## Least Cost Entry Method

This method is also known as Matrix Minima Method.

### Step 1

Select the smallest cost in the cost matrix of the transportation table. Let it be $c_{ij}$. Allocate $x_{ij} = min_{i,j}(a_i, b_j)$ in the cell $(i,j)$.

### Step 2

• If $x_{ij} = a_i$, then cross-out the $i^{th}$ row of the transportation table and decrease $b_j$ by $a_i$ and goto Step 3.
• If $x_{ij} = b_j$, then cross-out the $j^{th}$ column of the transportation table and decrease $a_i$ by $b_j$ and goto Step 3.
• If $x_{ij} = a_i=b_j$, then cross-out the $i^{th}$ row of the, cross-out $i^{th}$ row and $j^{th}$ column. transportation table and decrease $b_j$ by $a_i$ and goto Step 3.

### Step 3

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

If the minimum cost is not unique, make an arbitrary choice among the minimum costs.