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Modeling and Optimizing the System Reliability Using Bounded Geometric Programming Approach

Author

Listed:
  • Shafiq Ahmad

    (Industrial Engineering Department, College of Engineering, King Saud University, P.O. Box 800, Riyadh 11421, Saudi Arabia
    These authors contributed equally to this work.)

  • Firoz Ahmad

    (Department of Management Studies, Indian Institute of Science, Bangalore 560012, India
    Department of Statistics and Operations Research, Aligarh Muslim University, Aligarh 202002, India
    These authors contributed equally to this work.)

  • Intekhab Alam

    (Department of Statistics and Operations Research, Aligarh Muslim University, Aligarh 202002, India)

  • Abdelaty Edrees Sayed

    (Industrial Engineering Department, College of Engineering, King Saud University, P.O. Box 800, Riyadh 11421, Saudi Arabia)

  • Mali Abdollahian

    (School of Science, College of Sciences, Technology, Engineering, Mathematics, RMIT University, GPO Box 2476, Melbourne, VIC 3001, Australia)

Abstract

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.

Suggested Citation

  • Shafiq Ahmad & Firoz Ahmad & Intekhab Alam & Abdelaty Edrees Sayed & Mali Abdollahian, 2022. "Modeling and Optimizing the System Reliability Using Bounded Geometric Programming Approach," Mathematics, MDPI, vol. 10(14), pages 1-19, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:14:p:2435-:d:861748
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    References listed on IDEAS

    as
    1. Sedaghat, Niloofar & Ardakan, Mostafa Abouei, 2021. "G-mixed: A new strategy for redundant components in reliability optimization problems," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    2. Islam, Sahidul & Roy, Tapan Kumar, 2006. "A new fuzzy multi-objective programming: Entropy based geometric programming and its application of transportation problems," European Journal of Operational Research, Elsevier, vol. 173(2), pages 387-404, September.
    3. Firoz Ahmad & Ahmad Yusuf Adhami, 2019. "Total cost measures with probabilistic cost function under varying supply and demand in transportation problem," OPSEARCH, Springer;Operational Research Society of India, vol. 56(2), pages 583-602, June.
    4. Armita Khorsandi & Bing-Yuan Cao & Hadi Nasseri, 2019. "A New Method to Optimize the Satisfaction Level of the Decision Maker in Fuzzy Geometric Programming Problems," Mathematics, MDPI, vol. 7(5), pages 1-18, May.
    Full references (including those not matched with items on IDEAS)

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