Tagged Questions

66 views

Forbidden range for a linear programming variable

I would like to express a linear program having a variable that can only be greater or equal than a constant $c$ or equal to $0$. The range $]0; c[$ being unallowed. Do you know a way to express this ...
23 views

On the injection of exactly two artificial variables into the Phase I of a two-phase simplex

I am relatively new still to linear optimization and as I understand it, the two phase method is a common practice for finding the bfs before using the simplex or a simplex like solver (a solver ...
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Is simplex method weaker than other methods?

Given linear program: $$\text{min } x_1 - x_2 + 2 x_3$$ s.t.: $$-3x_1 + x_2 + x_3 = 4$$ $$x_1 - x_2 + x_3 = 3$$ $$x_i \geq 0; i = \{1,2,3\}$$ solution by simplex method (with double pass) is ...
134 views

linear program-Simplex method-Dual problem

At an exercise I am asked to solve a linear program using the simplex method(in Matlab).Then I have to formulate the dual of this problem and read off an optimal solution of the dual problem from the ...
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Linear Program Transformations

I have a Linear Program with constrains of the form: $$a_{11}x_1+a_{12}x_2+\ldots\le 0$$ $$a_{21}x_1+a_{22}x_2+\ldots\le 0$$ $$a_{31}x_1+a_{32}x_2+\ldots\le 0$$ My problem is that if I try to ...
376 views

Reduced cost in the Phase II of the two-phase Simplex?

My lecture slides outline how the two-phase simplex works: this table shows the end result of the phase I for the standard-form problem and the auxliary table of the phase I here. I understood until ...
280 views

Reduced cost vector in the phase I of the Two-phase simplex?

I am trying to understand the part in red. The left is the standard form problem and the right is the auxiliary problem. Now I can understand until the red i.e. $\bar c =(-1,-1,-3,-1,-2,0,0,0)$. The ...
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How does the two phase method for linear programs work…

I understand that by adding artificial variables the problem can be reformulated as a new problem where the "starting point" is readily found. What I don't get is how when this extended problem is ...
I cannot understand the line -12, -4, -5, 1, 1, -1, 0, 0, 0. Now the formula $\bf c - \bf A ^t \bf y$ when $c=0$ will result into the line. It is just many times a ...