Dual simplex method for solving fully fuzzy linear programming problems

2015 ◽  
Author(s):  
Akbar Hashemi Borzabadi ◽  
Hossein Alemy
Keyword(s):  
Linear Programming ◽  
Simplex Method ◽  
Fuzzy Linear Programming ◽  
Dual Simplex Method ◽  
Dual Simplex ◽  
Linear Programming Problems

A dual simplex method for grey linear programming problems based on duality results

2020 ◽  
Vol 10 (2) ◽  
pp. 145-157
Author(s):  
Davood Darvishi Salookolaei ◽  
Seyed Hadi Nasseri
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Simplex Method ◽  
Dual Problem ◽  
Complementary Slackness ◽  
Dual Simplex Method ◽  
Content Type ◽  
Dual Simplex ◽  
Linear Programming Problems

PurposeFor extending the common definitions and concepts of grey system theory to the optimization subject, a dual problem is proposed for the primal grey linear programming problem.Design/methodology/approachThe authors discuss the solution concepts of primal and dual of grey linear programming problems without converting them to classical linear programming problems. A numerical example is provided to illustrate the theory developed.FindingsBy using arithmetic operations between interval grey numbers, the authors prove the complementary slackness theorem for grey linear programming problem and the associated dual problem.Originality/valueComplementary slackness theorem for grey linear programming is first presented and proven. After that, a dual simplex method in grey environment is introduced and then some useful concepts are presented.

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.

scholarly journals A Note on Branch and Bound Algorithm for Integer Linear Programming

2019 ◽  
pp. 1-6
Author(s):  
Syed Inayatullah ◽  
Wajiha Riaz ◽  
Hafsa Athar Jafree ◽  
Tanveer Ahmed Siddiqi ◽  
Muhammad Imtiaz ◽  
...  
Keyword(s):  
Linear Programming ◽  
Branch And Bound ◽  
Integer Linear Programming ◽  
Simplex Method ◽  
Phase 1 ◽  
Branch And Bound Algorithm ◽  
Dual Simplex Method ◽  
Dual Simplex ◽  
Efficient Alternative ◽  
A New Technique

In branch and bound algorithm for integer linear programming the usual approach is incorporating dual simplex method to achieve feasibility for each sub-problem. Although one can also employ the phase 1 simplex method but the simplicity and easy implementation of the dual simplex method bounds the users to use it. In this paper a new technique for handling sub-problems in branch and bound method has been presented, which is an efficient alternative of dual simplex method.

scholarly journals PEMODELAN PEMROGRAMAN LINIER DENGAN KOEFISIEN FUNGSI OBJEKTIF, FUNGSI KENDALA DAN VARIABEL KEPUTUSAN BERBENTUK BILANGAN KABUR BESERTA APLIKASINYA

2019 ◽  
Vol 16 (1) ◽  
pp. 85
Author(s):  
Muhammad Amrullah
Keyword(s):  
Decision Making ◽  
Linear Programming ◽  
Simplex Method ◽  
Fuzzy Linear Programming ◽  
Rank Function ◽  
New Method ◽  
Linear Programming Problems ◽  
Paper Author

Abstrak Dalam penelitian ini penulis akan mengusulkan algoritma untuk memodelkan masalah pemrograman linear kabur dengan bilangan kabur trapesium menggunakan metode simpleks. Secara khusus dalam aplikasi teori ini adalah masalah pengambilan keputusan pemrograman linear kabur dengan menyajikan metode baru untuk menyelesaikan masalah pemrograman linier kabur dengan menggunakan fungsi ranking. Pada dasarnya, langkah-langkah dalam metode penelitian ini sama dengan dengan metode simpleks yang digunakan untuk memecahkan masalah pemrograman linier tegas.Kata kunci: Fuzzy linear programming, fungsi ranking, metode simpleks. AbstractIn this paper author shall propose an algorithm for solving fuzzy linear programming problems with trapezoidal numbers using a simplex method. In particular, an application of  this theory in decision making problems is fuzzy linear programming with a new method for solving fuzzy linear programming problems, by use of rank function. Basically, our method is similar to simplex method that was used for solving linear programming problems in crisp environment before.Keywords: Fuzzy linier programming, rank function, simplex method.

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