Abstract
In this paper, a dual of a given linear fractional program is defined and the weak, direct and converse duality theorems are proved. Both the primal and the dual are linear fractional programs. This duality theory leads to necessary and sufficient conditions for the optimality of a given feasible solution. A unmerical example is presented to illustrate the theory in this connection. The equivalence of Charnes and Cooper dual and Dinkelbach’s parametric dual of a linear fractional program is also established.
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References
Bector C R 1973Z. Opns. Res. 17 183
Chadha S S 1971Z. Angew. Math. Mech. 51 560
Charnes A and Cooper W W 1962Nav. Res. Log. Q. 9, 181
Craven B D and Mond B 1973J. Math. Anal. Appl. 42 507
Dinkelbach W 1967Manage. Sci. 13 492
Jagannathan R 1973Z. Opns. Res. 17 1
Kaska J 1969Econ. Mat. Obzor. 5 442
Schaible S 1974Z. Opns. Res. 17 187
Schaible S 1976Manage. Sci. 22 858
Sharma I C and Swarup K 1972Z. Opns. Res. 16 91
Swarup K 1968Unternehmensforchung 12 106
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Seshan, C.R. On duality in linear fractional programming. Proc. Indian Acad. Sci. (Math. Sci.) 89, 35–42 (1980). https://doi.org/10.1007/BF02881023
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DOI: https://doi.org/10.1007/BF02881023