IDEAS home Printed from https://ideas.repec.org/a/spr/opsear/v56y2019i1d10.1007_s12597-018-00351-2.html
   My bibliography  Save this article

Solution approach to multi-objective linear fractional programming problem using parametric functions

Author

Listed:
  • Suvasis Nayak

    (Indian Institute of Technology Bhubaneswar)

  • Akshay Kumar Ojha

    (Indian Institute of Technology Bhubaneswar)

Abstract

In this paper, an iterative technique based on the use of parametric functions is proposed to obtain the best preferred optimal solution of a multi-objective linear fractional programming problem. The decision maker ascertains own desired tolerance values for the objectives as termination constants and imposes them on each iteratively computed objective functions in terms of termination conditions. Each fractional objective is transformed into non-fractional parametric function using certain initial values of parameters. The parametric values are iteratively computed and $$\epsilon $$ ϵ -constraint method is used to obtain the pareto (weakly) optimal solutions in each step. The computations get terminated when all the termination conditions are satisfied at a pareto optimal solution of an iterative step. A numerical example is discussed at the end to illustrate the proposed method and fuzzy max–min operator method is applied to validate the obtained results.

Suggested Citation

  • Suvasis Nayak & Akshay Kumar Ojha, 2019. "Solution approach to multi-objective linear fractional programming problem using parametric functions," OPSEARCH, Springer;Operational Research Society of India, vol. 56(1), pages 174-190, March.
    • Handle: RePEc:spr:opsear:v:56:y:2019:i:1:d:10.1007_s12597-018-00351-2
    DOI: 10.1007/s12597-018-00351-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s12597-018-00351-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s12597-018-00351-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. R. E. Bellman & L. A. Zadeh, 1970. "Decision-Making in a Fuzzy Environment," Management Science, INFORMS, vol. 17(4), pages 141-164, December.
    2. Y. Almogy & O. Levin, 1971. "A Class of Fractional Programming Problems," Operations Research, INFORMS, vol. 19(1), pages 57-67, February.
    3. Wolf, Hartmut, 1986. "Solving special nonlinear fractional programming problems via parametric linear programming," European Journal of Operational Research, Elsevier, vol. 23(3), pages 396-400, March.
    4. G. R. Bitran & A. G. Novaes, 1973. "Linear Programming with a Fractional Objective Function," Operations Research, INFORMS, vol. 21(1), pages 22-29, February.
    5. Costa, Joao Paulo, 2007. "Computing non-dominated solutions in MOLFP," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1464-1475, September.
    6. Werner Dinkelbach, 1967. "On Nonlinear Fractional Programming," Management Science, INFORMS, vol. 13(7), pages 492-498, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Vandana Goyal & Namrata Rani & Deepak Gupta, 2022. "Rouben Ranking Function and parametric approach to quadratically constrained multiobjective quadratic fractional programming with trapezoidal fuzzy number coefficients," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 13(2), pages 923-932, April.
    2. Vandana Goyal & Namrata Rani & Deepak Gupta, 2022. "An algorithm for quadratically constrained multi-objective quadratic fractional programming with pentagonal fuzzy numbers," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 32(1), pages 49-71.
    3. Vandana Goyal & Namrata Rani & Deepak Gupta, 2021. "Parametric approach to quadratically constrained multi-level multi-objective quadratic fractional programming," OPSEARCH, Springer;Operational Research Society of India, vol. 58(3), pages 557-574, September.
    4. Vandana Goyal & Namrata Rani & Deepak Gupta, 2022. "FGP approach to quadratically constrained multi-objective quadratic fractional programming with parametric functions," OPSEARCH, Springer;Operational Research Society of India, vol. 59(2), pages 594-602, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. S. Morteza Mirdehghan & Hassan Rostamzadeh, 2016. "Finding the Efficiency Status and Efficient Projection in Multiobjective Linear Fractional Programming: A Linear Programming Technique," Journal of Optimization, Hindawi, vol. 2016, pages 1-8, September.
    2. Vandana Goyal & Namrata Rani & Deepak Gupta, 2021. "Parametric approach to quadratically constrained multi-level multi-objective quadratic fractional programming," OPSEARCH, Springer;Operational Research Society of India, vol. 58(3), pages 557-574, September.
    3. Tunjo Perić & Josip Matejaš & Zoran Babić, 2023. "Advantages, sensitivity and application efficiency of the new iterative method to solve multi-objective linear fractional programming problem," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 31(3), pages 751-767, September.
    4. Vandana Goyal & Namrata Rani & Deepak Gupta, 2022. "An algorithm for quadratically constrained multi-objective quadratic fractional programming with pentagonal fuzzy numbers," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 32(1), pages 49-71.
    5. Vandana Goyal & Namrata Rani & Deepak Gupta, 2022. "Rouben Ranking Function and parametric approach to quadratically constrained multiobjective quadratic fractional programming with trapezoidal fuzzy number coefficients," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 13(2), pages 923-932, April.
    6. Agarwal, Deepika & Singh, Pitam & El Sayed, M.A., 2023. "The Karush–Kuhn–Tucker (KKT) optimality conditions for fuzzy-valued fractional optimization problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 861-877.
    7. J.-Y. Lin & S. Schaible & R.-L. Sheu, 2010. "Minimization of Isotonic Functions Composed of Fractions," Journal of Optimization Theory and Applications, Springer, vol. 146(3), pages 581-601, September.
    8. Juan S. Borrero & Colin Gillen & Oleg A. Prokopyev, 2017. "Fractional 0–1 programming: applications and algorithms," Journal of Global Optimization, Springer, vol. 69(1), pages 255-282, September.
    9. Mojtaba Borza & Azmin Sham Rambely, 2021. "A Linearization to the Sum of Linear Ratios Programming Problem," Mathematics, MDPI, vol. 9(9), pages 1-10, April.
    10. Chen, Fang & Huang, Guohe & Fan, Yurui, 2015. "A linearization and parameterization approach to tri-objective linear programming problems for power generation expansion planning," Energy, Elsevier, vol. 87(C), pages 240-250.
    11. Pandian Ponnaiah & Jayalakshmi Mohan, 2013. "On Solving Linear Fractional Programming Problems," Modern Applied Science, Canadian Center of Science and Education, vol. 7(6), pages 1-90, June.
    12. Neha Gupta, 2019. "Optimization of fuzzy bi-objective fractional assignment problem," OPSEARCH, Springer;Operational Research Society of India, vol. 56(3), pages 1091-1102, September.
    13. Vuciterna, Rina & Thomsen, Michael & Popp, Jennie & Musliu, Arben, 2017. "Efficiency and Competitiveness of Kosovo Raspberry Producers," 2017 Annual Meeting, February 4-7, 2017, Mobile, Alabama 252770, Southern Agricultural Economics Association.
    14. Gourav Gupta & Shivani & Deepika Rani, 2024. "Neutrosophic goal programming approach for multi-objective fixed-charge transportation problem with neutrosophic parameters," OPSEARCH, Springer;Operational Research Society of India, vol. 61(3), pages 1274-1300, September.
    15. Berna Tektas Sivrikaya & Ferhan Cebi & Hasan Hüseyin Turan & Nihat Kasap & Dursun Delen, 2017. "A fuzzy long-term investment planning model for a GenCo in a hybrid electricity market considering climate change impacts," Information Systems Frontiers, Springer, vol. 19(5), pages 975-991, October.
    16. Collan, Mikael, 2008. "New Method for Real Option Valuation Using Fuzzy Numbers," Working Papers 466, IAMSR, Åbo Akademi.
    17. M. Golbabapour & M. Reza Zahabi, 2024. "Sum rate maximization for mm-wave multi-user hybrid IRS-assisted MIMO systems," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 87(3), pages 593-604, November.
    18. Tien Mai & Arunesh Sinha, 2022. "Safe Delivery of Critical Services in Areas with Volatile Security Situation via a Stackelberg Game Approach," Papers 2204.11451, arXiv.org.
    19. Kim, Jong Soon & Whang, Kyu-Seung, 1998. "A tolerance approach to the fuzzy goal programming problems with unbalanced triangular membership function," European Journal of Operational Research, Elsevier, vol. 107(3), pages 614-624, June.
    20. Berna Tektaş & Hasan Hüseyin Turan & Nihat Kasap & Ferhan Çebi & Dursun Delen, 2022. "A Fuzzy Prescriptive Analytics Approach to Power Generation Capacity Planning," Energies, MDPI, vol. 15(9), pages 1-26, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:opsear:v:56:y:2019:i:1:d:10.1007_s12597-018-00351-2. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.