Nothing Special   »   [go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/ems/eureir/1325.html
   My bibliography  Save this paper

Generalized Fractional Programming With User Interaction

Author

Listed:
  • Birbil, S.I.
  • Frenk, J.B.G.
  • Zhang, S.
Abstract
The present paper proposes a new approach to solve generalized fractional programming problems through user interaction. Capitalizing on two alternatives, we review the Dinkelbach-type methods and set forth the main difficulty in applying these methods. In order to cope with this difficulty, we propose an approximation approach that can be controlled by a predetermined parameter. The proposed approach is promising particularly when a decision maker is involved in the solution process and agrees upon finding an effective but nearoptimal value in an efficient manner. The decision maker is asked to decide the parameter and our analysis shows how good is the value found by the approximation corresponding to this parameter. In addition, we present several observations that may be suitable for boosting up the performance of the proposed approach. Finally, we support our discussion through extensive numerical experiments.

Suggested Citation

  • Birbil, S.I. & Frenk, J.B.G. & Zhang, S., 2004. "Generalized Fractional Programming With User Interaction," Econometric Institute Research Papers ERS-2004-033-LIS, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    • Handle: RePEc:ems:eureir:1325
    as

    Download full text from publisher

    File URL: https://repub.eur.nl/pub/1325/ERS%202004%20033%20LIS.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. R. Jagannathan, 1985. "An Algorithm for a Class of Nonconvex Programming Problems with Nonlinear Fractional Objectives," Management Science, INFORMS, vol. 31(7), pages 847-851, July.
    2. M. Gugat, 1998. "Prox-Regularization Methods for Generalized Fractional Programming," Journal of Optimization Theory and Applications, Springer, vol. 99(3), pages 691-722, December.
    3. A. Roubi, 2000. "Method of Centers for Generalized Fractional Programming," Journal of Optimization Theory and Applications, Springer, vol. 107(1), pages 123-143, October.
    4. Jonathan S. H. Kornbluth & Ralph E. Steuer, 1981. "Multiple Objective Linear Fractional Programming," Management Science, INFORMS, vol. 27(9), pages 1024-1039, September.
    5. 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. Frenk, J.B.G. & Schaible, S., 2004. "Fractional Programming," Econometric Institute Research Papers ERS-2004-074-LIS, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    2. Frenk, J.B.G. & Schaible, S., 2004. "Fractional Programming," ERIM Report Series Research in Management ERS-2004-074-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.

    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. Birbil, S.I. & Frenk, J.B.G. & Zhang, S., 2004. "Generalized Fractional Programming With User Interaction," ERIM Report Series Research in Management ERS-2004-033-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    2. Smail Addoune & Karima Boufi & Ahmed Roubi, 2018. "Proximal Bundle Algorithms for Nonlinearly Constrained Convex Minimax Fractional Programs," Journal of Optimization Theory and Applications, Springer, vol. 179(1), pages 212-239, October.
    3. K. Boufi & A. Roubi, 2017. "Dual method of centers for solving generalized fractional programs," Journal of Global Optimization, Springer, vol. 69(2), pages 387-426, October.
    4. Feng Guo & Liguo Jiao, 2023. "A new scheme for approximating the weakly efficient solution set of vector rational optimization problems," Journal of Global Optimization, Springer, vol. 86(4), pages 905-930, August.
    5. H. Boualam & A. Roubi, 2019. "Proximal bundle methods based on approximate subgradients for solving Lagrangian duals of minimax fractional programs," Journal of Global Optimization, Springer, vol. 74(2), pages 255-284, June.
    6. 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.
    7. 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.
    8. Luca Consolini & Marco Locatelli & Jiulin Wang & Yong Xia, 2020. "Efficient local search procedures for quadratic fractional programming problems," Computational Optimization and Applications, Springer, vol. 76(1), pages 201-232, May.
    9. Sakawa, Masatoshi & Kato, Kosuke, 1998. "An interactive fuzzy satisficing method for structured multiobjective linear fractional programs with fuzzy numbers," European Journal of Operational Research, Elsevier, vol. 107(3), pages 575-589, June.
    10. Harald Dyckhoff & Katrin Allen, 1999. "Theoretische Begründung einer Effizienzanalyse mittels Data Envelopment Analysis (DEA)," Schmalenbach Journal of Business Research, Springer, vol. 51(5), pages 411-436, May.
    11. Maziar Sahamkhadam, 2021. "Dynamic copula-based expectile portfolios," Journal of Asset Management, Palgrave Macmillan, vol. 22(3), pages 209-223, May.
    12. Cook, Wade D. & Zhu, Joe, 2007. "Within-group common weights in DEA: An analysis of power plant efficiency," European Journal of Operational Research, Elsevier, vol. 178(1), pages 207-216, April.
    13. Laurent Alfandari & Alborz Hassanzadeh & Ivana Ljubić, 2021. "An Exact Method for Assortment Optimization under the Nested Logit Model," Working Papers hal-02463159, HAL.
    14. A. Roubi, 2000. "Method of Centers for Generalized Fractional Programming," Journal of Optimization Theory and Applications, Springer, vol. 107(1), pages 123-143, October.
    15. Andrés Gómez & Oleg A. Prokopyev, 2021. "A Mixed-Integer Fractional Optimization Approach to Best Subset Selection," INFORMS Journal on Computing, INFORMS, vol. 33(2), pages 551-565, May.
    16. Keshav Singh & Meng-Lin Ku & Sudip Biswas & Tharmalingam Ratnarajah, 2017. "Energy-Efficient Subcarrier Pairing and Power Allocation for DF Relay Networks with an Eavesdropper," Energies, MDPI, vol. 10(12), pages 1-13, November.
    17. Claassen, G.D.H., 2014. "Mixed integer (0–1) fractional programming for decision support in paper production industry," Omega, Elsevier, vol. 43(C), pages 21-29.
    18. Bo Zhang & YueLin Gao & Xia Liu & XiaoLi Huang, 2022. "An Outcome-Space-Based Branch-and-Bound Algorithm for a Class of Sum-of-Fractions Problems," Journal of Optimization Theory and Applications, Springer, vol. 192(3), pages 830-855, March.
    19. Hasuike, Takashi & Ishii, Hiroaki, 2009. "On flexible product-mix decision problems under randomness and fuzziness," Omega, Elsevier, vol. 37(4), pages 770-787, August.
    20. João Costa & Maria Alves, 2013. "Enhancing computations of nondominated solutions in MOLFP via reference points," Journal of Global Optimization, Springer, vol. 57(3), pages 617-631, November.

    More about this item

    Keywords

    approximation approach; error analysis; generalized fractional programming; performance improvement; user interaction;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • M - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics
    • M11 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Administration - - - Production Management
    • R4 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Transportation Economics

    Statistics

    Access and download statistics

    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:ems:eureir:1325. 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: RePub (email available below). General contact details of provider: https://edirc.repec.org/data/feeurnl.html .

    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.