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The Minmax Regret Reverse 1-Median Problem on Trees with Uncertain Vertex Weights

Author

Listed:
  • Tran Hoai Ngoc Nhan

    (Faculty of Basic Science, Vinh Long University of Technology Education, Vinh Long, Vietnam)

  • Kien Trung Nguyen

    (Department of Mathematics, Teacher College, Can Tho University, Can Tho, Vietnam)

  • Huong Nguyen-Thu

    (Department of Mathematics, Teacher College, Can Tho University, Can Tho, Vietnam)

Abstract

The classical reverse 1-median problem on trees is to adjust the edge lengths within a budget so as to reduce the 1-median function at a predetermined vertex as much as possible. This paper concerns the corresponding problem with uncertain vertex weights presented by linear functions. Moreover, we use the minmax regret criterion to measure the maximum loss of a feasible solution with respect to the worst-case scenario. The regarding problem is called the minmax regret reverse 1-median problem on trees. We first partition the set of scenarios into parts such that the optimal solution of the corresponding reverse 1-median problem does not change in each part. Then the problem can be reformulated as the minimization of a quadratic number of affine linear functions. We finally develop a greedy algorithm that solves the problem in O(n3) time where n is the number of vertices in the underlying tree.

Suggested Citation

  • Tran Hoai Ngoc Nhan & Kien Trung Nguyen & Huong Nguyen-Thu, 2023. "The Minmax Regret Reverse 1-Median Problem on Trees with Uncertain Vertex Weights," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 40(03), pages 1-17, June.
    • Handle: RePEc:wsi:apjorx:v:40:y:2023:i:03:n:s0217595922500336
    DOI: 10.1142/S0217595922500336
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