Abstract
This paper provides an introduction to the nature of multiple objective linear fractional programming. By graphically illustrating several examples, the differences between a multiple objective linear fractional program (MOLFP) and a MOLP are identified in terms of the efficient sets they produce. Instead of relying upon the usual notion of efficiency, a more relaxed definition of efficiency is used for computation. By exploiting its “near linearity”, a simplex-based algorithm for a MOLFP has been designed in [7]. It is similar to, but somewhat more elaborate than, those that have been devised for linear vector-maximum problems. The salient features of the MOLFP algorithm are reviewed in the light of the graphical examples that are provided.
This research was conducted while J. S. H. Kornbluth was on sabbatical at the Wharton School of the University of Pennsylvania and R. E. Steuer was on sabbatical with the Department of Civil Engineering at Princeton University.
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References
Bitran, G. R. and A. G. Novaes, “Linear Programming with a Fractional Objective Function,” Operations Research, Vol. 21, No. 1, 1973, pp. 22–29.
Charnes, A. and W. W. Cooper, “Programming with Linear Fractional Functionals,” Naval Research Logistics Quarterly, Vol. 9, 1962, pp. 181–186.
Ecker, J. G. and I. A. Kouada, “Finding All Efficient Extreme Points for Multiple Objective Linear Programs,” Mathematical Programming, Vol. 14, 1978. pp. 249–261.
Evans, J. P. and R. E. Steuer, “A Revised Simplex Method for Linear Multiple Objective Programs,” Mathematical Programming, Vol. 5, No. 1, 1973, pp. 54–72.
Gal, T., “A General Method for Determining the Set of All Efficient Solutions to a Linear Vectormaximum Problem,” European Journal of Operational Research, Vol. 1, 1977, pp. 307–322.
Isermann, H., “The Enumeration of the Set of All Efficient Solutions for a Linear Multiple Objective Program”, Operational Research Quarterly, Vol. 28, No. 3, 1977, pp. 711–725.
Kornbluth, J. S. H. and R. E. Steuer, “Multiple Objective Linear Fractional Programming,” Technical Report EES-79-7, Department of Civil Engineering, Princeton University, 1979.
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© 1980 Springer-Verlag Berlin Heidelberg
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Kornbluth, J.S.H., Steuer, R.E. (1980). On Computing the Set of all Weakly Efficient Vertices in Multiple Objective Linear Fractional Programming. In: Fandel, G., Gal, T. (eds) Multiple Criteria Decision Making Theory and Application. Lecture Notes in Economics and Mathematical Systems, vol 177. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-48782-8_15
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DOI: https://doi.org/10.1007/978-3-642-48782-8_15
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