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Optimal location with equitable loads

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The problem considered in this paper is to find p locations for p facilities such that the weights attracted to each facility will be as close as possible to one another. We model this problem as minimizing the maximum among all the total weights attracted to the various facilities. We propose solution procedures for the problem on a network, and for the special cases of the problem on a tree or on a path. The complexity of the problem is analyzed, O(n) algorithms and an O(pn 3 ) dynamic programming algorithm are proposed for the problem on a path respectively for p=2 and p>2 facilities. Heuristic algorithms (two types of a steepest descent approach and tabu search) are proposed for its solution. Extensive computational results are presented. Copyright Springer Science+Business Media, LLC 2009

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  • Oded Berman & Zvi Drezner & Arie Tamir & George Wesolowsky, 2009. "Optimal location with equitable loads," Annals of Operations Research, Springer, vol. 167(1), pages 307-325, March.
    • Handle: RePEc:spr:annopr:v:167:y:2009:i:1:p:307-325:10.1007/s10479-008-0339-9
    DOI: 10.1007/s10479-008-0339-9
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    4. Karsu, Özlem & Morton, Alec, 2015. "Inequity averse optimization in operational research," European Journal of Operational Research, Elsevier, vol. 245(2), pages 343-359.
    5. Marín, Alfredo, 2011. "The discrete facility location problem with balanced allocation of customers," European Journal of Operational Research, Elsevier, vol. 210(1), pages 27-38, April.
    6. Kalczynski, Pawel & Drezner, Zvi, 2022. "The Obnoxious Facilities Planar p-Median Problem with Variable Sizes," Omega, Elsevier, vol. 111(C).
    7. 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.
    8. Jesús Sánchez-Oro & Ana D. López-Sánchez & Anna Martínez-Gavara & Alfredo G. Hernández-Díaz & Abraham Duarte, 2021. "A Hybrid Strategic Oscillation with Path Relinking Algorithm for the Multiobjective k -Balanced Center Location Problem," Mathematics, MDPI, vol. 9(8), pages 1-21, April.
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    10. Ramamoorthy, Prasanna & Jayaswal, Sachin & Sinha, Ankur & Vidyarthi, Navneet, 2018. "Multiple allocation hub interdiction and protection problems: Model formulations and solution approaches," European Journal of Operational Research, Elsevier, vol. 270(1), pages 230-245.
    11. Faiz, Tasnim Ibn & Noor-E-Alam, Md, 2019. "Data center supply chain configuration design: A two-stage decision approach," Socio-Economic Planning Sciences, Elsevier, vol. 66(C), pages 119-135.
    12. Xu, Jing & Murray, Alan T. & Church, Richard L. & Wei, Ran, 2023. "Service allocation equity in location coverage analytics," European Journal of Operational Research, Elsevier, vol. 305(1), pages 21-37.
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    14. Liu, Yanchao, 2023. "An elliptical cover problem in drone delivery network design and its solution algorithms," European Journal of Operational Research, Elsevier, vol. 304(3), pages 912-925.
    15. Espejo, Inmaculada & Marín, Alfredo & Rodríguez-Chía, Antonio M., 2012. "Closest assignment constraints in discrete location problems," European Journal of Operational Research, Elsevier, vol. 219(1), pages 49-58.
    16. Xin Tang & Ameur Soukhal & Vincent T’kindt, 2014. "Preprocessing for a map sectorization problem by means of mathematical programming," Annals of Operations Research, Springer, vol. 222(1), pages 551-569, November.
    17. Ramamoorthy, Prasanna & Jayaswal, Sachin & Sinha, Ankur & Vidyarthi, Navneet, 2016. "Hub Interdiction & Hub Protection problems: Model formulations & Exact Solution methods. (Revised)," IIMA Working Papers WP2016-10-01, Indian Institute of Management Ahmedabad, Research and Publication Department.
    18. Shahede Omidi & Jafar Fathali & Morteza Nazari, 2020. "Inverse and reverse balanced facility location problems with variable edge lengths on trees," OPSEARCH, Springer;Operational Research Society of India, vol. 57(2), pages 261-273, June.
    19. Bronfman, Andrés & Marianov, Vladimir & Paredes-Belmar, Germán & Lüer-Villagra, Armin, 2015. "The maximin HAZMAT routing problem," European Journal of Operational Research, Elsevier, vol. 241(1), pages 15-27.
    20. Lin, Yun Hui & Tian, Qingyun, 2023. "Facility location and pricing problem: Discretized mill price and exact algorithms," European Journal of Operational Research, Elsevier, vol. 308(2), pages 568-580.
    21. John Gunnar Carlsson, 2012. "Dividing a Territory Among Several Vehicles," INFORMS Journal on Computing, INFORMS, vol. 24(4), pages 565-577, November.
    22. Sardar Ansari & Laura Albert McLay & Maria E. Mayorga, 2017. "A Maximum Expected Covering Problem for District Design," Transportation Science, INFORMS, vol. 51(1), pages 376-390, February.
    23. John Gunnar Carlsson & Mehdi Behroozi & Xiang Li, 2016. "Geometric partitioning and robust ad-hoc network design," Annals of Operations Research, Springer, vol. 238(1), pages 41-68, March.

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