand

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  • Suzuki, Atsuo
  • Drezner, Zvi

Abstract

We analyze the location of p facilities satisfying continuous area demand. Three objectives are considered: (i) the p-center objective (to minimize the maximum distance between all points in the area and their closest facility), (ii) equalizing the load service by the facilities, and (iii) the minimum equitable radius - minimizing the maximum radius from each point to its closest facility subject to the constraint that each facility services the same load. The paper offers three contributions: (i) a new problem - the minimum equitable radius is presented and solved by an efficient algorithm, (ii) an improved and efficient algorithm is developed for the solution of the p-center problem, and (iii) an improved algorithm for the equitable load problem is developed. Extensive computational experiments demonstrated the superiority of the new solution algorithms.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:195:y:2009:i:1:p:17-30
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    References listed on IDEAS

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    1. A Okabe & A Suzuki, 1987. "Stability of Spatial Competition for a Large Number of Firms on a Bounded Two-Dimensional Space," Environment and Planning A, , vol. 19(8), pages 1067-1082, August.
    2. Baron, Opher & Berman, Oded & Krass, Dmitry & Wang, Qian, 2007. "The equitable location problem on the plane," European Journal of Operational Research, Elsevier, vol. 183(2), pages 578-590, December.
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    Cited by:

    1. Drezner, Tammy & Drezner, Zvi & Hulliger, Beat, 2014. "The Quintile Share Ratio in location analysis," European Journal of Operational Research, Elsevier, vol. 238(1), pages 166-174.
    2. Karsu, Özlem & Morton, Alec, 2015. "Inequity averse optimization in operational research," European Journal of Operational Research, Elsevier, vol. 245(2), pages 343-359.
    3. John Gunnar Carlsson & Raghuveer Devulapalli, 2013. "Dividing a Territory Among Several Facilities," INFORMS Journal on Computing, INFORMS, vol. 25(4), pages 730-742, November.
    4. Thomas Byrne & Sándor P. Fekete & Jörg Kalcsics & Linda Kleist, 2023. "Competitive location problems: balanced facility location and the One-Round Manhattan Voronoi Game," Annals of Operations Research, Springer, vol. 321(1), pages 79-101, February.
    5. Richard Francis & Timothy Lowe, 2014. "Comparative error bound theory for three location models: continuous demand versus discrete demand," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 144-169, April.
    6. Zvi Drezner & George Wesolowsky, 2014. "Covering Part of a Planar Network," Networks and Spatial Economics, Springer, vol. 14(3), pages 629-646, December.
    7. Tammy Drezner & Zvi Drezner & Atsuo Suzuki, 2019. "A cover based competitive facility location model with continuous demand," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(7), pages 565-581, October.
    8. Kalczynski, Pawel & Drezner, Zvi, 2022. "The Obnoxious Facilities Planar p-Median Problem with Variable Sizes," Omega, Elsevier, vol. 111(C).
    9. Rongbing Huang, 2016. "A short note on locating facilities on a path to minimize load range equity measure," Annals of Operations Research, Springer, vol. 246(1), pages 363-369, November.
    10. Z Drezner & A Suzuki, 2010. "Covering continuous demand in the plane," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(5), pages 878-881, May.

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