A model for the inverse 1-median problem on trees under uncertain costs
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 confidenc...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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AGH Univeristy of Science and Technology Press
2016-01-01
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| Series: | Opuscula Mathematica |
| Subjects: | |
| Online Access: | http://www.opuscula.agh.edu.pl/vol36/4/art/opuscula_math_3630.pdf |
| _version_ | 1818159737400721408 |
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| author | Kien Trung Nguyen Nguyen Thi Linh Chi |
| author_facet | Kien Trung Nguyen Nguyen Thi Linh Chi |
| author_sort | Kien Trung Nguyen |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-11T15:50:44Z |
| format | Article |
| id | doaj.art-1174b1f2d69d4639a7dcac10cd1f9f4f |
| institution | Directory Open Access Journal |
| issn | 1232-9274 |
| language | English |
| last_indexed | 2024-12-11T15:50:44Z |
| publishDate | 2016-01-01 |
| publisher | AGH Univeristy of Science and Technology Press |
| record_format | Article |
| series | Opuscula Mathematica |
| spelling | doaj.art-1174b1f2d69d4639a7dcac10cd1f9f4f2022-12-22T00:59:34ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742016-01-01364513523http://dx.doi.org/10.7494/OpMath.2016.36.4.5133630A model for the inverse 1-median problem on trees under uncertain costsKien Trung Nguyen0Nguyen Thi Linh Chi1Cantho University, Mathematics Department, Teacher College, Cantho, VietnamCantho University, Mathematics Department, Science College, Cantho, VietnamWe 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.http://www.opuscula.agh.edu.pl/vol36/4/art/opuscula_math_3630.pdflocation problemuncertain variableinverse optimization problemtree |
| spellingShingle | Kien Trung Nguyen Nguyen Thi Linh Chi A model for the inverse 1-median problem on trees under uncertain costs Opuscula Mathematica location problem uncertain variable inverse optimization problem tree |
| title | A model for the inverse 1-median problem on trees under uncertain costs |
| title_full | A model for the inverse 1-median problem on trees under uncertain costs |
| title_fullStr | A model for the inverse 1-median problem on trees under uncertain costs |
| title_full_unstemmed | A model for the inverse 1-median problem on trees under uncertain costs |
| title_short | A model for the inverse 1-median problem on trees under uncertain costs |
| title_sort | model for the inverse 1 median problem on trees under uncertain costs |
| topic | location problem uncertain variable inverse optimization problem tree |
| url | http://www.opuscula.agh.edu.pl/vol36/4/art/opuscula_math_3630.pdf |
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