An Extension of Karmarkar’s Algorithm for Bounded Linear Programming Problems

1988 ◽  
pp. 88-95
Author(s):  
Angelika Steger
Keyword(s):  
Linear Programming ◽  
Karmarkar's Algorithm ◽  
Bounded Linear ◽  
Linear Programming Problems ◽  
Karmarkar’S Algorithm

An implementation of Karmarkar's algorithm for linear programming

1989 ◽  
Vol 44 (1-3) ◽  
pp. 297-335 ◽  
Author(s):  
Ilan Adler ◽  
Mauricio G. C. Resende ◽  
Geraldo Veiga ◽  
Narendra Karmarkar
Keyword(s):  
Linear Programming ◽  
Karmarkar's Algorithm ◽  
Karmarkar’S Algorithm

Some experiments with Karmarkar's algorithm for linear programming

Optimization ◽  
1988 ◽  
Vol 19 (5) ◽  
pp. 653-664 ◽  
Author(s):  
R. Hettich ◽  
G. Margraff
Keyword(s):  
Linear Programming ◽  
Karmarkar's Algorithm ◽  
Karmarkar’S Algorithm

BOUNDED LINEAR PROGRAMS WITH TRAPEZOIDAL FUZZY NUMBERS

2010 ◽  
Vol 18 (03) ◽  
pp. 269-286 ◽  
Author(s):  
ALI EBRAHIMNEJAD ◽  
SEYED HADI NASSERI ◽  
FARHAD HOSSEINZADEH LOTFI
Keyword(s):  
Linear Programming ◽  
Fuzzy Numbers ◽  
Natural Extension ◽  
Upper Bounds ◽  
Linear Programs ◽  
Bounded Linear ◽  
New Approach ◽  
Trapezoidal Fuzzy Numbers ◽  
Linear Programming Problems ◽  
Crisp Linear Programming

Recently Ganesan and Veeramani introduced a new approach for solving a kind of linear programming problems involving symmetric trapezoidal fuzzy numbers without converting them to the crisp linear programming problems. But their approach is not efficient for situations in which some or all variables are restricted to lie within fuzzy lower and fuzzy upper bounds. In this paper, by a natural extension of their approach we obtain some new results leading to a new method to overcome this shortcoming.

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.

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