Vogel Approximation Methods ( VAM):
Step 1: For each row the transportation table identify the smallest and next to smallest cost. Determine the different between them for each row. These are called penalties. Put them along side the transportation table by enclosing them in the parentheses against the respective rows similarly compute these penalties for each column.
Step 2: Identify the row or column with the largest penalty among all the rows and columns. If a tie occurs use any arbitrary tie breaking choice. Let the largest penalty correspond to itn row and let c be the smallest cost in the row. Allocate the largest possible amount t- t X_{ij} = min ( a_{i} ,b_{i}) in the cell ( i, j,) and cross out the i row or the j column in the usual manner.
Step 3: Again compute the column and row penalties for the reduced transportation table and then go to step 2. Repeat the procedure until all the requirements are satisfied.