Talk:Simplex algorithm

To the anonymous editor from IP-address 4.250.xxx.xxx: I don't understand why you want to associate Dantzig's method to mathematical optimization and the other simplex method, with which you have apparently some experience, with computer programming. Surely both methods are part of mathematical optimization, since they both solve optimization problems. Similarly, both methods are part of computer programming, since they can be programmed on a computer. -- Jitse Niesen 18:38, 10 Jan 2005 (UTC)

I associate "Dantzig's method to mathematical optimization" with "the other simplex method" because the documentation I read in order to fulfill the customer's request for implementing the simplex method optimization was derived by computation scientists (not me, I just implemented their algorithms in 6809 assembly code) from what appears to my eyes as what you descibe as "Dantzig's method to mathematical optimization". As I did this around 1985, I no longer recall the exact materials I read. In any case, I'll make no reverts to the current article. Cheers from user 4.250.xxx.xxx

In the Problem Input section, shouldn`t it be the transpose of -c, and not -c? Perhaps I am missing something, in which case I apologize. --Tomas

The example of the pivot operation states:

"Columns 2, 3, and 4 can be selected as pivot columns, for this example column 4 is selected. The values of z resulting from the choice of rows 2 and 3 as pivot rows are 10/1 = 10 and 15/3 = 5 respectively. Of these the minimum is 5, so row 3 must be the pivot row."

The earlier statement on the pivot operation reads:

"The row containing this element is multiplied by its reciprocal to change this element to 1.."

But in the example after the pivot, the value at row 3, column 4 is 3, not 1.

Hyphz (talk) 19:15, 1 November 2021 (UTC) [reply ]

It seems that all of the elements of the tableau have been scaled by three without saying. This appears to have been done to coerce it as a canonical form. The example could write a big ${\displaystyle {\frac {1}{3}}}${\displaystyle {\frac {1}{3}}} to the left of the tableau and indicate this has been done. An alternative could be to put a denominator of 3 below all of the elements, but that wouldn't look great. I was quite confused by this example. As I am new to wikipedia and linear programming I don't feel confident making an edit until I'm absolutely sure of what I'm doing. Phebenet (talk) 23:47, 23 October 2023 (UTC) [reply ]

The example could explain the choice of the pivot row better. "Now select column 3 as a pivot column, for which row 3 must be the pivot row". Why? By doing the ratio check described earlier in the article, the choices for the ratios are 15/7 (row 1), -60/-2 (row 2), 15/7 (row 3), and 15/2 (row 4). Both row 1 and 3 have the same ratio that happens to be the minimum. So at this point the choice between row 1 and row 3 is arbitrary, it doesn't follow that row 3 must be the one to choose. The logical step that led to the choice of row 3 vs row 1 should be added. Gyorokpeter (talk) 12:48, 10 December 2025 (UTC) [reply ]

In the example, there are implicit multiplications of the rows that should be better explained. So we choose row 5 and column 4 for the pivot. Then it seems that all rows other than row 4 are multiplied by 3 before performing the subtraction. So is the rule that we need to multiply by the pivot element? I can go with that, as it's convenient to avoid fractions showing up in the other rows. But then we choose row 3, column 3, which contains a 7. If we continue this logic, that means we multiply by 7 before doing the subtractions. However, that would make us end up with the first nonzero elements in each row being 21, 21, 7, 33. Well, another step we can perform is dividing each row by the greatest common divisor, but then the corresponding elements would be 1, 7, 7, 11. Notice the first row has 1, not 7. The only explanation is that we divided by 3. But why 3? Where does that number come from? Also, does it matter for the final solution if the first row has 7 or if it has 1? It doesn't seem so based on the fact that we drop the entire first row in the final step, and in that case it would make more sense to spell out that it's actually dividing by the GCD that is happening here, or if there is a strong reason to divide by 3, then that should be spelled out instead. Gyorokpeter (talk) 13:25, 10 December 2025 (UTC) [reply ]