Modeling and Optimizing the System Reliability Using Bounded Geometric Programming Approach
The geometric programming problem (GPP) is a beneficial mathematical programming problem for modeling and optimizing nonlinear optimization problems in various engineering fields. The structural configuration of the GPP is quite dynamic and flexible in modeling and fitting the reliability optimizati...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-07-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/14/2435 |
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| author | Shafiq Ahmad Firoz Ahmad Intekhab Alam Abdelaty Edrees Sayed Mali Abdollahian |
| author_facet | Shafiq Ahmad Firoz Ahmad Intekhab Alam Abdelaty Edrees Sayed Mali Abdollahian |
| author_sort | Shafiq Ahmad |
| collection | DOAJ |
| description | The geometric programming problem (GPP) is a beneficial mathematical programming problem for modeling and optimizing nonlinear optimization problems in various engineering fields. The structural configuration of the GPP is quite dynamic and flexible in modeling and fitting the reliability optimization problems efficiently. The work’s motivation is to introduce a bounded solution approach for the GPP while considering the variation among the right-hand-side parameters. The bounded solution method uses the two-level mathematical programming problems and obtains the solution of the objective function in a specified interval. The benefit of the bounded solution approach can be realized in that there is no need for sensitivity analyses of the results output. The demonstration of the proposed approach is shown by applying it to the system reliability optimization problem. The specific interval is determined for the objective values and found to be lying in the optimal range. Based on the findings, the concluding remarks are presented. |
| first_indexed | 2024-03-09T06:15:18Z |
| format | Article |
| id | doaj.art-0af02d7449864c6d87cc8eeab01a7060 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T06:15:18Z |
| publishDate | 2022-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-0af02d7449864c6d87cc8eeab01a70602023-12-03T11:53:36ZengMDPI AGMathematics2227-73902022-07-011014243510.3390/math10142435Modeling and Optimizing the System Reliability Using Bounded Geometric Programming ApproachShafiq Ahmad0Firoz Ahmad1Intekhab Alam2Abdelaty Edrees Sayed3Mali Abdollahian4Industrial Engineering Department, College of Engineering, King Saud University, P.O. Box 800, Riyadh 11421, Saudi ArabiaDepartment of Management Studies, Indian Institute of Science, Bangalore 560012, IndiaDepartment of Statistics and Operations Research, Aligarh Muslim University, Aligarh 202002, IndiaIndustrial Engineering Department, College of Engineering, King Saud University, P.O. Box 800, Riyadh 11421, Saudi ArabiaSchool of Science, College of Sciences, Technology, Engineering, Mathematics, RMIT University, GPO Box 2476, Melbourne, VIC 3001, AustraliaThe geometric programming problem (GPP) is a beneficial mathematical programming problem for modeling and optimizing nonlinear optimization problems in various engineering fields. The structural configuration of the GPP is quite dynamic and flexible in modeling and fitting the reliability optimization problems efficiently. The work’s motivation is to introduce a bounded solution approach for the GPP while considering the variation among the right-hand-side parameters. The bounded solution method uses the two-level mathematical programming problems and obtains the solution of the objective function in a specified interval. The benefit of the bounded solution approach can be realized in that there is no need for sensitivity analyses of the results output. The demonstration of the proposed approach is shown by applying it to the system reliability optimization problem. The specific interval is determined for the objective values and found to be lying in the optimal range. Based on the findings, the concluding remarks are presented.https://www.mdpi.com/2227-7390/10/14/2435interval-based parametersgeometric programming problemsbounded optimization approachsystem reliability |
| spellingShingle | Shafiq Ahmad Firoz Ahmad Intekhab Alam Abdelaty Edrees Sayed Mali Abdollahian Modeling and Optimizing the System Reliability Using Bounded Geometric Programming Approach Mathematics interval-based parameters geometric programming problems bounded optimization approach system reliability |
| title | Modeling and Optimizing the System Reliability Using Bounded Geometric Programming Approach |
| title_full | Modeling and Optimizing the System Reliability Using Bounded Geometric Programming Approach |
| title_fullStr | Modeling and Optimizing the System Reliability Using Bounded Geometric Programming Approach |
| title_full_unstemmed | Modeling and Optimizing the System Reliability Using Bounded Geometric Programming Approach |
| title_short | Modeling and Optimizing the System Reliability Using Bounded Geometric Programming Approach |
| title_sort | modeling and optimizing the system reliability using bounded geometric programming approach |
| topic | interval-based parameters geometric programming problems bounded optimization approach system reliability |
| url | https://www.mdpi.com/2227-7390/10/14/2435 |
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