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Fuzzy goal programming approach to multilevel programming problems. (English) Zbl 1110.90084

Summary: The purpose of this paper is to propose a procedure for solving multilevel programming problems in a large hierarchical decentralized organization through linear fuzzy goal programming approach. Here, the tolerance membership functions for the fuzzily described objectives of all levels as well as the control vectors of the higher level decision makers are defined by determining individual optimal solution of each of the level decision makers. Since the objectives are potentially conflicting in nature, a possible relaxation of the higher level decision is considered for avoiding decision deadlock. Then fuzzy goal programming approach is used for achieving highest degree of each of the membership goals by minimizing negative deviational variables. Sensitivity analysis with variation of tolerance values on decision vectors is performed to present how the solution is sensitive to the change of tolerance values. The efficiency of our concept is ascertained by comparing results with other fuzzy programming approaches.

MSC:

90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
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[1] Anandalingam, G., A mathematical programming model of decentralized multi-level systems, Journal of the operational research society, 39, 11, 1021-1033, (1988) · Zbl 0657.90061
[2] Anandalingam, G.; Apprey, V., Multilevel programming and conflicting resolution, European journal of operational research, 51, 233-247, (1991) · Zbl 0743.90127
[3] Bard, J.F., An efficient point algorithm for a linear two-stage optimization problem, Operations research, 31, 670-684, (1983) · Zbl 0525.90086
[4] Bard, J.F., Coordination of a multidivisional organization through two levels of management, Omega, 11, 457-468, (1983)
[5] Bard, J.F., Optimality conditions for the bilevel programming problem, Naval research logistics quarterly, 31, 13-26, (1984) · Zbl 0537.90087
[6] Bard, J.F.; Falk, J.E., An explicit solution to the multi-level programming problems, Computers and operations research, 9, 77-100, (1982)
[7] Bard, J.F.; Plummer, J.; Sourie, J.C., A bilevel programming approach to determining tax credits for biofuel production, European journal of operational research, 120, 30-46, (2000) · Zbl 0976.90099
[8] Ben-Ayed, O., Bilevel linear programming, Computers and operations research, 20, 485-501, (1993) · Zbl 0783.90068
[9] Ben-Ayed, O.; Blair, C.E., Computational difficulties of bilevel linear programming, Operations research, 38, 556-560, (1990) · Zbl 0708.90052
[10] Bialas, W.F.; Karwan, M.H., On two-level linear optimization, IEEE transaction automatic control, 27, 211-214, (1982) · Zbl 0487.90005
[11] Bialas, W.F.; Karwan, M.H., Two level linear programming, Management science, 30, 1004-1020, (1984) · Zbl 0559.90053
[12] Biswas, A.; Pal, B.B., Application of fuzzy goal programming technique to land use planning in agricultural systems, Omega, 33, 391-398, (2005)
[13] Burton, R.M., The multilevel approach to organizational issues of the firm, Omega, 5, 457-468, (1977)
[14] Candler, W.; Townsley, R., A linear bilevel programming problems, Computers and operations research, 9, 59-76, (1982)
[15] Charness, A.; Cooper, W.W., Management models and industrial applications of linear programming, (1961), Wiley New York · Zbl 0107.37004
[16] Dyson, R.G., Maximum programming, fuzzy linear programming and multi-criteria decision making, Journal of operational research society, 31, 3, 263-267, (1988) · Zbl 0436.90106
[17] Hannan, E.L., On fuzzy goal programming, Decision sciences, 12, 522-531, (1981)
[18] J.P. Ignizio, Goal Programming and Extensions, Lexington, Massachusetts, D.C. Health, 1976.
[19] Ignizio, J.P., On the (re)discovery of fuzzy goal programming, Decision sciences, 13, 331-336, (1982)
[20] Lai, Y.J., Hierarchical optimization: A satisfactory solution, Fuzzy sets and systems, 77, 321-335, (1996) · Zbl 0869.90042
[21] Lai, Y.J.; Hwang, C.L., Fuzzy mathematical programming—methods and applications, (1993), Springer Berlin
[22] Mohamed, R.H., The relationship between goal programming and fuzzy programming, Fuzzy sets and systems, 89, 215-222, (1997)
[23] Narashimhan, R., Goal programming in a fuzzy environment, Decision sciences, 11, 325-336, (1980)
[24] Romero, C., Handbook of critical issues in goal programming, (1991), Pergamon Press Oxford · Zbl 0817.68034
[25] Sakawa, M.; Nishizaki, I.; Hitaka, M., Interactive fuzzy programming for multi-level 0-1 programming through genetic algorithms, European journal of operational research, 144, 3, 580-588, (1999) · Zbl 0938.90077
[26] Sakawa, M.; Nishizaki, I.; Uemura, Y., Interactive fuzzy programming for multi-level linear programming problems with fuzzy parameters, Fuzzy sets and systems, 109, 1, 3-19, (2000) · Zbl 0956.90063
[27] Shi, X.; Xia, H., Interactive bilevel multiobjective decision making, Journal of the operational research society, 48, 943-949, (1997) · Zbl 0892.90200
[28] Shih, H.S.; Lai, Y.J.; Lee, E.S., Fuzzy approach for multi-level programming problems, Computers and operations research, 23, 73-91, (1996) · Zbl 0838.90140
[29] Shih, H.S.; Lee, E.S., Compensatory fuzzy multiple level decision making, Fuzzy sets and systems, 14, 71-87, (2000) · Zbl 0963.91029
[30] Sinha, S., Fuzzy mathematical programming applied to multi-level programming problems, Computers and operations research, 30, 1259-1268, (2003) · Zbl 1036.90077
[31] Sinha, S., Fuzzy programming approach to multi-level programming problems, Fuzzy sets and systems, 136, 189-202, (2003) · Zbl 1013.90143
[32] Tiwari, R.N.; Dharmar, S.; Rao, J.R., Fuzzy goal programming—an additive model, Fuzzy sets and systems, 24, 27-34, (1987) · Zbl 0627.90073
[33] Wen, U.P.; Hsu, S.T., Efficient solution for the linear bilevel programming problem, European journal of operational research, 62, 354-362, (1991)
[34] Wen, U.P.; Hsu, S.T., Linear bilevel programming problems—a review, Journal of the operational research society, 42, 125-133, (1991)
[35] White, D.J.; Anandalingam, G., A penalty function approach for solving bilevel linear programs, Journal of global optimization, 3, 393-419, (1993) · Zbl 0791.90047
[36] Yu, P.L., A class of solutions for group decision problems, Management science, 19, 936-946, (1973) · Zbl 0264.90008
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