Risk-Control Approach for a Bottleneck Spanning Tree Problem with the Total Network Reliability under Uncertainty
This paper considers a new risk-control and management approach for a bottleneck spanning tree problem under the situation where edge costs in a given network include randomness and reliability. Particularly, this paper focuses on the case that only mean value and variance of edge costs are calculat...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/364086 |
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| _version_ | 1832558577752997888 |
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| author | Takashi Hasuike Hideki Katagiri Hiroshi Tsuda |
| author_facet | Takashi Hasuike Hideki Katagiri Hiroshi Tsuda |
| author_sort | Takashi Hasuike |
| collection | DOAJ |
| description | This paper considers a new risk-control and management approach for a bottleneck spanning tree problem under the situation where edge costs in a given network include randomness and reliability. Particularly, this paper focuses on the case that only mean value and variance of edge costs are calculated without assuming a specific random distribution. In order to develop the risk control approach, a confidence interval-based formulation is introduced. Using this interval, as well as minimizing the maximum value of worse edge costs, maximizing the minimum value of robust
parameters to edge costs is introduced as objective functions in the risk-control. Furthermore, in order to maintain the constructing spanning tree network entirely, the reliability for each edge is introduced, and maximizing the total reliability of spanning tree is assumed as the third objective function. The proposed model is a multiobjective programming problem, and hence, it is difficult to solve it directly without setting some optimal criterion. Therefore, satisfaction functions for each object and the integrated function are introduced, and the exact solution algorithm is developed by performing deterministic equivalent transformations. A numerical example is provided by comparing our proposed model with previous standard models. |
| format | Article |
| id | doaj-art-341f6b5e1ef34a72af60783e2f31dda1 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-341f6b5e1ef34a72af60783e2f31dda12025-02-03T01:32:02ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/364086364086Risk-Control Approach for a Bottleneck Spanning Tree Problem with the Total Network Reliability under UncertaintyTakashi Hasuike0Hideki Katagiri1Hiroshi Tsuda2Graduate School of Information Science and Technology, Osaka University, 2-1 Yamadaoka, Suita, Osaka 565-0871, JapanGraduate School of Engineering, Hiroshima University, 1-4-1 Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8527, JapanDepartment of Mathematical Sciences, Faculty of Science and Engineering, Doshisha University, 1-3 Tatara Miyakodani, Kyotanabe, Kyoto 610-0321, JapanThis paper considers a new risk-control and management approach for a bottleneck spanning tree problem under the situation where edge costs in a given network include randomness and reliability. Particularly, this paper focuses on the case that only mean value and variance of edge costs are calculated without assuming a specific random distribution. In order to develop the risk control approach, a confidence interval-based formulation is introduced. Using this interval, as well as minimizing the maximum value of worse edge costs, maximizing the minimum value of robust parameters to edge costs is introduced as objective functions in the risk-control. Furthermore, in order to maintain the constructing spanning tree network entirely, the reliability for each edge is introduced, and maximizing the total reliability of spanning tree is assumed as the third objective function. The proposed model is a multiobjective programming problem, and hence, it is difficult to solve it directly without setting some optimal criterion. Therefore, satisfaction functions for each object and the integrated function are introduced, and the exact solution algorithm is developed by performing deterministic equivalent transformations. A numerical example is provided by comparing our proposed model with previous standard models.http://dx.doi.org/10.1155/2012/364086 |
| spellingShingle | Takashi Hasuike Hideki Katagiri Hiroshi Tsuda Risk-Control Approach for a Bottleneck Spanning Tree Problem with the Total Network Reliability under Uncertainty Journal of Applied Mathematics |
| title | Risk-Control Approach for a Bottleneck Spanning Tree Problem with the Total Network Reliability under Uncertainty |
| title_full | Risk-Control Approach for a Bottleneck Spanning Tree Problem with the Total Network Reliability under Uncertainty |
| title_fullStr | Risk-Control Approach for a Bottleneck Spanning Tree Problem with the Total Network Reliability under Uncertainty |
| title_full_unstemmed | Risk-Control Approach for a Bottleneck Spanning Tree Problem with the Total Network Reliability under Uncertainty |
| title_short | Risk-Control Approach for a Bottleneck Spanning Tree Problem with the Total Network Reliability under Uncertainty |
| title_sort | risk control approach for a bottleneck spanning tree problem with the total network reliability under uncertainty |
| url | http://dx.doi.org/10.1155/2012/364086 |
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