International Journal of Innovative Research in Engineering and Management
Year: 2016, Volume: 3, Issue: 4
First page : ( 314) Last page : ( 319)
Online ISSN : 2350-0557.
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Samir A. Abass , Asmaa S. Abdallah
This paper proposes a solution method for three level programming (TLP) problem with interval coefficients in both of objective functions and constraints. This method uses the concepts of tolerance membership function at each level to develop a fuzzy Max–Min decision model for generating Pareto optimal (satisfactory) solution. The first level decision maker (FLDM) specifies his/her objective functions and decisions with possible tolerances. Then, the second level decision-maker (SLDM) specifies his/her objective functions and decisions, in the view of the FLDM, with possible. Finally, the third level decision-maker (TLDM) uses the preference information for the FLDM and SLDM to solve his/her problem subject to the two upper level decision-makers restrictions. An illustrative numerical example is provided to clarify the proposed approach.
[1] Abo-Sinna, M.A., 2001. A bi-level non-linear multi-objective decision-making under Fuzziness. Journal of Operational Research Society (OPSEARCH), 38 (5), 484–495.
[2] Anandolingam, G., 1988. A mathematical programming model of decentralized multi-level system. Journal of Operational Research Society, 39, 1021–1033.
[3] Anandalingam, G. and Apprey, V., 1991. Multi-level programming and conflict resolution. European Journal of Operational Research, 51, 233–247.
[4] Bialas, W.F. and Karwan, M.H., 1984. Two-level linear programming, Management Science, 30, 1004–1020.
[5] Cassidy, R., Kirby, M. and Raike, W., 1971. Efficient distribution of resources through three levels of government. Management Science, 17, 462–473.
[6] Emam, O., El-Araby, E. M. and Belal, M. A., 2015. On Rough Multi-Level Linear Programming Problem. Information Sciences Letters, 4 (1), 41-49.
[7] Hsu, S.S., Lai, Y.J. and Stanley, L.E., 2001. Fuzzy and Multi Level Decision-Making. Springer-Verlag Ltd, London.
[8] Hu, Y.D., 1990. Applied Multiobjective Optimization. Shanghai Science and Technology Press. Shanghai. China.
[9] Inuiguchi, M. and Kume, Y., 1991. Goal Programming Problems with interval coefficients and target intervals. European Journal of Operational Research, 52, 345-360.
[10] Jiang, C., Han, X., Liu, G.R. and Liu, G.P., 2008. A nonlinear interval number programming method for uncertain optimization problems. European Journal of Operational Research, 188, 1–13.
[11] Olivera, C. and Antunes, C.H., 2007. Multiple objective Linear Programming Models with Interval Coefficients – an illustrated overview. European Journal Of Operational Research, 181, 1434-1463.
[12] Osman, M.S., Abo-Sinna, M.A., Amer, A.H. and Emam, O.E., 2004. A multi-level non-linear multi-objective decisionmaking under fuzziness. Applied Mathematics and Computation, 153, 239–252.
[13] Sakawa, M., 1993. Fuzzy Sets and Interactive MultiObjective Optimization. New York : Plenum Press.
[14] Shi, X. and Xia, H., 1997. Interactive bi-level multi-objective decision-making. Journal of Operational Research Society, 48, 943–949.
[15] Sinha, S., 2003. Fuzzy mathematical Programming applied to multi-level programming problems. Computers and Operations Research, 30, 1259-1268.
[16] Wen, U.P. and Bialas, W.F., 1986. The hybrid algorithm for solving the three-level linear programming problem. Computers and Operations Research, 13, 367–377.
Atomic Energy Authority, Nuclear Research Center, Cairo, Egypt. P.O. Box 13759, Egypt.
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