Abstract
In this paper an algorithm to solve a Bilevel Programming Problem in which the leader’s and the follower’s both objective functions are linear fractional is developed. The algorithm is based on Preemptive Goal Programming. The Bilevel Programming problem is solved by converting it into a goal programming problem. An example to illustrate it is also presented.
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Bard, J. F. and Falk, J. E. (1982), “An explicit solution to the multilevel programming problem”, Computers and Operations Research, 8, No. 2, 260–272.
Bard, J. F. (1983), “An algorithm for solving the general bilevel programming problem”, Mathematics of Operations Research, 8, No. 2, 260–272.
Bard, J. F. (1984), “Optimality conditions for the bilevel programming problem”, Naval Research Logistics Quarterly, 31, 13–26.
Bard, J. F. (1985), “Geometric and algorithmic development for a hierarchical planning problem”, European Journal of Operations Research Vol. 19, 372–383.
Bersekas, D. P. and Gafni, E. (1982), “Projection Method for variational inequalities and application to a traffic assignment problem”, Mathematical Programming Study, 17, 139–159.
Bialas, W. F. and Karwan, M. H. (1984), “Two level linear programming”, Management Science, 30, No. 8, 1001–1020.
Candler, W. and Townsley, R. J. (1982), “A linear two level programming problem”, Computers and Operations Research, Vol. 9, No. 1, 59–76.
Harker, P. T. (1988), “Alternative models of spactral competiton”, Operations Research, 34, 410–425.
Ignizio, J. P. (1976), Goal Programming and extensions, Lexington Books, London.
Kornbluth, I. S. H. and Steur, R. E. (1981), “Goal programming with linear fractional criteria”, Euro, J. Op. Res., 8, 58–65.
Marcotte, P. (1983), “Network optimization with continuous control parameters”, Transportation Science, 17, No. 2, 181–197.
Pant, J. C. and Shah, S. (1992), “Linear approach to linear fractional goal programming”, Opsearch, 29, 297–304.
Thirwani, D. and Arora, S. R. (1983), “Bi-Level linear fractional programming problem”, Cahiers Du Cero, 35, No. 1–2, 135–149.
Tobin, R. L. and Friez, T. L. (1986), “Spatial competition facility location models: Definition formulation and solution approach”, Annals of Operations Research 6, 49–74.
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Malhotra, N., Arora, S.R. An Algorithm to Solve Linear Fractional Bilevel Programming Problem Via Goal Programming. OPSEARCH 37, 1–13 (2000). https://doi.org/10.1007/BF03398596
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DOI: https://doi.org/10.1007/BF03398596