Vogel’s Approximation Method: Vogel’s approximation method (VAM) can be regarded as an improved version of the least-cost method. Instead of using the direct cost of the transportation, VAM utilizes the concept of the penalty cost. Each row or column has its own penalty cost, which is used for determining which variables are the basic ones. A penalty cost is the difference between the smallest cost of a row (or column) and the cost that is smaller than the others except the smallest one for that row (or column).