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The max-sum inverse median location problem on trees with budget constraint

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  • Nguyen-Thu, Huong
  • Nguyen, Kien Trung
  • Toan, Nguyen Thanh

Abstract

The theory of inverse location involves modifying parameters in such a way that the total cost is minimized and one/several prespecified facilities become optimal based on these perturbed parameters. When the modifying parameters are grouped into sets, with each group's cost measured under the rectilinear norm and the overall cost measured under the Chebyshev norm, the resulting problem is known as the max-sum inverse location problem. This paper addresses the max-sum inverse median location problem on trees with a budget constraint, where the objective is to modify the vertex weights so that a specified vertex becomes a 1-median, while minimizing the max-sum objective within the available budget. To solve this problem, a uni-variable optimization problem is first induced, where the objective function for each specified value of the variable can be obtained through a continuous knapsack problem. Leveraging the monotonicity of the cost function, a combinatorial algorithm is developed, which solves the problem in O(nlog⁡n) time, where n denotes the number of vertices present in the tree.

Suggested Citation

  • Nguyen-Thu, Huong & Nguyen, Kien Trung & Toan, Nguyen Thanh, 2024. "The max-sum inverse median location problem on trees with budget constraint," Applied Mathematics and Computation, Elsevier, vol. 460(C).
    • Handle: RePEc:eee:apmaco:v:460:y:2024:i:c:s0096300323004654
    DOI: 10.1016/j.amc.2023.128296
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    References listed on IDEAS

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    1. Nguyen, Kien Trung & Chassein, André, 2015. "The inverse convex ordered 1-median problem on trees under Chebyshev norm and Hamming distance," European Journal of Operational Research, Elsevier, vol. 247(3), pages 774-781.
    2. Kien Trung Nguyen, 2019. "The inverse 1-center problem on cycles with variable edge lengths," 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. 27(1), pages 263-274, March.
    3. Kien Trung Nguyen & Nguyen Thanh Hung, 2020. "The inverse connected p-median problem on block graphs under various cost functions," Annals of Operations Research, Springer, vol. 292(1), pages 97-112, September.
    4. Behrooz Alizadeh & Rainer Burkard, 2013. "A linear time algorithm for inverse obnoxious center location problems on networks," 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. 21(3), pages 585-594, September.
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