Solving (CGLP)k on the LP Simplex Tableau

2018 ◽  
pp. 107-119
Author(s):  
Egon Balas
Keyword(s):  
Simplex Tableau

Sensitivity Analysis on Linear Programming Problems with Trapezoidal Fuzzy Variables

2013 ◽  
pp. 64-82
Author(s):  
Seyed Hadi Nasseri ◽  
Ali Ebrahimnejad
Keyword(s):  
Linear Programming ◽  
Simplex Algorithm ◽  
Programming Models ◽  
Fuzzy Data ◽  
Fuzzy Variables ◽  
Fuzzy Environment ◽  
Dual Simplex ◽  
Linear Programming Problems ◽  
Simplex Tableau ◽  
Dual Simplex Algorithm

In the real word, there are many problems which have linear programming models and sometimes it is necessary to formulate these models with parameters of uncertainty. Many numbers from these problems are linear programming problems with fuzzy variables. Some authors considered these problems and have developed various methods for solving these problems. Recently, Mahdavi-Amiri and Nasseri (2007) considered linear programming problems with trapezoidal fuzzy data and/or variables and stated a fuzzy simplex algorithm to solve these problems. Moreover, they developed the duality results in fuzzy environment and presented a dual simplex algorithm for solving linear programming problems with trapezoidal fuzzy variables. Here, the authors show that this presented dual simplex algorithm directly using the primal simplex tableau algorithm tenders the capability for sensitivity (or post optimality) analysis using primal simplex tableaus.

Sensitivity Analysis on Linear Programming Problems with Trapezoidal Fuzzy Variables

2011 ◽  
Vol 2 (2) ◽  
pp. 22-39 ◽  
Author(s):  
Seyed Hadi Nasseri ◽  
Ali Ebrahimnejad
Keyword(s):  
Linear Programming ◽  
Simplex Algorithm ◽  
Fuzzy Data ◽  
Fuzzy Variables ◽  
Fuzzy Environment ◽  
Tableau Algorithm ◽  
Dual Simplex ◽  
Linear Programming Problems ◽  
Simplex Tableau ◽  
Dual Simplex Algorithm

In the real word, there are many problems which have linear programming models and sometimes it is necessary to formulate these models with parameters of uncertainty. Many numbers from these problems are linear programming problems with fuzzy variables. Some authors considered these problems and have developed various methods for solving these problems. Recently, Mahdavi-Amiri and Nasseri (2007) considered linear programming problems with trapezoidal fuzzy data and/or variables and stated a fuzzy simplex algorithm to solve these problems. Moreover, they developed the duality results in fuzzy environment and presented a dual simplex algorithm for solving linear programming problems with trapezoidal fuzzy variables. Here, the authors show that this presented dual simplex algorithm directly using the primal simplex tableau algorithm tenders the capability for sensitivity (or post optimality) analysis using primal simplex tableaus.

A Two-Phase Method for the Simplex Tableau

1956 ◽  
Vol 4 (4) ◽  
pp. 443-447 ◽  
Author(s):  
Harvey M. Wagner
Keyword(s):  
Phase Method ◽  
Two Phase ◽  
Simplex Tableau

scholarly journals When Lift-and-Project Cuts Are Different

2020 ◽  
Vol 32 (3) ◽  
pp. 822-834 ◽  
Author(s):  
Egon Balas ◽  
Thiago Serra
Keyword(s):  
Numerical Procedure ◽  
Linear Program ◽  
Mixed Integer ◽  
Basic Solution ◽  
Research Activity ◽  
Mixed Integer Linear Program ◽  
Intersection Cuts ◽  
Programming Library ◽  
Necessary And Sufficient ◽  
Simplex Tableau

In this paper, we present a method to determine if a lift-and-project cut for a mixed-integer linear program is irregular, in which case the cut is not equivalent to any intersection cut from the bases of the linear relaxation. This is an important question due to the intense research activity for the past decade on cuts from multiple rows of simplex tableau as well as on lift-and-project cuts from nonsplit disjunctions. Although it has been known for a while that lift-and-project cuts from split disjunctions are always equivalent to intersection cuts and consequently to such multirow cuts, it has been recently shown that there is a necessary and sufficient condition in the case of arbitrary disjunctions: a lift-and-project cut is regular if, and only if, it corresponds to a regular basic solution of the Cut Generating Linear Program (CGLP). This paper has four contributions. First, we state a result that simplifies the verification of regularity for basic CGLP solutions. Second, we provide a mixed-integer formulation that checks whether there is a regular CGLP solution for a given cut that is regular in a broader sense, which also encompasses irregular cuts that are implied by the regular cut closure. Third, we describe a numerical procedure based on such formulation that identifies irregular lift-and-project cuts. Finally, we use this method to evaluate how often lift-and-project cuts from simple t-branch split disjunctions are irregular, and thus not equivalent to multirow cuts, on 74 instances of the Mixed Integer Programming Library (MIPLIB) benchmarks.

An algorithm for simplex tableau reduction: the push-to-pull solution strategy

2003 ◽  
Vol 137 (2-3) ◽  
pp. 525-547 ◽  
Author(s):  
H. Arsham ◽  
T. Damij ◽  
J. Grad
Keyword(s):  
Solution Strategy ◽  
Simplex Tableau

Constrained Cutting Rate-Tool Life Characteristic Curve, Part 2: Convex Programs

1998 ◽  
Vol 120 (1) ◽  
pp. 160-165 ◽  
Author(s):  
C. L. Hough ◽  
Y. Chang
Keyword(s):  
Sensitivity Analysis ◽  
Tool Life ◽  
Simplex Method ◽  
End Milling ◽  
Characteristic Curve ◽  
Convex Programs ◽  
Machining Economics ◽  
Cutting Rate ◽  
Primal Dual ◽  
Simplex Tableau

Based on the concept in Part 1, Theory and General Case, algorithms to determine the constrained R-T characteristic curve are established for convex constrained machining economics problems. The first algorithm is for posynomial problems with the linear-logarithmic tool life equation. The R-T curve may be determined by applying the simplex method to the log-dual problems. Sensitivity analysis of the optimal simplex tableau enables obtaining the loci of optima easily. The second algorithm is for the quadratic posylognomial problems with quadratic-logarithmic tool life equation using the property of primal-dual feasibility. End milling examples constructed in Part 1 illustrate the algorithm comparing to the exhaustive method.

scholarly journals Inequalities from Two Rows of a Simplex Tableau

2007 ◽  
pp. 1-15 ◽  
Author(s):  
Kent Andersen ◽  
Quentin Louveaux ◽  
Robert Weismantel ◽  
Laurence A. Wolsey
Keyword(s):  
Simplex Tableau
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