PL EN


2014 | 24 | 1 | 5-21
Article title

Solving linear fractional multilevel programs

Selected contents from this journal
Title variants
Languages of publication
EN
Abstracts
EN
The linear fractional multilevel programming (LFMP) problem has been studied and it has been proved that an optimal solution to this problem occurs at a boundary feasible extreme point. Hence the Kth-best algorithm can be proposed to solve the problem. This property can be applied to quasiconcave multilevel problems provided that the first (n – 1) level objective functions are explicitly quasimonotonic, otherwise it cannot be proved that there exists a boundary feasible extreme point that solves the LFMP problem.
Year
Volume
24
Issue
1
Pages
5-21
Physical description
Contributors
  • Department of Mathematics, B.S.A. College, Mathura (U.P), India
References
  • BARD J.F., FALK J.E., An explicit solution to the multilevel programming problem, Computers and Operations Research, 1982, 9, 77–100.
  • BIALAS W.F., KARWAN M.H., Multilevel Linear Programming, Research Report No. 78-1, Department of Industrial Engineering, State University of New York, Buffalo, New York 1978.
  • CALVETE H.I., GALE C., On the quasiconcave bilevel programming problem, Journal of Optimization Theory and Applications, 1998, 98 (3), 613–622.
  • CALVETE H.I., GALE C., Solving linear fractional bilevel programs, Operations Research Letters, 2004, 32, 143–151.
  • CHARNES A., COOPER W.W., Programming with linear fractionals, Naval Research Logistics Quarterly, 1962, 9, 181–186.
  • DANAO R.A., Some properties of explicitly quasiconcave functions, Journal of Optimization Theory and Applications, 1992, 74 (3), 457–468.
  • DEMPE S., Foundations of Bilevel Programming, Kluwer Academic Publishers, Dordrecht 2002.
  • KONNO H., KUNO T., Multiplicative programming problems, [in:] Handbook of Global Optimization, E. Horst, P.M. Pardalos (Eds.), Kluwer Academic Publishers, Dordrecht 1995.
  • LIU Y.H., HART S.M., Characterizing an optimal solution to the linear bilevel programming problem, European Journal of Operational Research, 1994, 73 (1), 164–166.
  • LIU Y., MEI J., Optimality conditions in bilevel multi-objective programming problems, Southeast Asian Bulletin of Mathematics, 2009, 33, 79–87.
  • MARTOS B., Nonlinear programming. Theory and Methods, North-Holland Publishing Company, Amsterdam 1975.
  • MISHRA S., Weighting method for bilevel linear fractional programming problems, European Journal of Operational Research, 2007, 183 (1), 296–302.
  • WANG G., JIANG B., ZHU K., WAN Z., Global convergent algorithm for the bilevel linear fractional- -linear programming based on modified convex simplex method, Journal of Systems Engineering and Electronics, 2010, 21 (2), 239–243
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.desklight-052dcee2-c344-42d3-84ab-9da70f17a6e9
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.