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An Equivalent Linear Programming Form of General Linear Fractional Programming: A Duality Approach

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  • Mehdi Toloo

    (Department of System Engineering, Faculty of Economics, Technical University of Ostrava, 702 000 Ostrava, Czech Republic
    Department of Operations Management & Business Statistics, College of Economics and Political Science, Sultan Qaboos University, PC 123 Muscat, Oman)

Abstract

Linear fractional programming has been an important planning tool for the past four decades. The main contribution of this study is to show, under some assumptions, for a linear programming problem, that there are two different dual problems (one linear programming and one linear fractional functional programming) that are equivalent. In other words, we formulate a linear programming problem that is equivalent to the general linear fractional functional programming problem. These equivalent models have some interesting properties which help us to prove the related duality theorems in an easy manner. A traditional data envelopment analysis (DEA) model is taken, as an instance, to illustrate the applicability of the proposed approach.

Suggested Citation

  • Mehdi Toloo, 2021. "An Equivalent Linear Programming Form of General Linear Fractional Programming: A Duality Approach," Mathematics, MDPI, vol. 9(14), pages 1-9, July.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:14:p:1586-:d:589455
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    References listed on IDEAS

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    1. S. Chadha & Veena Chadha, 2007. "Linear fractional programming and duality," 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. 15(2), pages 119-125, June.
    2. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
    3. Arabi, Behrouz & Munisamy, Susila & Emrouznejad, Ali & Toloo, Mehdi & Ghazizadeh, Mohammad Sadegh, 2016. "Eco-efficiency considering the issue of heterogeneity among power plants," Energy, Elsevier, vol. 111(C), pages 722-735.
    4. Joe Zhu, 2009. "Quantitative Models for Performance Evaluation and Benchmarking," International Series in Operations Research and Management Science, Springer, number 978-0-387-85982-8, September.
    5. A. Charnes & W. W. Cooper, 1962. "Programming with linear fractional functionals," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 9(3‐4), pages 181-186, September.
    6. R. D. Banker & A. Charnes & W. W. Cooper, 1984. "Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis," Management Science, INFORMS, vol. 30(9), pages 1078-1092, September.
    7. William W. Cooper & Lawrence M. Seiford & Kaoru Tone, 2007. "Data Envelopment Analysis," Springer Books, Springer, edition 0, number 978-0-387-45283-8, September.
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    Cited by:

    1. Mehdi Toloo & Rouhollah Khodabandelou & Amar Oukil, 2022. "A Comprehensive Bibliometric Analysis of Fractional Programming (1965–2020)," Mathematics, MDPI, vol. 10(11), pages 1-21, May.

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