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Multiple Objective Linear Fractional Programming

Author

Listed:
  • Jonathan S. H. Kornbluth

    (Hebrew University)

  • Ralph E. Steuer

    (University of Georgia)

Abstract

This paper presents a simplex-based solution procedure for the multiple objective linear fractional programming problem. By (1) departing slightly from the traditional notion of efficiency and (2) augmenting the feasible region as in goal programming, the solution procedure solves for all weakly efficient vertices of the augmented feasible region. The article discusses the difficulties that must be addressed in multiple objective linear fractional programming and motivates the solution algorithm that is developed.

Suggested Citation

  • Jonathan S. H. Kornbluth & Ralph E. Steuer, 1981. "Multiple Objective Linear Fractional Programming," Management Science, INFORMS, vol. 27(9), pages 1024-1039, September.
    • Handle: RePEc:inm:ormnsc:v:27:y:1981:i:9:p:1024-1039
    DOI: 10.1287/mnsc.27.9.1024
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    Citations

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    Cited by:

    1. Zerdani, Ouiza & Moulai, Mustapha, 2011. "Optimization over an integer efficient set of a Multiple Objective Linear Fractional Problem," MPRA Paper 35579, University Library of Munich, Germany.
    2. 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.
    3. 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.
    4. Davtalab-Olyaie, Mostafa & Asgharian, Masoud, 2021. "On Pareto-optimality in the cross-efficiency evaluation," European Journal of Operational Research, Elsevier, vol. 288(1), pages 247-257.
    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. 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.
    7. Riccardo Cambini, 1995. "Funzioni scalari affini generalizzate," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 18(2), pages 153-163, September.
    8. 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.
    9. 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.
    10. Hamiden Abd El- Wahed Khalifa & Pavan Kumar, 2022. "A goal programming approach for multi-objective linear fractional programming problem with LR possibilistic variables," 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(4), pages 2053-2061, August.
    11. Goedhart, Marc H. & Spronk, Jaap, 1995. "Financial planning with fractional goals," European Journal of Operational Research, Elsevier, vol. 82(1), pages 111-124, April.
    12. Chergui, M. E-A & Moulai, M., 2007. "An exact method for a discrete multiobjective linear fractional optimization," MPRA Paper 12097, University Library of Munich, Germany, revised 09 Jan 2008.
    13. 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.
    14. Washington Alves Oliveira & Marko Antonio Rojas-Medar & Antonio Beato-Moreno & Maria Beatriz Hernández-Jiménez, 2019. "Necessary and sufficient conditions for achieving global optimal solutions in multiobjective quadratic fractional optimization problems," Journal of Global Optimization, Springer, vol. 74(2), pages 233-253, June.
    15. Ahlatcioglu, Mehmet & Tiryaki, Fatma, 2007. "Interactive fuzzy programming for decentralized two-level linear fractional programming (DTLLFP) problems," Omega, Elsevier, vol. 35(4), pages 432-450, August.
    16. Lara, P. & Stancu-Minasian, I., 1999. "Fractional programming: a tool for the assessment of sustainability," Agricultural Systems, Elsevier, vol. 62(2), pages 131-141, November.
    17. Animesh Biswas & Shyamali Dewan, 2012. "Priority based fuzzy goal programming technique to fractional fuzzy goals using dynamic programming," Fuzzy Information and Engineering, Springer, vol. 4(2), pages 165-180, June.

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    Keywords

    programming: multiple criteria;

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