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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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    1. Opher Baron & Oded Berman & Dmitry Krass, 2008. "Facility Location with Stochastic Demand and Constraints on Waiting Time," Manufacturing & Service Operations Management, INFORMS, vol. 10(3), pages 484-505, August.
    2. O. Berman & R. C. Larson & C. Parkan, 1987. "The Stochastic Queue p -Median Problem," Transportation Science, INFORMS, vol. 21(3), pages 207-216, August.
    3. Mladenovic, Nenad & Brimberg, Jack & Hansen, Pierre & Moreno-Perez, Jose A., 2007. "The p-median problem: A survey of metaheuristic approaches," European Journal of Operational Research, Elsevier, vol. 179(3), pages 927-939, June.
    4. O Berman & Z Drezner, 2007. "The multiple server location problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(1), pages 91-99, January.
    5. Tony J. Van Roy, 1986. "A Cross Decomposition Algorithm for Capacitated Facility Location," Operations Research, INFORMS, vol. 34(1), pages 145-163, February.
    6. Oded Berman & Richard C. Larson, 1985. "Optimal 2-Facility Network Districting in the Presence of Queuing," Transportation Science, INFORMS, vol. 19(3), pages 261-277, August.
    7. Fernando Chiyoshi & Roberto Galvão, 2000. "A statistical analysis of simulated annealing applied to the p-median problem," Annals of Operations Research, Springer, vol. 96(1), pages 61-74, November.
    8. Anuj Mehrotra & Ellis L. Johnson & George L. Nemhauser, 1998. "An Optimization Based Heuristic for Political Districting," Management Science, INFORMS, vol. 44(8), pages 1100-1114, August.
    9. Osman Alp & Erhan Erkut & Zvi Drezner, 2003. "An Efficient Genetic Algorithm for the p-Median Problem," Annals of Operations Research, Springer, vol. 122(1), pages 21-42, September.
    10. Rolland, Erik & Schilling, David A. & Current, John R., 1997. "An efficient tabu search procedure for the p-Median Problem," European Journal of Operational Research, Elsevier, vol. 96(2), pages 329-342, January.
    11. S. W. Hess & J. B. Weaver & H. J. Siegfeldt & J. N. Whelan & P. A. Zitlau, 1965. "Nonpartisan Political Redistricting by Computer," Operations Research, INFORMS, vol. 13(6), pages 998-1006, December.
    12. Michael B. Teitz & Polly Bart, 1968. "Heuristic Methods for Estimating the Generalized Vertex Median of a Weighted Graph," Operations Research, INFORMS, vol. 16(5), pages 955-961, October.
    13. 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.
    14. GARFINKEL, Robert S. & NEMHAUSER, Geroge L., 1970. "Optimal political districting by implicit enumeration techniques," LIDAM Reprints CORE 54, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    15. R. S. Garfinkel & G. L. Nemhauser, 1970. "Optimal Political Districting by Implicit Enumeration Techniques," Management Science, INFORMS, vol. 16(8), pages 495-508, April.
    16. Qian Wang & Rajan Batta & Christopher Rump, 2002. "Algorithms for a Facility Location Problem with Stochastic Customer Demand and Immobile Servers," Annals of Operations Research, Springer, vol. 111(1), pages 17-34, March.
    17. Tammy Drezner & Zvi Drezner, 2001. "A Note on Applying the Gravity Rule to the Airline Hub Problem," Journal of Regional Science, Wiley Blackwell, vol. 41(1), pages 67-72, February.
    18. A. J. Goldman, 1971. "Optimal Center Location in Simple Networks," Transportation Science, INFORMS, vol. 5(2), pages 212-221, May.
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    Cited by:

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    3. John 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.
    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.
    9. Bruno, Giuseppe & Cavola, Manuel & Diglio, Antonio & Elizalde, Javier & Piccolo, Carmela, 2022. "A locational analysis of deregulation policies in the Spanish retail pharmaceutical sector," Socio-Economic Planning Sciences, Elsevier, vol. 82(PA).
    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. Levent Eriskin & Mumtaz Karatas, 2024. "Applying robust optimization to the shelter location–allocation problem: a case study for Istanbul," Annals of Operations Research, Springer, vol. 339(3), pages 1589-1635, August.
    20. 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.
    21. 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.
    22. John Gunnar Carlsson, 2012. "Dividing a Territory Among Several Vehicles," INFORMS Journal on Computing, INFORMS, vol. 24(4), pages 565-577, November.
    23. 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.
    24. 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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