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.

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 Self-Regulating Artificial-Free Linear Programming Solver Using a Jump and Simplex Method

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 356
Author(s):  
Rujira Visuthirattanamanee ◽  
Krung Sinapiromsaran ◽  
Aua-aree Boonperm
Keyword(s):  
Linear Programming ◽  
Simplex Method ◽  
Phase 1 ◽  
Simplex Algorithm ◽  
Linear Programs ◽  
Feasible Point ◽  
Optimal Point ◽  
Dual Simplex Method ◽  
Feasible Points ◽  
Initial Starting

An enthusiastic artificial-free linear programming method based on a sequence of jumps and the simplex method is proposed in this paper. It performs in three phases. Starting with phase 1, it guarantees the existence of a feasible point by relaxing all non-acute constraints. With this initial starting feasible point, in phase 2, it sequentially jumps to the improved objective feasible points. The last phase reinstates the rest of the non-acute constraints and uses the dual simplex method to find the optimal point. The computation results show that this method is more efficient than the standard simplex method and the artificial-free simplex algorithm based on the non-acute constraint relaxation for 41 netlib problems and 280 simulated linear programs.

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