On bilevel fractional programming

References

• Ahuja , R K. 1986 . Algorithms for the Minimax Transportation Problem . Naval Research Logistics Quarterly , 33 : 725 – 739 .
   Google Scholar
• Aiyoshi , Eitaro. and Shimizu , Kiyotaka. 1984 . A Solution method for the Static Constrained Stackelberg Problem via Penalty Method . IEEE Transactions on Automatic Control , AC-29 ( 12 ) : 1111 – 1114 .
   Web of Science ®Google Scholar
• Akgül , Mustafa. 1984 . On a Min Max Problem . Opsearch , 21 ( 1 ) : 30 – 37 .
   Google Scholar
• Anandalingam , G. 1988 . A Mathematical Programming Model of Decentralized Multi-Level Systems . Journal of the Operational Research Society , 39 ( 11 ) : 1021 – 1033 .
   Web of Science ®Google Scholar
• Anandalingam , G. and White , D.J. 1990 . A Solution Method for the Linear Static Stackelberg Problem using Penalty Functions . IEEE Transactions of Automatic Control , 35 ( 10 ) : 1170 – 1173 .
   Web of Science ®Google Scholar
• Anandalingam , G. and Victor , Apprey. 1991 . Multi-level programming and conflict resolution . European Journal of Operational Research , 51 ( 10 ) : 233 – 247 .
   Google Scholar
• Anandalingam , G. and Friesz , T L. 1992 . Hierarchical Optimization . An Introduction, Annals of Operations Research , 34 ( 10 ) : 1 – 11 .
   Google Scholar
• Bansal , S. and Puri , M C. 1980 . A Min-Max Problem . Zeitschrift für Operations Research , 24 ( 10 ) : 191 – 200 .
   Google Scholar
• Bard , Jonathan F. 1983 . An Efficient Point Algorithm for a Linear Two-Stage Optimization problem . Operations Research , 31 ( 10 ) : 670 – 684 .
   Google Scholar
• Bard , Jonathan F. 1988 . Convex Two-Level Optimization . Mathematical Programming , 40 ( 10 ) : 15 – 27 .
   Google Scholar
• Bard , Jonathan F. and James , T Moore. 1992 . An Algorithm for the Discrete Bilevel Programming Problem . Naval Research Logistics Quarterly , 39 ( 10 ) : 419 – 435 .
   Google Scholar
• Ben-Ayed , Omar. and Blair , C E. 1990 . Computatinal difficulties of bilevel linear programming . Operations Research , 38 ( 10 ) : 556 – 559 .
   Google Scholar
• Ben-Ayed Omar Charles E Blair David E Boyce Larry J Lablanc Construction of a real-world bilevel programming model of the highway network design approach Annals of Operations Research 1992 34 1/4 219 354 Switzerland
   Google Scholar
• Benson , H P. 1989 . On the Structure and Properties of the Linear Multilevel Programming Problem . Journal of Optimization Theory and Applications , 60 ( 3 ) : 353 – 373 .
   Web of Science ®Google Scholar
• Bertsekas , D P. and Gafni , E. 1982 . Projection Method for Variational Inequalites and Application to a Traffic Assignment Problem . Mathematical Programming Study , 17 ( 3 ) : 139 – 159 .
   Google Scholar
• Bialas , Wayne F. and Mark , H K. 1982 . On Two-Level Optimization . IEEE Transactions on Automatic Control , AC-27 ( 1 ) : 211 – 214 .
   Web of Science ®Google Scholar
• Bialas and Wayne , F. 1984 . Two Level Linear Programming . Management Science , 30 ( 8 ) : 1004 – 1020 .
   Web of Science ®Google Scholar
• Bialas , Wayne , F. and Shaw , J.P. 1980 . “ A Parametric Complementary Pivot Approach for Two-Level Linear Programming, Research Report no 80-2 ” . In Operation Program , Buffalo : State University of New York . Department of Industrial Engineering
   Google Scholar
• Bracken , J. , Falk , J E. and Miercort , F A. 1977 . A Strategic Weapons Exchange Allocation Model Operations Research , 25 : 968 – 976 .
   Google Scholar
• Burkard , Rainer , E. and Rendl , Franz. 1991 . Lexicographic Bottleneck Problems . Operational Reserach Letters , 10 : 303 – 308 .
   Web of Science ®Google Scholar
• Candler , Wilfred. and Townsley , Robert. 1982 . A Linear Two Level Programming Problem . Computers and Operations Research , 9 ( 1 ) : 59 – 76 .
   Web of Science ®Google Scholar
• Cassidy , R G. , Kirby , M J L. and Raike , W H. 1971 . Efficient Distributions of Resources through Three Levels of Government . Management Science , 17 ( 1 ) : 462 – 473 .
   Google Scholar
• Derigs , Ulrich. 1982 . On three basic methods for solving Bottleneck Transportation Problems . Naval Research Logistics Quarterly , 29 ( 3 ) : 505 – 515 .
   Google Scholar
• Edmunds Thomas A. Jonathan F.Bard An algorithm for the mixed-integer non-linear bilevel programming problem Annals of Operations Research 1992 34 1/4 149 162 Switzerland
   Google Scholar
• Frieze , A M. 1975 . “ Bottleneck Linear Programming ” . In Operational Research Quartely , Vol. 26 , 871 – 874 . Pergamon Press . 4(ii)
   Google Scholar
• Garfinkel , R S. 1971 . An improved algorithm for the bottleneck assignment problem . Operations Research , 19 : 1747 – 1751 .
   Web of Science ®Google Scholar
• Garfinkel , R S. and Rao , M R. 1971 . The Bottleneck Transportation Problem . Naval Research Logistics Quarterly , 18 : 465 – 472 .
   Google Scholar
• Geetha , S. and Nair , K P K. 1993 . A Variation of the Assignment Problem . European Journal of Operational Research , 68 : 422 – 426 .
   Web of Science ®Google Scholar
• Gross , O. 1971 . The Bottleneck Transportation Problem . Naval Research Logistics Quarterly , 18 : 465 – 472 .
   Google Scholar
• Gupta , S K. and Ashok , K.Mittal. 1982 . A min max problem as a linear programming problem . Opsearch , 19 ( 1 ) : 49 – 53 .
   Google Scholar
• Hammer , P L. 1969 . Time Minimizing Transportation Problems . Naval Research Logistics Quarterly , 16 ( 3 ) : 345 – 357 .
   Google Scholar
• Harker , P T. 1986 . Alternative Models of Spatial Competition . Operation Research , 34 ( 3 ) : 410 – 425 .
   Web of Science ®Google Scholar
• Haurie , A. , Savard , G. and White , D J. 1990 . A note on: An Efficient Point Algorithm for a linear Two-Stage Optimization Problem . Operations Research , 38 ( 3 ) : 553 – 555 .
   Web of Science ®Google Scholar
• Kornai , J J. and Liptak , T. 1965 . Two level Planning . Econometrica , 33 ( 3 ) : 141 – 169 .
   Google Scholar
• Marcotte , P. 1983 . Network Optimization with Continuous Control Parameters . Transportation Science , 17 ( 2 ) : 181 – 197 .
   Web of Science ®Google Scholar
• Minoux , M. 1989 . Solving Combinatorial Problems with min-max-min-sum objective and applications . Mathematical Programming , 45 ( 2 ) : 361 – 372 .
   Web of Science ®Google Scholar
• Moore , James , T. and Bard , Jonathan F. 1990 . The mixed integer linear bilevel programming problem . Operations Research , 38 ( 5 ) : 911 – 921 .
   Web of Science ®Google Scholar
• Murty , K G. 1983 . Linear Programming , John Wiley and Sons .
   Google Scholar
• Önal , Hayri. 1993 . A modified simplex approach for solving bilevel linear programming problems . European Journal of Operational Research , 67 : 126 – 135 .
   Web of Science ®Google Scholar
• Schaible , Siegfried. and Ibaraki , Toshihide. 1983 . Fractional Programming . European Journal of Operational Research , 12 : 325 – 338 .
   Web of Science ®Google Scholar
• Seshan , C R. and Achary , K K. 1982 . On the Bottleneck Linear Programming Problem . European Journal of Operational Research , 9 : 347 – 352 .
   Google Scholar
• Shimuzu , K. and Aiyoshi , E. 1981 . A New Computational Method for Stackelberg and Mini-Max Problems by the use of a Penalty method . IEEE Transactions on Automatic Control , 26 ( 2 ) : 460 – 466 .
   Web of Science ®Google Scholar
• Simaan , M. and Cruz , J B. 1973 . On the Stackelberg Strategy in Non-Zero-Sum Games . Journal of Optimization Theory and Applications , 11 ( 5 ) : 533 – 555 .
   Web of Science ®Google Scholar
• Stackelberg , H.Von. 1982 . The Theory of the Market Economy , Oxford University Press .
   Google Scholar
• Tobin , R L. and Friesz , T L. 1986 . Spatial Competition Facility Location Models Definition Formulation and Solution Approach . Annals of Operations Research , 6 : 49 – 74 .
   Google Scholar
• Ünulü , Gülseren. 1987 . A Linear Bilevel Programming Algorithm based on Bicriteria Programming . Computers and Operations Research , 14 ( 2 ) : 173 – 179 .
   Google Scholar
• Wen , W P. and Bialas , W F. 1986 . The hybrid algorithm for solving the three-level linear programming problem . Computers and Operations Research , 13 ( 2 ) : 367 – 377 .
   Google Scholar
• White , D J. and Anandalingam , G. 1993 . A Penalty Function Approach for solving Bi-level Linear Programs . Journal of Global Optimization , 3 ( 2 ) : 397 – 419 .
   Google Scholar