A fuzzy primal simplex algorithm and its application for solving flexible linear programming problems

European Journal of Industrial Engineering

Volumn 4, Issue 3, 2010, Pages 372-389

  Nasseri, S H ^a   Ebrahimnejad, A ^b  

^a UNIVERSITY OF MAZANDARAN   (Iran)

^b ISLAMIC AZAD UNIVERSITY   (Iran)

Author keywords

Flexible linear programming; Fuzzy linear programming; Membership function; Trapezoidal fuzzy number

Indexed keywords

FUZZY SETS; MEMBERSHIP FUNCTIONS; SENSITIVITY ANALYSIS;

AUXILIARY PROBLEM; FUZZY LINEAR PROGRAMMING; FUZZY VARIABLE; ITS APPLICATIONS; LINEAR PROGRAMMING PROBLEM; SIMPLEX ALGORITHM; SIMPLEX METHODS; TRAPEZOIDAL FUZZY NUMBERS;

LINEAR PROGRAMMING;

EID: 77952271778     PISSN: 17515254     EISSN: 17515262     Source Type: Journal    
DOI: 10.1504/EJIE.2010.033336     Document Type: Article

References (22)

1. Ahuja, R.K., Magnanti, T.L. and Orlin, J.B. (1993) Network Flows: Theory, Algorithms, and Applications, Englewood Cliffs, NJ: Prentice-Hall.
2. Bellman, R.E. and Zadeh, L.A. (1970) 'Decision making in a fuzzy environment', Management Sciences, Vol.17, pp.141-164.
3. Campos, L. and Verdegay, J.L. (1989) 'Linear programming problems and ranking of fuzzy numbers', Fuzzy Sets and Systems, Vol.32, pp.1-11.
4. Ebrahimnejad, A. and Nasseri, S.H. (2009) 'Using complementary slackness property to solve linear programming with fuzzy parameters', Fuzzy Information and Engineering, Vol.3, pp.233-245.
5. Ebrahimnejad, A., Nasseri, S.H., Hosseinzadeh Lotfi, F. and Soltanifar, M. (2009) 'A primal dual method for linear programming problems with fuzzy variables', European J. Industrial Engineering, forthcoming.
6. Fortemps, P. and Roubens, M. (1996) 'Ranking and defuzzification methods based on area compensation', Fuzzy Sets and Systems, Vol.82, pp.319-330.
7. Ganesan, K. and Veeramani, P. (2006) 'Fuzzy linear programming with trapezoidal fuzzy numbers', Ann. Oper. Res., Vol.143, pp.305-315.
8. Itoh, T., Ishii, H. and Nanseki, T. (2003) 'A model of crop planning under uncertainty in agricultural management', International Journal of Production Economics, Vols. 81-82, pp.555-558.
9. Lai, Y.J. and Hwang, C.L. (1992) Fuzzy Mathematical Programming Methods and Applications, Berlin: Springer.
10. Mahdavi-Amiri, N. and Nasseri, S.H. (2006) 'Duality in fuzzy number linear programming by use of a certain linear ranking function', Applied Mathematics and Computation, Vol.180, pp.206-216.
11. Mahdavi-Amiri, N. and Nasseri, S.H. (2007) 'Duality results and a dual simplex method for linear programming problems with trapezoidal fuzzy variables', Fuzzy Sets and Systems, Vol.158, pp.1961-1978.
12. Mahdavi-Amiri, N., Nasseri, S.H. and Yazadi, A. (2009) 'Fuzzy primal simplex algorithms for solving fuzzy linear programming problems', Iranian Journal of Operational Research, Vol.1, pp.68-84.
13. Maleki, H.R. (2002) 'Ranking functions and their applications to fuzzy linear programming', Far East J. Math. Sci., Vol.4, pp.283-301.
14. Maleki, H.R., Tata, M. and Mashinchi, M. (2000) 'Linear programming with fuzzy variables', Fuzzy Sets and Systems, Vol.109, pp.21-33.
15. Miller, W.A., Leung, L.C., Azhar, T.M. and Sargent, S. (1997) 'Fuzzy production planning model for fresh tomato packing', International Journal of Production Economics, Vol.53, pp.227-238.
16. Mula, J., Poler, R. and Garcia, J.P. (2006) 'MRP with flexible constraints: a fuzzy mathematical programming approach', Fuzzy Sets and Systems, Vol.157, pp.74-97.
17. Nasseri, S.H. and Mahdavi-Amiri, N. (2009) 'Some duality results on linear programming problems with symmetric fuzzy numbers', Fuzzy Information and Engineering, Vol.1, pp.59-66.
18. Pendharkar, P.C. (1997) 'A fuzzy linear programming model for production planning in coal mines', Computers Operations Research, Vol.24, pp.1141-1149.
19. Roubens, M. (1991) 'Inequality constraints between fuzzy numbers and their use in mathematical programming', in R. Slowinski and J. Teghem (Eds.) Stochastic Versus Fuzzy Approaches to Multi-Objective Mathematical Programming Under Uncertainty, Dordrecht: Kluwer Academic Publishers, pp.321-330.
20. Tanaka, H., Okuda, T. and Asai, K. (1974) 'On fuzzy mathematical programming', The Journal of Cybernetics, Vol.3, pp.37-46.
21. Yager, R.R. (1981) 'A procedure for ordering fuzzy subsets of the unit interval', Information Sciences, Vol.24, pp.143-161.
22. Zimmermann, H.J. (1985) 'Applications of fuzzy sets theory to mathematical programming', Information Sciences, Vol.36, pp.29-58.