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Reverse selective obnoxious center location problems on tree graphs

Author

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  • 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
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    References listed on IDEAS

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    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. Zhang, Jianzhong & Liu, Zhenhong & Ma, Zhongfan, 2000. "Some reverse location problems," European Journal of Operational Research, Elsevier, vol. 124(1), pages 77-88, July.
    3. 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.
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    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.

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