Row Minima Method
Step 1
Select the smallest cost in the first row of the transportation table. Let it be $c_{1j}$. Allocate as much as possible amount $x_{1j} = min_j(a_1, b_j)$ in the cell $(1,j)$, so that either the capacity of origin $O_1$ is exhausted or the requirement at destination $D_j$ is satisfied or both.
Step 2
- If $x_{1j} = a_1$, the availability at origin $O_1$ is completely exhausted, cross-out the first row of the table and move down to the second row.
- If $x_{1j}= b_j$, the requirement at destination $D_j$ is satisfied, cross-out the $j^{th}$ column and reconsider the first row with the remaining availability of origin $O_i$.
- If $x_{1j} = a_1= b_j$, the availability at origin $O_1$ and the requirement at destination $D_j$ are completely exhausted. So cross-out $1^{st}$ row and $j^{th}$ column simultaneously. Move down to the second row.
Step 3
Repeat Step 1 and Step 2 for the reduced transportation table until all the requirements and availabilities are satisfied.
