IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v87y2018i3d10.1007_s00186-017-0624-y.html
   My bibliography  Save this article

Reverse selective obnoxious center location problems on tree graphs

Author

Listed:
  • Roghayeh Etemad

    (Sahand University of Technology)

  • Behrooz Alizadeh

    (Sahand University of Technology)

Abstract

In this paper, we investigate a variant of the reverse obnoxious center location problem on a tree graph $$T=(V,E)$$ T = ( V , E ) in which a selective subset of the vertex set V is considered as locations of the existing customers. The aim is to augment or reduce the edge lengths within a given budget with respect to modification bounds until a predetermined undesirable facility location becomes as far as possible from the customer points under the new edge lengths. An $${\mathcal {O}}(|E|^2)$$ O ( | E | 2 ) time combinatorial algorithm is developed for the problem with arbitrary modification costs. For the uniform-cost case, one obtains the improved $${\mathcal {O}}(|E|)$$ O ( | E | ) time complexity. Moreover, optimal solution algorithms with $${\mathcal {O}}(|E|^2)$$ O ( | E | 2 ) and $${\mathcal {O}}(|E|)$$ O ( | E | ) time complexities are proposed for the integer version of the problem with arbitrary and uniform cost coefficients, respectively.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:87:y:2018:i:3:d:10.1007_s00186-017-0624-y
    DOI: 10.1007/s00186-017-0624-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00186-017-0624-y
    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/s00186-017-0624-y?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. Jens Vygen, 2002. "On dual minimum cost flow algorithms," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 56(1), pages 101-126, August.
    2. Kien Trung Nguyen & Ali Reza Sepasian, 2016. "The inverse 1-center problem on trees with variable edge lengths under Chebyshev norm and Hamming distance," Journal of Combinatorial Optimization, Springer, vol. 32(3), pages 872-884, October.
    3. Zhang, Jianzhong & Liu, Zhenhong & Ma, Zhongfan, 2000. "Some reverse location problems," European Journal of Operational Research, Elsevier, vol. 124(1), pages 77-88, July.
    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. Esmaeil Afrashteh & Behrooz Alizadeh & Fahimeh Baroughi, 2020. "Optimal approaches for upgrading selective obnoxious p-median location problems on tree networks," Annals of Operations Research, Springer, vol. 289(2), pages 153-172, June.

    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. 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. 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.
    3. 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.
    4. Burkard, Rainer E. & Galavii, Mohammadreza & Gassner, Elisabeth, 2010. "The inverse Fermat-Weber problem," European Journal of Operational Research, Elsevier, vol. 206(1), pages 11-17, October.
    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. Clemens Heuberger, 2004. "Inverse Combinatorial Optimization: A Survey on Problems, Methods, and Results," Journal of Combinatorial Optimization, Springer, vol. 8(3), pages 329-361, September.
    7. Jianzhong Zhang & Zhenhong Liu, 2002. "A General Model of Some Inverse Combinatorial Optimization Problems and Its Solution Method Under l ∞ Norm," Journal of Combinatorial Optimization, Springer, vol. 6(2), pages 207-227, June.
    8. Yi Zhang & Liwei Zhang & Yue Wu, 2014. "The augmented Lagrangian method for a type of inverse quadratic programming problems over second-order cones," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 45-79, April.
    9. Alizadeh, Behrooz & Afrashteh, Esmaeil, 2020. "Budget-constrained inverse median facility location problem on tree networks," Applied Mathematics and Computation, Elsevier, vol. 375(C).
    10. Franco Rubio-López & Obidio Rubio & Rolando Urtecho Vidaurre, 2023. "The Inverse Weber Problem on the Plane and the Sphere," Mathematics, MDPI, vol. 11(24), pages 1-23, December.
    11. Xianyue Li & Xichao Shu & Huijing Huang & Jingjing Bai, 2019. "Capacitated partial inverse maximum spanning tree under the weighted Hamming distance," Journal of Combinatorial Optimization, Springer, vol. 38(4), pages 1005-1018, November.
    12. Elisabeth Gassner, 2008. "The inverse 1-maxian problem with edge length modification," Journal of Combinatorial Optimization, Springer, vol. 16(1), pages 50-67, July.
    13. Dorit S. Hochbaum, 2008. "The Pseudoflow Algorithm: A New Algorithm for the Maximum-Flow Problem," Operations Research, INFORMS, vol. 56(4), pages 992-1009, August.
    14. 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.
    15. Burkard, Rainer E. & Lin, Yixun & Zhang, Jianzhong, 2004. "Weight reduction problems with certain bottleneck objectives," European Journal of Operational Research, Elsevier, vol. 153(1), pages 191-199, February.
    16. Ioannis Panageas & Thorben Trobst & Vijay V. Vazirani, 2021. "Combinatorial Algorithms for Matching Markets via Nash Bargaining: One-Sided, Two-Sided and Non-Bipartite," Papers 2106.02024, arXiv.org, revised Aug 2022.
    17. Baldomero-Naranjo, Marta & Kalcsics, Jörg & Marín, Alfredo & Rodríguez-Chía, Antonio M., 2022. "Upgrading edges in the maximal covering location problem," European Journal of Operational Research, Elsevier, vol. 303(1), pages 14-36.
    18. Lindong Liu & Xiangtong Qi & Zhou Xu, 2024. "Stabilizing Grand Cooperation via Cost Adjustment: An Inverse Optimization Approach," INFORMS Journal on Computing, INFORMS, vol. 36(2), pages 635-656, March.
    19. Konstantinos Paparrizos & Nikolaos Samaras & Angelo Sifaleras, 2015. "Exterior point simplex-type algorithms for linear and network optimization problems," Annals of Operations Research, Springer, vol. 229(1), pages 607-633, June.
    20. Jianzhong Zhang & Liwei Zhang & Xiantao Xiao, 2010. "A Perturbation approach for an inverse quadratic programming problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 72(3), pages 379-404, December.

    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:mathme:v:87:y:2018:i:3:d:10.1007_s00186-017-0624-y. 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.