Abstract
In this paper, we propose an alternate technique based on fuzzy goal programming approach for solving multi-level multi objective linear programming problem (ML-MOLPP) which is simpler and requires less computational works than that of proposed algorithm by Baky, I. A. (Applied Mathematical Modelling, 34(2010), 2377–2387). In formulation of FGP model each objective functions at each level are transformed into fuzzy goals. Suitable membership function for every fuzzily described transformed objective functions at each level as well as the control vectors of each level decision makers are defined by determining individual optimal solution of each objective function at each of the decision making level. Then FGP approach is used for achieving highest degree of each of these membership goals by minimizing the sum of negative deviational variables. To avoid decision deadlock, solution preferences by the decision makers at each level are not taken into account of proposed FGP technique. The aim of this paper is to present simple technique to obtain compromise optimal solution of ML-MOLP problems. A comparative analysis based on numerical examples is also carried out to show similarity between two solution methodologies.
References
Bellmann, R.E.: Dynamic Programming. Princeton University Press, Princeton (1957)
Anandilingam, G.: A mathematical programming model of decentralized multi level system. J. Oper. Res. Soc. 39(11), 1021–1033 (1988)
Anandilingam, G., Apprey, V.: Multi level programming and conflicting resolution. Eur. J. Oper. Res. 51, 233–247 (1991)
Arora, S.R., Gupta, R.: Interactive fuzzy goal programming approach for bilevel programming problem. Eur. J. Oper. Res. 194, 368–376 (2009)
Bard, J.F.: Practical Bi-Level Optimization: Algorithm and Application. Kluwer Academic Publisher, The Netherlands (1998)
Lai, Y.J.: Hierarchical optimization: a satisfactory solution. Fuzzy Set Syst. 77, 321–335 (1996)
Shih, H.S., Lai, Y.J., Lee, E.S.: Fuzzy approach for multi-level programming problems. Comput. Oper. Res. 23(1), 773–791 (1983)
Shih, H.S., Lee, E.S.: Compensatory fuzzy multiple decision making. Fuzzy Set Syst. 14, 71–87 (2000)
Sinha, S.: Fuzzy mathematical approach to multi level programming problems. Comput. Oper. Res. 30, 1259–1268 (2003)
Sinha, S.: Fuzzy programming approach to multi level programming problems. Fuzzy Set Syst. 136, 189–202 (2003)
Mohamed, R.H.: The relationship between goal programming and fuzzy programming. Fuzzy Set Syst. 89, 215–222 (1997)
Pal, B.B., Moitra, B.N., Malik, U.: A goal programming procedure for fuzzy multiobjective linear fractional programming problems. Fuzzy Set Syst. 139(2), 395–405 (2003)
Moitra, B.N., Pal, B.B.: A fuzzy goal programming approach for solving bilevel programming problems. In: Pal, N.R., Sugeno, M. (eds.) AFSS 2002, lecture notes in artificial intelligence, 2275, pp. 91–98. Springer, Berlin (2002)
Pal, B.B., Moitra, B.N.: A fuzzy goal programming procedure for solving quadratic bilevel programming problems. Int. J. Intell. Syst. 18(5), 529–540 (2003)
Pramanik, S., Roy, T.K.: Fuzzy goal programming approach to multi level programming problems. Eur. J. Oper. Res. 176, 1151–1166 (2007)
Lachhwani, K., Poonia, M.P.: Mathematical solution of multi level fractional programming problem with fuzzy goal programming approach. J Ind. Eng. Int. 8, 12 (2012). doi:10.1186/2251-712x-8-16
Baky, I.A.: Solving multi-level multi-objective linear programming problems through fuzzy goal programming approach. Appl. Math. Model. 34, 2377–2387 (2010)
Abo-Sinha, M.A., Baky, I.A.: Interactive balance space approach for solving multi-level multi-objective programming problems. Inf. Sci. 177, 3397–3410 (2007)
Baky, I.A.: Fuzzy goal programming algorithm for solving decentralized bilevel multiobjective programming problems. Fuzzy Set Syst. 160, 2701–2710 (2009)
Zeleny, M.: Multiple Criteria Decision Making. McGraw-Hill Book Company, New York (1982)
Charnes, A., Cooper, W.W.: Programming with linear fractional functional. Nov. Res. Logistics Quart 9, 181–186 (1962)
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Lachhwani, K. On solving multi-level multi objective linear programming problems through fuzzy goal programming approach. OPSEARCH 51, 624–637 (2014). https://doi.org/10.1007/s12597-013-0157-y
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DOI: https://doi.org/10.1007/s12597-013-0157-y