Abstract
An algorithm is developed for solving a special structured linear-fractional program. The structure under study hasM+L constraints equations,L of which have the property that each variable has at most one nonzero coefficient. The proposed method is similar toDantzig andVan Slyke and, from the basis, a working basis of orderM is derived and is used for pivoting, pricing and inversion which for largeL can be significantly lower order than that of the original system.
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References
Dantzig, George B., andRichard Van Slyke: Generalized Upper Bounded Techniques for Linear Programming-II. ORC 64-18 (RR) Operations Research Center, University of California, Berkeley.
Chadha, S. S.: A Decomposition Principle for Fractional Programming OPSEARCH, Vol. 4, No. 3, 1967.
Martos, Bela: Hyperbolic Programming, translated by Andrew and Vernika, Whinston, Naval. Res. Log. Quart. 11, 1964.
Swarup, Kanti: Linear Fractional Programming, Operations Research13, 1965, 1029–1036.
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Chadhà, S.S. A generalized upper bounded technique for a linear fractional program. Metrika 20, 25–35 (1973). https://doi.org/10.1007/BF01893797
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DOI: https://doi.org/10.1007/BF01893797