DOI:
https://doi.org/10.14483/23448393.3830Published:
2011-12-18Issue:
Vol. 16 No. 2 (2011): July - DecemberSection:
ArticleAlgoritmo iterativo para la planeación de la producción mixta basado en la función acumulativa de pertenencia
An iterative algorithm for fuzzy mixed production planning based on the cumulative membership function
Keywords:
Fuzzy linear programming, Cumulative membership function, Production planning. (en).Keywords:
Programación Lineal Difusa, Función Acumulativa de Pertenencia, Planeación de la Producción (es).Downloads
Abstract (es)
Este artículo presenta una aplicación de un algoritmo nuevo para problemas de programación lineal difusa (FLP) con restricciones y coeficientes difusos, con restricciones difusas lineales y coeficientes tecnológicos difusos con funciones de pertenencia no-lineales.
El modelo propuesto usa un método iterativo que encuentra una solución estable aproblems con parámetros difusos en ambos lados de las restricciones de un problema de programación lineal. El algoritmo se basa en el método de restricciones suaves propuesto por Zimmermann, combinado con una rutina iterativa que llega a soluciones óptmas únicas.
Abstract (en)
This paper shows an application of a novel algorithm for Fuzzy Linear Programming (FLP) problems with both fuzzy technological coefficients and constraints, which deals with any kind of fuzzy membership functions for technological parameters and fuzzy linear constraints.
The presented approach uses an iterative algorithm which finds stable solutions to problems with fuzzy parameter sinboth sides of an FLP problem. The algorithm is based on the soft constraints method proposed by Zimmermann combined with an iterative procedure which gets a single optimal solution.
References
María Angeles Gil, Miguel López-Díaz, and Dan A. Ralescu. Overview on the development of fuzzy random variables. Fuzzy Sets and Systems, 157(16):2546–2557, 2007.
S. Chanas, M. Delgado, J.L. Verdegay, and M.A. Vila. Interval and fuzzy extensions of classical transportation problems. Transportation Planning and Technology, 17:202–218, 1993.
Juan Carlos Figueroa. Linear programming with interval type-2 fuzzy right hand side parameters. In 2008 Annual Meeting of the IEEE North American Fuzzy Information Processing Society (NAFIPS), 2008.
Juan Carlos Figueroa. Solving fuzzy linear programming problems with interval type-2 RHS. In 2009 Conference on Systems, Man and Cybernetics, pages 1–6. IEEE, 2009.
Juan Carlos Figueroa. An iterative procedure for fuzzy linear programming problems. In 2011 Annual Meeting of the North American Fuzzy Information Processing Society (NAFIPS), pages 1–6. IEEE, 2011.
Juan Carlos Figueroa and Cesar Amilcar López. Linear programming with fuzzy joint parameters: A cumulative membership function approach. In 2008 Annual Meeting of the IEEE North American Fuzzy Information Processing Society (NAFIPS), 2008.
Juan Carlos Figueroa and Cesar Amilcar López. Pseudo-optimal solutions of FLP problems by using the cumulative membership function. In 2009 Annual Meeting of the North American Fuzzy Information Processing Society (NAFIPS), volume 28, pages 1–6. IEEE, 2009.
Juan Carlos Figueroa, Yamile Olarte, and Freddy Camargo. Linear programming with fuzzy joint parameters: An iterative method. In 2010 Conference on Systems, Man and Cybernetics, pages 1–6. IEEE, 2010.
M. Gen, Y. Tsujimura, and K. Ida. Method for solving multiobjective aggregate production planning problem with fuzzy parameters. Computers & Industrial Engineering, 23:117–120, 1992.
A. Ghodousiana and E. Khorram. Solving a linear programming problem with the convex combination of the max-min and the max-average fuzzy relation equations. Applied Mathematics and Computation, 180(1):411–418, 2006.
M. Inuiguchi and M. Sakawa. Possible and necessary optimality tests in possibilistic linear programming problems. Fuzzy Sets and Systems, 67:29–46, 1994.
M. Inuiguchi and M. Sakawa. A possibilistic linear program is equivalent to a stochastic linear program in a special case. Fuzzy Sets and Systems, 76(1):309–317, 1995.
Masahiro Inuiguchi and Jaroslav Ram´ık. Possibilistic linear programming: a brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem. Fuzzy Sets and Systems, 111:3–28, 2000.
R. Baker Kearfott and Vladik Kreinovich. Beyond convex? global optimization is feasible only for convex objective functions: A theorem. Journal of Global Optimization, 33(4):617–624, 2005.
Y.H. Lee, S.H. Kim, and C. Moon. Production-distribution planning in supply chain using a hybrid approach. Production Planning & Control, 13:35–46, 2002.
Weldon A. Lodwick and K. A. Bachman. Solving Large-Scale Fuzzy and Possibilistic Optmization Problems. Fuzzy Optimization and Decision Making, 4:257–78, 2005.
N. Mahdavi-Amiri and S.H. Nasseri. Duality results and a dual simplex method for linear programming problems with trapezoidal fuzzy variables. Fuzzy Sets and Systems, 158(17):1961–1978, 2007.
J. Mula, R. Poler, and J.P. Garc´ıa. MRP with flexible constraints: a fuzzy mathematical programming approach. Fuzzy Sets and Systems, 157:74–97, 2006.
D. Peidro, J. Mula, and R. Poler. Supply chain planning under uncertainty: a fuzzy linear programming approach. 2007 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), 1:1–6, 2007.
D. Peidro, J. Mula, R. Poler, and J.L. Verdegay. Fuzzy optimization for supply chain planning under supply, demand and process uncertainties. Fuzzy Sets and Systems, 160:2640–2657, 2009.
Guu Sy-Ming and Wu Yan-Kuen. Minimizing a linear objective function with fuzzy relation equation constraints. Fuzzy Optimiza-tion and Decision Making, 1(4):347, 2002.
H. Tanaka and K. Asai. Fuzzy Solution in Fuzzy Linear Programming Problems. IEEE Transactions on Systems, Man and Cybernetics., 14:325–328, 1984.
H. Tanaka, K. Asai, and T. Okuda. On Fuzzy Mathematical Programming. Journal of Cybernetics., 3:37–46, 1974.
H. J. Zimmermann. Fuzzy programming and Linear Programming with several objective functions. Fuzzy Sets and Systems, 1(1):45–55, 1978.
H. J. Zimmermann and Robert Fuller. Fuzzy Reasoning for solving fuzzy Mathematical Programming Problems. Fuzzy Sets and Systems, 60(1):121–133, 1993.
How to Cite
APA
ACM
ACS
ABNT
Chicago
Harvard
IEEE
MLA
Turabian
Vancouver
Download Citation
License
From the edition of the V23N3 of year 2018 forward, the Creative Commons License "Attribution-Non-Commercial - No Derivative Works " is changed to the following:
Attribution - Non-Commercial - Share the same: this license allows others to distribute, remix, retouch, and create from your work in a non-commercial way, as long as they give you credit and license their new creations under the same conditions.
2.jpg)
