Sensitivity Analysis on Linear Programming Problems with Trapezoidal Fuzzy Variables

2011 ◽  
Vol 2 (2) ◽  
pp. 22-39 ◽  
Author(s):  
Seyed Hadi Nasseri ◽  
Ali Ebrahimnejad
Keyword(s):  
Linear Programming ◽  
Simplex Algorithm ◽  
Fuzzy Data ◽  
Fuzzy Variables ◽  
Fuzzy Environment ◽  
Tableau Algorithm ◽  
Dual Simplex ◽  
Linear Programming Problems ◽  
Simplex Tableau ◽  
Dual Simplex Algorithm

In the real word, there are many problems which have linear programming models and sometimes it is necessary to formulate these models with parameters of uncertainty. Many numbers from these problems are linear programming problems with fuzzy variables. Some authors considered these problems and have developed various methods for solving these problems. Recently, Mahdavi-Amiri and Nasseri (2007) considered linear programming problems with trapezoidal fuzzy data and/or variables and stated a fuzzy simplex algorithm to solve these problems. Moreover, they developed the duality results in fuzzy environment and presented a dual simplex algorithm for solving linear programming problems with trapezoidal fuzzy variables. Here, the authors show that this presented dual simplex algorithm directly using the primal simplex tableau algorithm tenders the capability for sensitivity (or post optimality) analysis using primal simplex tableaus.

Sensitivity Analysis on Linear Programming Problems with Trapezoidal Fuzzy Variables

2013 ◽  
pp. 64-82
Author(s):  
Seyed Hadi Nasseri ◽  
Ali Ebrahimnejad
Keyword(s):  
Linear Programming ◽  
Simplex Algorithm ◽  
Programming Models ◽  
Fuzzy Data ◽  
Fuzzy Variables ◽  
Fuzzy Environment ◽  
Dual Simplex ◽  
Linear Programming Problems ◽  
Simplex Tableau ◽  
Dual Simplex Algorithm

In the real word, there are many problems which have linear programming models and sometimes it is necessary to formulate these models with parameters of uncertainty. Many numbers from these problems are linear programming problems with fuzzy variables. Some authors considered these problems and have developed various methods for solving these problems. Recently, Mahdavi-Amiri and Nasseri (2007) considered linear programming problems with trapezoidal fuzzy data and/or variables and stated a fuzzy simplex algorithm to solve these problems. Moreover, they developed the duality results in fuzzy environment and presented a dual simplex algorithm for solving linear programming problems with trapezoidal fuzzy variables. Here, the authors show that this presented dual simplex algorithm directly using the primal simplex tableau algorithm tenders the capability for sensitivity (or post optimality) analysis using primal simplex tableaus.

Bounded Primal Simplex Algorithm for Bounded Linear Programming with Fuzzy Cost Coefficients

2013 ◽  
pp. 40-63
Author(s):  
Ali Ebrahimnejad ◽  
Seyed Hadi Nasseri ◽  
Sayyed Mehdi Mansourzadeh
Keyword(s):  
Linear Programming ◽  
Auxiliary Problem ◽  
Simplex Algorithm ◽  
Upper Bounds ◽  
Bounded Linear ◽  
Fuzzy Variables ◽  
Decision Variables ◽  
Bounded Variables ◽  
Linear Programming Problems ◽  
Fuzzy Cost

In most practical problems of linear programming problems with fuzzy cost coefficients, some or all variables are restricted to lie within lower and upper bounds. In this paper, the authors propose a new method for solving such problems called the bounded fuzzy primal simplex algorithm. Some researchers used the linear programming problem with fuzzy cost coefficients as an auxiliary problem for solving linear programming with fuzzy variables, but their method is not efficient when the decision variables are bounded variables in the auxiliary problem. In this paper the authors introduce an efficient approach to overcome this shortcoming. The bounded fuzzy primal simplex algorithm starts with a primal feasible basis and moves towards attaining primal optimality while maintaining primal feasibility throughout. This algorithm will be useful for sensitivity analysis using primal simplex tableaus.

scholarly journals A Proposed Technique for Solving Linear Fractional Bounded Variable Problems

2012 ◽  
Vol 60 (2) ◽  
pp. 223-230
Author(s):  
H.K. Das ◽  
M. Babul Hasan
Keyword(s):  
Linear Programming ◽  
Objective Function ◽  
Programming Language ◽  
Simplex Algorithm ◽  
Computational Effort ◽  
New Method ◽  
Bounded Variables ◽  
Primal Dual ◽  
Dual Simplex ◽  
Dual Simplex Algorithm

In this paper, a new method is proposed for solving the problem in which the objective function is a linear fractional Bounded Variable (LFBV) function, where the constraints functions are in the form of linear inequalities and the variables are bounded. The proposed method mainly based upon the primal dual simplex algorithm. The Linear Programming Bounded Variables (LPBV) algorithm is extended to solve Linear Fractional Bounded Variables (LFBV).The advantages of LFBV algorithm are simplicity of implementation and less computational effort. We also compare our result with programming language MATHEMATICA.DOI: http://dx.doi.org/10.3329/dujs.v60i2.11522 Dhaka Univ. J. Sci. 60(2): 223-230, 2012 (July) 

Bounded Primal Simplex Algorithm for Bounded Linear Programming with Fuzzy Cost Coefficients

2011 ◽  
Vol 2 (1) ◽  
pp. 96-120 ◽  
Author(s):  
Ali Ebrahimnejad ◽  
Seyed Hadi Nasseri ◽  
Sayyed Mehdi Mansourzadeh
Keyword(s):  
Linear Programming ◽  
Auxiliary Problem ◽  
Simplex Algorithm ◽  
Lower And Upper Bounds ◽  
Bounded Linear ◽  
Fuzzy Variables ◽  
Decision Variables ◽  
Bounded Variables ◽  
Linear Programming Problems ◽  
Fuzzy Cost

In most practical problems of linear programming problems with fuzzy cost coefficients, some or all variables are restricted to lie within lower and upper bounds. In this paper, the authors propose a new method for solving such problems called the bounded fuzzy primal simplex algorithm. Some researchers used the linear programming problem with fuzzy cost coefficients as an auxiliary problem for solving linear programming with fuzzy variables, but their method is not efficient when the decision variables are bounded variables in the auxiliary problem. In this paper the authors introduce an efficient approach to overcome this shortcoming. The bounded fuzzy primal simplex algorithm starts with a primal feasible basis and moves towards attaining primal optimality while maintaining primal feasibility throughout. This algorithm will be useful for sensitivity analysis using primal simplex tableaus.

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