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An iterative goal programming approach for solving fuzzy multiobjective integer linear programming problems. (English) Zbl 1082.65542
Summary: This paper presents an iterative goal programming approach for solving fuzzy multiobjective integer linear programming problems. These problems involve fuzzy parameters in the right-hand side of the constraints. The concept of a level set of these fuzzy parameters is introduced with the definition of their membership function. A solution algorithm is described in sequential steps to solve the formulated model. The suggested approach is mainly based on the iterative goal programming technique together with Gomory cuts. An illustrative numerical example is given to clarify the theory and the solution algorithm.

MSC:
65K05Mathematical programming (numerical methods)
90C29Multi-objective programming; goal programming
90C05Linear programming
90C10Integer programming
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References:
[1] Balinski, M.: An algorithm for finding all vertices of convex polyhedral sets. Journal of the society of industrial and applied mathematics 1, 72-88 (1961) · Zbl 0108.33203
[2] Charnes, A.; Cooper, W. W.: Management models and industrial applications of linear programming. (1961) · Zbl 0107.37004
[3] Dauer, J. P.; Krueger, R. J.: An iterative approach to goal programming. Operational research quarterly 28, 671-681 (1977) · Zbl 0373.90062
[4] Dubois, D.; Prade, H.: Fuzzy sets and systems. Theory and applications (1980) · Zbl 0444.94049
[5] J.B. Hughes, O.M. Saad, Stability sets for integer linear multiobjective and goal programming, Paper presented at EuroX, The 10th European Conference on Operational Research, Belgrade, Yugoslavia, June 27-30, 1989.
[6] Ignizio, J. P.: GP-GN: an approach to certain large scale multiobjective integer programming models. Large scale systems 4, 177-188 (1983) · Zbl 0517.90071
[7] Ignizio, J. P.: The determination of a subset of efficient solutions via goal programming. Computers and operations research 8, 9-16 (1981)
[8] Ignizio, J. P.: Goal programming and extensions. (1976)
[9] Klein, D.; Holm, S.: Integer programming post-optimal analysis with cutting-planes. Management science 25, No. 1, 64-72 (1979) · Zbl 0442.90067
[10] Lee, S. M.; Morris, R. L.: Integer goal programming methods. TIMS studies in the management sciences 6, 273-289 (1977)
[11] Osman, M. S.; Awad, M. M.; Saad, O. M.: Stability in multiobjective integer programming. AMSE review 9, No. 3, 13-22 (1989)
[12] Saad, O. M.; Sharif, W. H.: Stability set for integer linear goal programming. Applied mathematics and computation 153, No. 3, 743-750 (2004) · Zbl 1048.65064
[13] Sasaki, M.; Gen, M.: A method for solving fuzzy multiobjective decision making problems by interactive sequential goal programming. Transactions of the institute of electronics, information and communication engineers 75-A, No. 10, 1590-1995 (1992)
[14] Sasaki, M.; Gen, M.; Ida, K.: Interactive sequential fuzzy goal programming. Computers and industrial engineering 19, No. 1-4, 567-571 (1990)
[15] Steuer, R.: S.ziontsvector-maximum gradient cone contraction techniques, multiple criteria problem solving. Vector-maximum gradient cone contraction techniques, multiple criteria problem solving (1978) · Zbl 0381.90103
[16] Taha, H. A.: Integer programming: theory, applications, and computations. (1975) · Zbl 0316.90042
[17] Zadeh, L.; Bellman, R.: Decision making in a fuzzy environment. Management sciences 17, 141-164 (1970) · Zbl 0224.90032
[18] Zimmermann, H. J.: Fuzzy programming and linear programming with several objective functions. Fuzzy sets and systems 1, 45-55 (1978) · Zbl 0364.90065