IDEAS home Printed from https://ideas.repec.org/a/spr/opsear/v61y2024i1d10.1007_s12597-023-00706-4.html
   My bibliography  Save this article

The reverse selective balance center location problem on trees

Author

Listed:
  • Nguyen Thanh Toan

    (University of Science
    Vietnam National University
    Vinh Long University of Technology Education)

  • Huy Minh Le

    (Van Lang University)

  • Kien Trung Nguyen

    (Can Tho University)

Abstract

The classically balanced facility location problems aim to find the location of one or several new facilities such that some balanced function is optimized. This paper concerns the problem of improving the balanced objective at a prespecified vertex of a tree as much as possible within a given budget. We call such a problem the reverse selective balance center location problem on trees. All vertices are partitioned into two disjoint sets, in which one set consists of selective vertices. The balanced function is considered to be the difference in distance between the furthest demand point in the selective set and the nearest one in the remaining set. We first formulate the problem as linear programming. Then we propose a strategy to reduce the objective value in the case of variable edge lengths. An algorithm is developed to solve the reverse selective balance center location problem on trees in quadratic time.

Suggested Citation

  • Nguyen Thanh Toan & Huy Minh Le & Kien Trung Nguyen, 2024. "The reverse selective balance center location problem on trees," OPSEARCH, Springer;Operational Research Society of India, vol. 61(1), pages 483-497, March.
    • Handle: RePEc:spr:opsear:v:61:y:2024:i:1:d:10.1007_s12597-023-00706-4
    DOI: 10.1007/s12597-023-00706-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s12597-023-00706-4
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s12597-023-00706-4?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. 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.
    2. 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.
    3. Roghayeh Etemad & Behrooz Alizadeh, 2018. "Reverse selective obnoxious center location problems on tree graphs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 87(3), pages 431-450, June.
    4. Ali Reza Sepasian & Javad Tayyebi, 2020. "Further Study on Reverse 1-Center Problem on Trees," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 37(06), pages 1-18, December.
    5. Ali Reza Sepasian, 2019. "Reverse 1-maxian problem with keeping existing 1-median," OPSEARCH, Springer;Operational Research Society of India, vol. 56(1), pages 1-13, March.
    6. 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.
    7. Fahimeh Baroughi Bonab & Rainer Burkard & Behrooz Alizadeh, 2010. "Inverse median location problems with variable coordinates," 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. 18(3), pages 365-381, September.
    8. Behrooz Alizadeh & Somayeh Bakhteh, 2017. "A modified firefly algorithm for general inverse p-median location problems under different distance norms," OPSEARCH, Springer;Operational Research Society of India, vol. 54(3), pages 618-636, September.
    Full references (including those not matched with items on IDEAS)

    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. Esmaeil Afrashteh & Behrooz Alizadeh & Fahimeh Baroughi & Kien Trung Nguyen, 2018. "Linear Time Optimal Approaches for Max-Profit Inverse 1-Median Location Problems," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(05), pages 1-22, October.
    2. Kien Trung Nguyen & Huong Nguyen-Thu & Nguyen Thanh Hung, 2018. "On the complexity of inverse convex ordered 1-median problem on the plane and on tree networks," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 88(2), pages 147-159, October.
    3. Alizadeh, Behrooz & Afrashteh, Esmaeil, 2020. "Budget-constrained inverse median facility location problem on tree networks," Applied Mathematics and Computation, Elsevier, vol. 375(C).
    4. Behrooz Alizadeh & Esmaeil Afrashteh & Fahimeh Baroughi, 2018. "Combinatorial Algorithms for Some Variants of Inverse Obnoxious Median Location Problem on Tree Networks," Journal of Optimization Theory and Applications, Springer, vol. 178(3), pages 914-934, September.
    5. Behrooz Alizadeh & Somayeh Bakhteh, 2017. "A modified firefly algorithm for general inverse p-median location problems under different distance norms," OPSEARCH, Springer;Operational Research Society of India, vol. 54(3), pages 618-636, September.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Zhao, Jinqiu & Yu, Le & Xie, Binglei, 2024. "An ellipse-based locating method for flexible deployment of emergency UAVs," Socio-Economic Planning Sciences, Elsevier, vol. 96(C).
    11. Christian Schmitt & Bismark Singh, 2024. "Quadratic Optimization Models for Balancing Preferential Access and Fairness: Formulations and Optimality Conditions," INFORMS Journal on Computing, INFORMS, vol. 36(5), pages 1150-1167, September.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. 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).
    19. 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.
    20. Kayhan Alamatsaz & S. M. T. Fatemi Ghomi & Mehdi Iranpoor, 2021. "Minimal covering unrestricted location of obnoxious facilities: bi-objective formulation and a case study," OPSEARCH, Springer;Operational Research Society of India, vol. 58(2), pages 351-373, June.

    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:opsear:v:61:y:2024:i:1:d:10.1007_s12597-023-00706-4. 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.