Solving linear fractional multi-level programs

• Autorzy: Bhargava S.

Identyfikatory

DOI

10.5277/ord140101

• Języki publikacji: EN

Abstrakty

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.

Słowa kluczowe

EN

multilevel; linear fractional; quasiconcave; quasiconvex, Kth-best

• Wydawca: Oficyna Wydawnicza Politechniki Wrocławskiej
• Czasopismo: Operations Research and Decisions
• Rocznik: 2014
• Tom: Vol. 24, No. 1
• Strony: 5--21
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Bhargava S.

• Department of Mathematics, B.S.A. College, Mathura (U.P), India

Bibliografia

• [1] BARD J.F., FALK J.E., An explicit solution to the multilevel programming problem, Computers and Operations Research, 1982, 9, 77–100.
• [2] 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.
• [3] CALVETE H.I., GALE C., On the quasiconcave bilevel programming problem, Journal of Optimization Theory and Applications, 1998, 98 (3), 613–622.
• [4] CALVETE H.I., GALE C., Solving linear fractional bilevel programs, Operations Research Letters, 2004, 32, 143–151.
• [5] CHARNES A., COOPER W.W., Programming with linear fractionals, Naval Research Logistics Quarterly,1962, 9, 181–186.
• [6] DANAO R.A., Some properties of explicitly quasiconcave functions, Journal of Optimization Theory and Applications, 1992, 74 (3), 457–468.
• [7] DEMPE S., Foundations of Bilevel Programming, Kluwer Academic Publishers, Dordrecht 2002.
• [8] KONNO H., KUNO T., Multiplicative programming problems, [in:] Handbook of Global Optimization,E. Horst, P.M. Pardalos (Eds.), Kluwer Academic Publishers, Dordrecht 1995.
• [9] 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.
• [10] LIU Y., MEI J., Optimality conditions in bilevel multi-objective programming problems, Southeast Asian Bulletin of Mathematics, 2009, 33, 79–87.
• [11] MARTOS B., Nonlinear programming. Theory and Methods, North-Holland Publishing Company,Amsterdam 1975.
• [12] MISHRA S., Weighting method for bilevel linear fractional programming problems, European Journal of Operational Research, 2007, 183 (1), 296–302.
• [13] 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.