# Column Minima Method

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In the column minima method, we begin with the first column and allocate gradually moving towards the lowest cost cell of the column. This system is continued until the first destination centre is satisfied or the capacity of the second is exhausted, or both happens. So there are three cases which are as follows:

1. You can cross the first column and move towards the right column if the demand of the first distribution centre is satisfied.
2. If the supply of the ith factoryis fulfilled, then the ith row must be crossed out, and the first column must be considered as the remaining demand.
3. Now the last case, if the demand for the distribution centresand the ith factories are satisfied, then it is said to make a zero allotment in the second lowest row of the cost cell of the first column. So in that case the ith row and the columns are crossed off to move to the second column.

This process is continued until all the reduced transportation table conditions are satisfied. The matrix below explains the whole row minima method.

Distribution centers

X                                   Y                             Supply

A              Rs. 2000                     Rs.5380

1000                                                                 1000

Factories                  B              Rs. 2500                    Rs. 2700

1300                            200                            1500

C            Rs. 2500                     Rs. 1700

1200                               1200

Demand           2300                         1400                                3700

So let’s now start solving in this mentioned method. So here we see the lowest cost cell in the column AX. We allocate the minimum amount which is 1000 out of 2300, 1000. With this, the capacity of the factory A is exhausted and the row one is crossed out. The next allocation is done with the cell BX. Similarly, the taking the minimum amount of the first column is 2500; we allocate with the minimum 1300 in this cell. This again satisfies the distribution centre X and hence the first column is also crossed.

Now moving to the second column with the minimum cost cell CY. We allocate 1200 in this cell among 1400 and 1200. Now considering the next one BY where we can allot, and all the conditions are satisfied.

Transportation cost associated with this solution is

Z = Rs. (2000 x 1000 + 2500 x 1300 + 1700 x 1200 + 2700 x 200)

= Rs. 78.34, 000

Which is same as a result obtained by row minima method.

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