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Maximizing a Linear Fractional Function on a Pareto Efficient Frontier

Author

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  • S.T. Hackman

    (Georgia Institute of Technology)

  • U. Passy

    (Israel Institute of Technology)

Abstract

We consider the problem of maximizing a linear fractional function on the Pareto efficient frontier of two other linear fractional functions. We present a finite pivoting-type algorithm that solves the maximization problem while computing simultaneously the efficient frontier. Application to multistage efficiency analysis is discussed. An example demonstrating the computational procedure is included.

Suggested Citation

  • S.T. Hackman & U. Passy, 2002. "Maximizing a Linear Fractional Function on a Pareto Efficient Frontier," Journal of Optimization Theory and Applications, Springer, vol. 113(1), pages 83-103, April.
    • Handle: RePEc:spr:joptap:v:113:y:2002:i:1:d:10.1023_a:1014857230393
    DOI: 10.1023/A:1014857230393
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    References listed on IDEAS

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    1. A. R. Warburton, 1985. "Parametric Solution of Bicriterion Linear Fractional Programs," Operations Research, INFORMS, vol. 33(1), pages 74-84, February.
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    3. Serpil Sayin, 2000. "Optimizing Over the Efficient Set Using a Top-Down Search of Faces," Operations Research, INFORMS, vol. 48(1), pages 65-72, February.
    4. Fried, Harold O. & Lovell, C. A. Knox & Schmidt, Shelton S. (ed.), 1993. "The Measurement of Productive Efficiency: Techniques and Applications," OUP Catalogue, Oxford University Press, number 9780195072181.
    5. 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.
    6. R. Horst & N. V. Thoai, 1997. "Utility Function Programs and Optimization over the Efficient Set in Multiple-Objective Decision Making," Journal of Optimization Theory and Applications, Springer, vol. 92(3), pages 605-631, March.
    7. Arthur M. Geoffrion, 1967. "Solving Bicriterion Mathematical Programs," Operations Research, INFORMS, vol. 15(1), pages 39-54, February.
    8. Dan Rosen & Claire Schaffnit & Joseph Paradi, 1998. "Marginal Rates and Two-dimensional Level Curves in DEA," Journal of Productivity Analysis, Springer, vol. 9(3), pages 205-232, March.
    9. J. Benoist, 1998. "Connectedness of the Efficient Set for Strictly Quasiconcave Sets," Journal of Optimization Theory and Applications, Springer, vol. 96(3), pages 627-654, March.
    10. J. Fülöp & L. D. Muu, 2000. "Branch-and-Bound Variant of an Outcome-Based Algorithm for Optimizing over the Efficient Set of a Bicriteria Linear Programming Problem," Journal of Optimization Theory and Applications, Springer, vol. 105(1), pages 37-54, April.
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