IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v167y2009i1p307-32510.1007-s10479-008-0339-9.html
   My bibliography  Save this article

Optimal location with equitable loads

Author

Listed:

Abstract

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

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-008-0339-9
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-008-0339-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Tony J. Van Roy, 1986. "A Cross Decomposition Algorithm for Capacitated Facility Location," Operations Research, INFORMS, vol. 34(1), pages 145-163, February.
    4. 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.
    5. 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.
    6. O. Berman & R. C. Larson & C. Parkan, 1987. "The Stochastic Queue p -Median Problem," Transportation Science, INFORMS, vol. 21(3), pages 207-216, August.
    7. 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.
    8. 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.
    9. 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.
    10. 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).
    11. R. S. Garfinkel & G. L. Nemhauser, 1970. "Optimal Political Districting by Implicit Enumeration Techniques," Management Science, INFORMS, vol. 16(8), pages 495-508, April.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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).
    2. 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.
    3. Jafar Fathali & Mehdi Zaferanieh, 2023. "The balanced 2-median and 2-maxian problems on a tree," Journal of Combinatorial Optimization, Springer, vol. 45(2), pages 1-16, March.
    4. 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.
    5. 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.
    6. Karsu, Özlem & Morton, Alec, 2015. "Inequity averse optimization in operational research," European Journal of Operational Research, Elsevier, vol. 245(2), pages 343-359.
    7. 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.
    8. 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.
    9. 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.
    10. Maria Barbati & Giuseppe Bruno & Alfredo Marín, 2016. "Balancing the arrival times of users in a two-stage location problem," Annals of Operations Research, Springer, vol. 246(1), pages 273-288, November.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. Kalczynski, Pawel & Drezner, Zvi, 2022. "The Obnoxious Facilities Planar p-Median Problem with Variable Sizes," Omega, Elsevier, vol. 111(C).
    18. 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.
    19. John Gunnar Carlsson, 2012. "Dividing a Territory Among Several Vehicles," INFORMS Journal on Computing, INFORMS, vol. 24(4), pages 565-577, November.
    20. 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.
    21. 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.
    22. 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.
    23. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. B. Jayalakshmi & Alok Singh, 2017. "A hybrid artificial bee colony algorithm for the p-median problem with positive/negative weights," OPSEARCH, Springer;Operational Research Society of India, vol. 54(1), pages 67-93, March.
    3. Antiopi Panteli & Basilis Boutsinas & Ioannis Giannikos, 2021. "On solving the multiple p-median problem based on biclustering," Operational Research, Springer, vol. 21(1), pages 775-799, March.
    4. Joshua Q. Hale & Enlu Zhou & Jiming Peng, 2017. "A Lagrangian search method for the P-median problem," Journal of Global Optimization, Springer, vol. 69(1), pages 137-156, September.
    5. F Caro & T Shirabe & M Guignard & A Weintraub, 2004. "School redistricting: embedding GIS tools with integer programming," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(8), pages 836-849, August.
    6. Balázs Fleiner & Balázs Nagy & Attila Tasnádi, 2017. "Optimal partisan districting on planar geographies," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 25(4), pages 879-888, December.
    7. Juan Carlos Duque & Raúl Ramos & Jordi Suriñach, 2007. "Supervised Regionalization Methods: A Survey," International Regional Science Review, , vol. 30(3), pages 195-220, July.
    8. Federica Ricca & Andrea Scozzari & Bruno Simeone, 2013. "Political Districting: from classical models to recent approaches," Annals of Operations Research, Springer, vol. 204(1), pages 271-299, April.
    9. Djordje Dugošija & Aleksandar Savić & Zoran Maksimović, 2020. "A new integer linear programming formulation for the problem of political districting," Annals of Operations Research, Springer, vol. 288(1), pages 247-263, May.
    10. Christian Haas & Lee Hachadoorian & Steven O Kimbrough & Peter Miller & Frederic Murphy, 2020. "Seed-Fill-Shift-Repair: A redistricting heuristic for civic deliberation," PLOS ONE, Public Library of Science, vol. 15(9), pages 1-34, September.
    11. Robert Aboolian & Oded Berman & Zvi Drezner, 2009. "The multiple server center location problem," Annals of Operations Research, Springer, vol. 167(1), pages 337-352, March.
    12. Michael Brusco & Hans-Friedrich Köhn, 2009. "Exemplar-Based Clustering via Simulated Annealing," Psychometrika, Springer;The Psychometric Society, vol. 74(3), pages 457-475, September.
    13. Anderson Kenji Hirose & Cassius Tadeu Scarpin & José Eduardo Pécora Junior, 2020. "Goal programming approach for political districting in Santa Catarina State: Brazil," Annals of Operations Research, Springer, vol. 287(1), pages 209-232, April.
    14. Hyun Kim & Yongwan Chun & Kamyoung Kim, 2015. "Delimitation of Functional Regions Using a p-Regions Problem Approach," International Regional Science Review, , vol. 38(3), pages 235-263, July.
    15. Han, Jialin & Hu, Yaoguang & Mao, Mingsong & Wan, Shuping, 2020. "A multi-objective districting problem applied to agricultural machinery maintenance service network," European Journal of Operational Research, Elsevier, vol. 287(3), pages 1120-1130.
    16. Sebastián Moreno & Jordi Pereira & Wilfredo Yushimito, 2020. "A hybrid K-means and integer programming method for commercial territory design: a case study in meat distribution," Annals of Operations Research, Springer, vol. 286(1), pages 87-117, March.
    17. Eduardo Álvarez-Miranda & Camilo Campos-Valdés & Maurcio Morales Quiroga & Matías Moreno-Faguett & Jordi Pereira, 2020. "A Multi-Criteria Pen for Drawing Fair Districts: When Democratic and Demographic Fairness Matter," Mathematics, MDPI, vol. 8(9), pages 1-26, August.
    18. Sommer Gentry & Eric Chow & Allan Massie & Dorry Segev, 2015. "Gerrymandering for Justice: Redistricting U.S. Liver Allocation," Interfaces, INFORMS, vol. 45(5), pages 462-480, October.
    19. Tammy Drezner & Zvi Drezner, 2011. "A note on equity across groups in facility location," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(7), pages 705-711, October.
    20. Sourirajan, Karthik & Ozsen, Leyla & Uzsoy, Reha, 2009. "A genetic algorithm for a single product network design model with lead time and safety stock considerations," European Journal of Operational Research, Elsevier, vol. 197(2), pages 599-608, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:annopr:v:167:y:2009:i:1:p:307-325:10.1007/s10479-008-0339-9. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.