## Vogel’s Approximation Method (VAM)

Vogel’s approximation method is an improved version of the least cost entry method. It gives better starting solution as compared to any other method.

### Step 1

For each row (column), determine the penalty measure by subtracting the **smallest unit cost** element in the row (column) from the **next smallest unit cost** element in the same row (column).

### Step 2

Select the row or column with the **largest** penalty. If a tie occurs, use any arbitrary tie breaking choice.

Let the largest penalty corresponds to $i^{th}$ row and let `$c_{ij}$`

be the smallest cost in the $i^{th}$ row. Allocate as much as possible amount `$x_{ij} = min(a_i, b_j)$`

in the cell $(i,j)$ and cross-out the $i^{th}$ row or $j^{th}$ column in the usual manner.

### Step 3

Again determine the penalties for rows and column ignoring the costs of cross-out row and column for the reduced transportation table. Then goto Step 2.

### Step 4

Repeat Step 2 and 3 until all the requirements and availabilities are satisfied.