Problem solution of linear programming using dual simplex method neural network

2005 ◽  
Author(s):  
Jun-Hyeok Son ◽  
Bo-Hyeok Scriber
Keyword(s):  
Neural Network ◽  
Linear Programming ◽  
Simplex Method ◽  
Problem Solution ◽  
Dual Simplex Method ◽  
Dual Simplex

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 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 إيجاد الحل المقبول (الممكن) والأمثل لأنموذج البرمجة الخطية في ظل عدم تحقق شرطّي الإمكانية والأمثلية

2008 ◽  
Vol 14 (52) ◽  
pp. 257
Author(s):  
سرمد علوان صالح
Keyword(s):  
Linear Programming ◽  
Decision Maker ◽  
Simplex Method ◽  
Feasible Solution ◽  
Optimal Solution ◽  
Dual Simplex Method ◽  
Effective Factor ◽  
Dual Simplex

Consider the Linear Programming (LP) active & effective factor in decision maker & taker process . So that given certain goals , the Significance of (LP) in solving & evaluation the activity during one tools (General Simplex Mehtod)that the solution is Feasible &no optimal then called (Primal Simplex Method) or vice-versa then called(Dual Simplex Method).Same of cases the solution is infeasible & no optimal then using the two methods alternatively once to find the feasible solution and other to find optimal solution              

AN UPPER BOUND FOR THE NUMBER OF DIFFERENT SOLUTIONS GENERATED BY THE PRIMAL SIMPLEX METHOD WITH ANY SELECTION RULE OF ENTERING VARIABLES

2013 ◽  
Vol 30 (03) ◽  
pp. 1340012 ◽  
Author(s):  
TOMONARI KITAHARA ◽  
SHINJI MIZUNO
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Upper Bound ◽  
Linear Programming Problem ◽  
Simplex Method ◽  
Selection Rule ◽  
Dual Simplex Method ◽  
Unimodular Matrix ◽  
Dual Simplex ◽  
Pivoting Rule

Recently, Kitahara, and Mizuno derived an upper bound for the number of different solutions generated by the primal simplex method with Dantzig's (the most negative) pivoting rule. In this paper, we obtain an upper bound with any pivoting rule which chooses an entering variable whose reduced cost is negative at each iteration. The upper bound is applied to a linear programming problem with a totally unimodular matrix. We also obtain a similar upper bound for the dual simplex method.

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