scholarly journals Very Large-Scale Linear Programming: A Case Study in Combining Interior Point and Simplex Methods

1991 ◽  
Author(s):  
Robert E. Bixby ◽  
John W. Gregory ◽  
Irvin J. Lustig ◽  
Roy E. Marsten ◽  
David F. Shanno
Keyword(s):  
Linear Programming ◽  
Interior Point ◽  
Large Scale ◽  
Simplex Methods

scholarly journals Very Large-Scale Linear Programming: A Case Study in Combining Interior Point and Simplex Methods

1992 ◽  
Vol 40 (5) ◽  
pp. 885-897 ◽  
Author(s):  
Robert E. Bixby ◽  
John W. Gregory ◽  
Irvin J. Lustig ◽  
Roy E. Marsten ◽  
David F. Shanno
Keyword(s):  
Linear Programming ◽  
Interior Point ◽  
Large Scale ◽  
Simplex Methods

scholarly journals Computer Oriented Interior Point Algorithm for Solving Linear Programming Problem with Application

2017 ◽  
Vol 65 (1) ◽  
pp. 41-47
Author(s):  
Farhana Ahmed Simi ◽  
Md Ainul Islam
Keyword(s):  
Linear Programming ◽  
Interior Point ◽  
Linear Programming Problem ◽  
Large Scale ◽  
Real Life ◽  
Computer Code ◽  
Interior Point Algorithm ◽  
Hand Calculation ◽  
Diet Problem ◽  
Do So

In this paper, we study the interior point algorithm for solving linear programming (LP) problem developed by Narendra Karmarkar. As interior point algorithm for LP problem involves tremendous calculations, it is quite impossible to do so by hand calculation. To fulfill the requirement we develop computer code in MATLAB for LP which is based on this algorithm procedure. To illustrate the purpose, we formulate a real life sizeable large-scale linear program for diet problem and solve it using our computer code for interior point algorithm in MATLAB. Dhaka Univ. J. Sci. 65(1): 41-47, 2017 (January)

scholarly journals Interior Point Method for Solving Fuzzy Number Linear Programming Problems Using Linear Ranking Function

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Yi-hua Zhong ◽  
Yan-lin Jia ◽  
Dandan Chen ◽  
Yan Yang
Keyword(s):  
Linear Programming ◽  
Interior Point ◽  
Fuzzy Number ◽  
Simplex Method ◽  
Interior Point Method ◽  
Large Scale ◽  
Ranking Function ◽  
Point Method ◽  
Fuzzy Linear Programming ◽  
Linear Programming Problems

Recently, various methods have been developed for solving linear programming problems with fuzzy number, such as simplex method and dual simplex method. But their computational complexities are exponential, which is not satisfactory for solving large-scale fuzzy linear programming problems, especially in the engineering field. A new method which can solve large-scale fuzzy number linear programming problems is presented in this paper, which is named a revised interior point method. Its idea is similar to that of interior point method used for solving linear programming problems in crisp environment before, but its feasible direction and step size are chosen by using trapezoidal fuzzy numbers, linear ranking function, fuzzy vector, and their operations, and its end condition is involved in linear ranking function. Their correctness and rationality are proved. Moreover, choice of the initial interior point and some factors influencing the results of this method are also discussed and analyzed. The result of algorithm analysis and example study that shows proper safety factor parameter, accuracy parameter, and initial interior point of this method may reduce iterations and they can be selected easily according to the actual needs. Finally, the method proposed in this paper is an alternative method for solving fuzzy number linear programming problems.

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