Column Minima Method

Step 1

Select the smallest cost in the first column of the transportation table. Let it be $c_{i1}$. Allocate as much as possible amount $x_{i1} = min_i(a_i, b_1)$ in the cell $(i,1)$, so that either the capacity of origin $O_i$ is exhausted or the requirement at destination $D_1$ is satisfied or both.

Step 2

• If $x_{i1} = b_1$, the requirement at destination $D_1$ is completely exhausted, cross-out the first column of the table and move down to the second column.
• If $x_{i1}= a_i$, the availability at origin $O_i$ is satisfied, cross-out the $i^{th}$ row and reconsider the first column with the remaining requirement of destination $D_1$.
• If $x_{i1} = a_i= b_1$, the availability at origin $O_i$ and the requirement at destination $D_1$ are completely exhausted. So cross-out $1^{st}$ column and $i^{th}$ row simultaneously. Move down to the second column.

Step 3

Repeat Step 1 and Step 2 for the reduced transportation table until all the requirements and availabilities are satisfied.