Questions tagged [two-phase-simplex]

For questions about the two phase simplex method, which is an algorithm to solve a linear program which has no initial basic feasible solution.

Filter by
Sorted by
Tagged with
1
vote
0answers
18 views

I want to know what is the relation between network flow min cost problem and max flow problem with simplex method linear programming,

I want to know what is the relation between network flow min cost problem and max flow problem with simplex method linear programming, such as primal dual and complementary slackness and how can i ...
0
votes
0answers
10 views

A doubt regarding Vogel's Approximation Method

In VAM, we usually start with the row/column with maximum of differences (and we select the row/column accordingly). But, if I don't select the 'absolute maximum' and go on to start the process with ...
0
votes
1answer
22 views

Artificial Variables in Two Phase Simplex Method

I am coding a Two-Phase Simplex solver, just as a part to improve my programming skills. I am testing this program on many LP problems, and I found one where it doesn't work as expected, so I want to ...
0
votes
1answer
1k views

Show that it as no feasible solution.

An optimization problem: $$\text{ maximize } z=8x+6y$$ $$\text{ such that: } x-y ≤ 0.6 \text{ and } x-y≥2$$ Show that it as no feasible solution using SIMPLEX METHOD. It seems very logical that ...
1
vote
1answer
52 views

General solution to linear program?

Source of the Problem The problem comes from an application in economics concerning trade between agents to maximize aggregate "wealth". More exactly, there are $m$ agents and $n$ groups and we ...
0
votes
1answer
36 views

Linear programming/seeing feasibility and unboudedness

Consider the dual linear programming problem and its simplex dually feasible table: $$\begin{array}{|c|c|c|c|c|c|c|c|}\hline -4& 0 & 1&5&16&0&4&0 \\ \hline -12& 0 &...
0
votes
0answers
90 views

Proof verification for simplex method problems

I was studying simplex method in LPP from "Introduction to Linear Optimization by Bertsimas and Tsitsiklis", and came across this problem: Consider the simplex method applied to a standard form ...
0
votes
1answer
70 views

Simplex algorithm/basic artificial variable

How do we continue in the simplex algorithm if some artificial variable is basic ? Do we still forget about this basic artificial variable in the second phase of the simplex algorithm as we do forget ...
1
vote
1answer
38 views

Simplex Algorithm, determining Two Phase is required and choice of artificial variables

Given the following system : \begin{align*} \text{minimise } z = &2x_1 &+ 3x_2 &+ 3x_3 &+ x_4 &- 2x_5& \\ \end{align*} Subject to \begin{align*} &...
1
vote
1answer
50 views

The simplex algorithm--example

Here on the page 30, why $(z_3,z_3)=1$: as written on that page 30: minimize the sum of the artificial variables, starting from the BFS where the absolute value of the artificial variable for each ...
2
votes
2answers
6k views

Simplex Method with negative R.H.S

Question: Maximize $2x_1 - 6x_2$ Subject to \begin{align*} -x_1 - x_2 - x_3 &\leq -2 \\ 2 \, x_1 - x_2 + x_3 &\leq 1 \end{align*} My Process: I create an auxiliary problem: Maximize $-...
0
votes
1answer
78 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 ...
0
votes
0answers
117 views

calculating the extreme rays of a polyhedra

How could I go about the problem finding the extreme rays of a polyhedral defined by constraints $x_1-x_2 \geq -2$ $x_1+x_2 \geq 1$ $x_1,x_2 \geq 0$ I know for certain that given a max or min ...
0
votes
0answers
18 views

In Simplex Method, can I move from a basic solution $x^{*}$ to the other $y^{*}$ by pivoting zero cost in Tableau?

Suppose that $B_1$ is the bases for $x^{*}$ and I want to go to the second solution $y^{*}$ with bases $B_2$, how to go to the second optimal solution through pivoting? My attempt was trying to prove ...
2
votes
2answers
85 views

simplex example 13.1: nocedal wright

I'm having a trouble understanding NW's example problem 13.1 (p.371 in 2e): \begin{aligned} \begin{equation} \min_x -4x_1 - 2x_2 \text{ s.t } \\ x_1 + x_2 + x_3 = 5 \\ 2x_1 + \tfrac {x_2}{2} + x_4 = ...
0
votes
1answer
222 views

Operations Research: Simplex Table Unbound Optimal Solution

The problem statement, all variables and given/known data Hi I am looking at this quesiton attached part c). Relevant equations The attempt at a solution I can by my notes which tell me that if I ...
1
vote
0answers
85 views

Simplex Algorithm: Why does Phase I deliver a BFS immediately?

When trying to solve a Linear Program (I call it primary problem below) of the form min $c^{T}x$ s.t. $ $ $Ax = b, x \geq 0, b \geq 0 $ The two phase simplex algorithm suggests to starts with the ...
0
votes
1answer
70 views

Complexity of the first phase method

(first post on math SE) I am looking for a formal upper-bound on the number of iterations in the first phase, in terms of the number of artificial variables (A.V). I have some intuition that it ...
0
votes
1answer
100 views

Simplex method and basic solutions

I have put this into the form $0.5x_1 + 0.25x_2 + x_3=6$ $-x_1 - 3x_2 + x_4=-2$ $x_1 + x_2 = 10$ Is this correct? If so, how do I find a basic solution so that I can begin the simplex algorithm?
1
vote
1answer
2k views

Duality Theorem - Optimal solution of both Primal and Dual

The Duality Theorem, in short, states that the optimal value of the Primal (P) and Dual (D) Linear Programs are the same if the solution, of either, is a basic feasible solution. My question is that ...
2
votes
1answer
569 views

Stuck on two phase simplex where RHS $= 0$

I'm stuck on the following linear program, it's a minimal example of the problem I'm having: Minimize $Z = y$ where $x \ge 1$ and $-2x+y \ge 0$ We start by rewriting this as a system of linear ...
2
votes
0answers
139 views

Two phase simplex when constraint is the same as minimize function

Consider the following linear program: Maximize $Z = x - y$ where $-x+y\ge 1$ and $x\ge 0, y\ge 0$ Add surplus and artificial variables to the constraint: $-x+y-s+a=1$ For phase 1 maximize $W = -...
2
votes
0answers
402 views

Two phase method in linear programming

Suppose following tableau came after one iteration in first phase of a two phase method problem, here $s_1$ is a surplus variable and $s_2$ is a slack variable $w$ is a artificial variable. I tried ...
1
vote
1answer
148 views

List the six possible bases of the LP P and find their corresponding solutions

Consider the following LP P: max z = 22x_1 - 12x_2 subject to: 8x_1 + 4x_2 \le 15 2x_1 + 6x_2 \le 7 x_1, x_2 \ge 0 ...
1
vote
0answers
354 views

Minimize using simplex method with mixed constraints

Using the simplex method, minimize $z= -2x_1+12x_2-3x_3-5x_4-x_5$ with $x_i \geq 0$ and subject to constraints: $x_1+4x_3-5x_4+2x_5 \leq 4$ $4x_2-x_4 \leq 1$ $5x_1-6x_2-3x_4 \leq 6$ $...
6
votes
1answer
1k views

Generating random linear programming problems

I've just finished writing a a linear programming problem solver which uses the simplex method. Now I would like to start optimizing my solver but before I can do this, I need a way of reliably ...
1
vote
0answers
303 views

Simplex Algorithm (Two-Phase) - Finding pivot entries consistent with the simplex method

I'm working through the examples in my professor's class notes, but I can't figure out how to solve this problem: Example: In the following standard tableau, mark by * the choices for the pivot ...
0
votes
1answer
87 views

Maximising a Linear Programming Problem

Maximize $w=2x+3y+6z$ subject to $2x+y+z \le 5$ $3y+2z \le 6$ $x,y,z \ge 0$ Is the optimal solution unique? Justify your answer. I tried to solve it by Simplex method. In the second iteration, ...
1
vote
1answer
76 views

Simplex: duplicate constraints

I'm trying to understand how the two-phase simplex algorithm works, this site explains it using a simple example: http://optlab.mcmaster.ca/feng/4O03/Two.Phase.Simplex.pdf I've tried to come up with ...
2
votes
1answer
268 views

Two- phase simplex method problem

I have this problem: Minimize: $x_1+3x_2-x_3$ Subject to: $$ \begin{align} 2x_1+x_2+3x_3 \geq 3\\ -x_1+x_2\geq1\\ -x_1-5x_2+x_3\leq4\\ x_1,x_2,x_3, \geq 0\\ \end{align}$$ I need help solving it ...
1
vote
0answers
67 views

Converting a primal feasible problem to dual LP problem, does it implies a feasible solution?

I'm new in this Stack exchange,a friend of mine and I are using the lindo, to solve this LP problem: $$ \begin{align*} \max z= 18x_{11}+18x_{12}+20x_{21}+20x_{22}-6x_{41}-10x_{51}-4x_{61}-4x_{42}-...
-1
votes
2answers
86 views

How to solve this question by the two-phase simplex algorithm?

A clever but ethically corrupted mathematics student used to sell assignment solutions to her lazy fellow students. The student, however, learned that she can make much more money by charging the ...
0
votes
1answer
98 views

How to configure simplex method to start from a specific point

If I have a linear programming problem e.g. $$\max 2x_1 + x_2$$ with these constraints $$x_1-2x_2 \leq 14$$ $$2x_1-x_2\leq 10$$ $$x_1-x_2 \leq 3$$ And I want to solve the problem starting from a ...
0
votes
1answer
4k views

Canonical form simplex method

In 2-phases simplex method what kind of operations must be done to get the canonical form tableau? In this step(phase 2 of 2-phases method) after the remotion of artificial variables columns of ...
0
votes
1answer
129 views

Simplex method state after first phase

I'm implementing a simplex method solver for a standard problem $$ \begin{aligned} \operatorname{minimize} \qquad&c^T x\\ \operatorname{subjected to} \qquad&Ax = b\\ &x \geq 0\\ \end{...
1
vote
1answer
179 views

General question about new objective function W using the simplex method

In regards to the two-phase simplex method; When creating a new objective function that consists the sum of the constraint(s) with artificial variables, I am told that if the Min value of (wmin) w is >...
2
votes
1answer
476 views

Two-phase simplex method to solve minimise problem

Using the two-phase simplex method I am asked to Minimise: z= 3x2-x3+8 Subject to: x1+x2+x3=10, 2x1+3x2+x3=15 x1,x2,x3>=0 I am not sure how to go about this ...
0
votes
0answers
119 views

How to Adequately Implement Phase I of Two-Phase Simplex Algorithm on a Computer with Floating Point Error

I'm currently trying to write some code that implements Phase I of the two-phase Simplex Algorithm described here: http://www.statslab.cam.ac.uk/~ff271/teaching/opt/notes/notes8.pdf In order to test ...
3
votes
1answer
376 views

Expressing problems in canonical form for solving with simplex

The Picnic Hamper Company has a store containing 10,000kg of nuts, 4000 packs of smoked salmon, 2000 bottles of wine and 1500 Victoria sponges. It intends to use these goods to make up three different ...
0
votes
1answer
260 views

If we start with a feasible tableau in simplex method, are we basically generating a different feasible point in every pivot step?

This is a true and false question. The actual question reads: "In solving a linear program by the simplex method, starting with a feasible tableau, a different feasible point is generated after every ...
2
votes
1answer
151 views

Two-phase simplex

The upper part of the image attached is the question and lower part is the solution. I did the exact same table as table4 in the picture, yet I put the ratio of [2] as 0.5/0.5=1 instead. Could someone ...
2
votes
2answers
553 views

Represent if-else or OR condition in a linear equation (optimisation with simplex algorithm)

I would like to write some linear equations and inequations to state that the sum of all possive x - C is smaller than L. As my ...
3
votes
2answers
1k 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 ...
0
votes
1answer
140 views

Simplex method Dual phase precision problem

I am trying to implement simplex method algorithm in PHP language. But I am facing with precision problem. For example if I try to solve these equations: ...
2
votes
0answers
280 views

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 ...
0
votes
0answers
706 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 ...
2
votes
0answers
73 views

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 ...
1
vote
1answer
22 views

Are these constraints correct?

A bike dealer buys at a wholesale: bikes, scooters and child's saddles. He wants maximum profit. He buys the bike (x) for 300, the scooter (y) for 1200 and the saddle (z) for 36. A bike takes 0,5$m^...
1
vote
1answer
1k 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 ...
0
votes
2answers
2k views

Reduced cost zero for the two-phase Simplex?

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 ...