What to do if there is a degeneration solution when using the Vogel method in operations research

When there is degradation, a 0 must be filled in the corresponding grid to indicate that this grid is a numerical grid. There are two cases:

1) When determining the supply and demand of the initial solution, if a number is filled in the (i, j) box, a appears; The margin is equal to b; At this time, fill in the number of - on the production and sales balance sheet, and correspondingly cross out a row and a column on the unit freight list. In order to have (m+n-1) number cells on the balance sheet. In this case, you need to add a "0".

It can be placed in any of the spaces corresponding to the row or column that was crossed out at the same time.

2) When adjusted with the closed-loop method, two or more equal minimum values with (-1) marks appear on the closed-loop path. Only one of them can be selected as the dial-in grid. After adjustment, it was degraded.

At this time, there is a number style that must be filled with 0, indicating that it is a base variable, when there is a degradation and adjustment, there may be a number grid marked as (-1) with a value of 0 on a closed loop, let the adjustment amount = 0.

The treatment method is the same as the "minimum element method", that is, add a zero to any space of the row or column that is crossed out at the same time to ensure that the number of base variables is m+n-1

Usually the optimal solution is not obtained, and the Vogel method is used to obtain an initial solution.

The one with the lowest unit freight rate in the line where the maximum penalty is located. Equivalent to the case where the column difference is largest (as shown in the example).

Usually the optimal solution is not obtained, and the Vogel method is used to obtain an initial solution.

Usually the optimal solution is not obtained, and the Vogel method is used to obtain an initial solution.

When the goal is to find the maximum, in the Vogel method, the difference should be calculated as the difference between the maximum profit and the next largest profit in the row or column, and the same is true for others.

In general, it is the reason for the insufficiency of conditions, because it can be proved that any non-fundamental variable in the transportation problem must find a closed loop.

If you're using the Vogel method to find the initial solution, it's probably because you've crossed out two rows or columns at once.

Usually the optimal solution is not obtained, and the Vogel method is used to obtain an initial solution.

When the maximum value of the line penalty and the column penalty are the same, find the row and column corresponding to the maximum value of the line spell and the column penalty to see which one has the lowest unit fare, and choose the one with the lowest unit fare.

Any one of the maximum penalties is sufficient.

Choose any one, but if you don't choose well, it will be a few troubles, and I would like to ask if there is a selection criterion to make the question easier.