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The reverse selective balance center location problem on trees

Author

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
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