Opuscula Mathematica
Opuscula Math. 36, no. 4 (), 513-523
http://dx.doi.org/10.7494/OpMath.2016.36.4.513
Opuscula Mathematica

A model for the inverse 1-median problem on trees under uncertain costs



Abstract. We consider the problem of justifying vertex weights of a tree under uncertain costs so that a prespecified vertex become optimal and the total cost should be optimal in the uncertainty scenario. We propose a model which delivers the information about the optimal cost which respect to each confidence level \(\alpha \in [0,1]\). To obtain this goal, we first define an uncertain variable with respect to the minimum cost in each confidence level. If all costs are independently linear distributed, we present the inverse distribution function of this uncertain variable in \(O(n^{2}\log n)\) time, where \(n\) is the number of vertices in the tree.
Keywords: location problem, uncertain variable, inverse optimization problem, tree.
Mathematics Subject Classification: 90B10, 90B80, 90C27.
Cite this article as:
Kien Trung Nguyen, Nguyen Thi Linh Chi, A model for the inverse 1-median problem on trees under uncertain costs, Opuscula Math. 36, no. 4 (2016), 513-523, http://dx.doi.org/10.7494/OpMath.2016.36.4.513
 
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ISSN 1232−9274, e-ISSN 2300−6919, DOI https://doi.org/10.7494/OpMath
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