Simplex Algorithm Puns

I am wondering if there an easy way to get a list of numbers and then pivot it using the simplex algorithm? I am not sure how I would make the algorithm though. Does anyone know how I might be able to easily implement this sort of thing?

For example if I had these numbers:

1 6 5 1 0 0 56

2 2 1 0 1 0 12

-1 -4 -2 0 0 1 0

and then pivoted it then I would get this as the set of pivoted numbers

-5 0 2 1 -3 0 20

2 2 1 0 1 0 12

3 0 0 2 1 24

So far what I am trying is this:

print(1, 6, 5, 1, 0, 0, 56)
print(2, 2, 1, 0, 1, 0, 12)
print(-1, -3, -2, 0, 0, 1, 0)

# print is the numbers I am using as the example
if -1 <= -3 and -2:
56/1
12/2
if 56/1 < 12/2:
elif -3 <=-1 and -2:
56/6
12/2
if 56/6 < 12/2:
else 12/2 < 56/6:
        then

I am probably making this more difficult than it has to be.

What I am trying to do is have to computer calculate the lowest negative value in the bottom list of numbers. Then calculate the smallest quotient for each of the first 2 rows and then I wanted it to calculate the zeroes for the other 2 numbers in the column and have the computer pivot all the numbers. I don't know how to code this though.

Hi Grant,

I am self - studying Linear Programming and the Simplex Algorithm for solving it, and I think it would be a great topic for a video: the problem of Linear Programming can be easily stated and the Simplex Algorithm is essentially Gaussian Elimination of Linear Algebra (plus few additional tricks).

Because of this, you could add the video to the Linear Algebra series.

Hello r/algorithms!

I would like some feedback on my project by people that have a basic at least knowledge on Linear Programming (Simplex Algorithm). The desktop application solves a Maximization problem using the Simplex Algoritmh, explaining each of the algorithm's steps while asking the user 20 questions. Some of the question are theoretical (True-False, Multiple Choise etc) while others may need some calculations from the user. After you finish the quiz there is an animation on the algorithm's geometrical interpretation made using manim (3Blue1Brown's animation tool) which is 5 minutes long.

This application is ideal for students with a basic knowledge on the algorithm, to train on its steps, the algebraic procedures it uses and its geometrical interpretation.

Google Drive Link Only for Window Users , Download Tableau folder, Run Tableau.exe

https://github.com/wenbenz/SAGo

I need it for a different project I wanna do, and in building it, I was reminded of my dark CO250 days. Some of you might find this useful :)

(Also any vetting/questioning would be helpful for me to find flaws and bugs and logic mistakes. Would also appreciate if you wanna add test cases)

Disclaimer: I will not be held responsible for any consequences of using this. In particular, I make no guarantee that this works perfectly 100% of the time.

According to the resources I found, all variables are restricted to nonnegative values. In fact, this is used to detect optimality.

Well, what if one of the conditions is x<=-1? What then?

I don't need this feature at the moment, but I found it odd that nobody seems to remark on it.

I am trying to understand simplex algorithm and make a program that could perform these calculations. So far I think I understand the core algorithm, and the step I got stuck at is finding the initial canonical tableau (I am following instructions and examples on wikipedia).

The exact problem that I got stuck on:

 x - y     + t = 10
-x     - z     = 0

minimize Z = t

So I construct the tableau:

1   0   0   0  -1   0
0   1  -1   0   1   10
0  -1   0  -1   0   0

To find initial canonical tableau I add two artificial variables, giving:

1   0   0   0   0   0  -1  -1   0
0   1   0   0   0  -1   0   0   0
0   0   1  -1   0   1   1   0   10
0   0  -1   0  -1   0   0   1   0

Then I do the priceout to make costs for artificial variables zero:

1   0   0  -1  -1   1   0   0  10
0   1   0   0   0  -1   0   0   0
0   0   1  -1   0   1   1   0  10   <--
0   0  -1   0  -1   0   0   1   0
                    ^

To solve it I chose element in row 3, column 6 as pivot element (marked above), and after one operation all entries except the first in the first row are non-positive, giving me a solution:

1   0  -1   0  -1   0  -1   0   0
0   1   1  -1   0   0   1   0  10
0   0   1  -1   0   1   1   0  10
0   0  -1   0  -1   0   0   1   0

So initial feasible solution is (x, y, z, t, a, b) = (0, 0, 0, 10, 0, 0), and the artificial variables are 0, so a solution for initial problem exists. However I don't understand how I am supposed to remove those artificial variables so I could solve Phase II. From the article I understood that I have to remove first column, first row, and columns of artificial variables. However in my case, column 8 is basic column, so if I do that I lose one basic column and the resulting tableau is not in canonical form:

1   1  -1   0   0   10
0   1  -1   0   1   10
0  -1   0  -1   0   0

In this case I can see that I could just multiply the third row by -1, but I don't understand what I need to do in the general case.

Hello everyone,

I am trying to get a grasp on the simplex algorithm, looking through several guides and explanations as well as using the material given by our teacher I fail to see what I am doing wrong, or what I am supposed to do.

&nbsp;

The function is the following:

&nbsp;

>max Z (x,y,z) 3x + 4y + 10z

&nbsp;

with the following restrictions:

>2x + 3y + 4z <= 92

>y >= 10

>x >= 7

>x + z <= 29

>y + z <= 30

&nbsp;

Now I know that the result is x = 7, y = 10, z = 12 and the maximum is 181. However, following the instruction given I am supposed to choose the column based on the most negative number in the most bottom row (in the first case that would be -10, under x3), but if I do start with -10 and calculate from there on the entire calculation messes up.

However, if I start with -3 (under x1), move onto -4 (x2) and then use -10 (under x3) last, I actually reach the wanted solution. But that is not according to instructions. What am I missing? I will upload the spreadsheets that gave me the wanted solutions: https://i.imgur.com/hJmjKAo.png

&nbsp;

/Edit: To give some additional information, I normalized the pivotline by dividing the entire line by the pivotelement and used the following formula on all other cells:

&nbsp;

>S(r,c) - (( S(r',c) * S(r,c') / S(r',c') )

&nbsp;

Basically a for-loop within a for-loop, with S being the Selected-Cell, r corresponding to rows, c corresponding to columns with r' and c' being the pivot column/row and r' c' being the pivot element. Hope this helps someone help me.

Does anyone know where I can find a good explanation of the simplex algorithm for solving linear programming?

I've been going through my lecture notes for it several times and it isn't really clicking. I guess it just seems like a bunch of arbitrary computation/variable replacement, and I don't understand why you're supposed to be doing any of the stuff the algorithm says to do.

ANSWERED

I have problems putting the following problem into a form that can be treated with simplex algorithm:

> You have 100 4-tonne boxes, and 48 2.5-tonne boxes, and a truck that can contain up to 12 tonnes of cargo. > Find a way to pack those boxes onto a truck (for several trips, of course), so that you waste as little space as possible."

I easily found the answer itself (only 8 tonnes wasted):

16 * (1 * 4 + 3 * 2.5) + 28 * (3 * 4 + 0 * 2.5)

...but can't find a way to represent the problem in a form that can be simplex-ified. All the forms I came up with were totally unsuitable for the simplex algorithm.

The equations I've used:

• f(x1,x2,x3,x4,n,m)= n * (12 - 4 * x1 - 2.5 * x2)+ m * (12 - 4 * x3 - 2.5 * x4) -> min
• 12 - 4 * x1 - 2.5 * x2 >= 0
• 12 - 4 * x3 - 2.5 * x4 >= 0
• n * x1 + m * x3 = 100
• n * x2 + m * x4 = 48
• n - number of trips with the first packing distribution
• m - with the second one
• x1,x2,x3,x4,n,m are natural or zero

...help?

I understand that Simplex generally performs well unless it is a Minty example, but still there are so many exceptions on infeasiblity, degeneracy and stalling cases. In my view, KKT conditions and Newton's Method as an interior point method seems to be very easy and involves only few rounds of matrix evaluation and multiplications, and as a result returns great approximation. I think for practical purposes it is the best.

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Hello r/OperationsResearch!

I would like some feedback on my project by people that have a basic at least knowledge on Linear Programming (Simplex Algorithm). The desktop application solves a Maximization problem using the Simplex Algoritmh, explaining each of the algorithm's steps while asking the user 20 questions. Some of the question are theoretical (True-False, Multiple Choise etc) while others may need some calculations from the user. After you finish the quiz there is an animation on the algorithm's geometrical interpretation made using manim (3Blue1Brown's animation tool) which is 5 minutes long.

This application is ideal for students with a basic knowledge on the algorithm, to train on its steps, the algebraic procedures it uses and its geometrical interpretation.

Google Drive Link Only for Window Users , Download Tableau folder, Run Tableau.exe

Hello r/math!

I would like some feedback on my project by people that have a basic at least knowledge on Linear Programming (Simplex Algorithm). The desktop application solves a Maximization problem using the Simplex Algoritmh, explaining each of the algorithm's steps while asking the user 20 questions. Some of the question are theoretical (True-False, Multiple Choise etc) while others may need some calculations from the user. After you finish the quiz there is an animation on the algorithm's geometrical interpretation made using manim (3Blue1Brown's animation tool) which is 5 minutes long.

This application is ideal for students with a basic knowledge on the algorithm, to train on its steps, the algebraic procedures it uses and its geometrical interpretation.

Google Drive Link Only for Window Users , Download Tableau folder, Run Tableau.exe

Hello r/optimization!

I would like some feedback on my project by people that have a basic at least knowledge on Linear Programming (Simplex Algorithm). The desktop application solves a Maximization problem using the Simplex Algoritmh, explaining each of the algorithm's steps while asking the user 20 questions. Some of the question are theoretical (True-False, Multiple Choise etc) while others may need some calculations from the user. After you finish the quiz there is an animation on the algorithm's geometrical interpretation made using manim (3Blue1Brown's animation tool) which is 5 minutes long.

This application is ideal for students with a basic knowledge on the algorithm, to train on its steps, the algebraic procedures it uses and its geometrical interpretation.

Google Drive Link Only for Window Users , Download Tableau folder, Run Tableau.exe