Vogel's Approximation Method (VAM) is a 3 step process for solving transportation problems: 1) Compute penalties for each row and column based on smallest costs. 2) Identify largest penalty and assign lowest cost variable the highest possible value, crossing out exhausted row or column. 3) Recalculate penalties and repeat until all requirements are satisfied.

1. Vogel’s Approximation Method (VAM) Step-I: Compute the penalty values for each row and each column. The penalty will be equal to the difference between the two smallest shipping costs in the row or column. Step-II: Identify the row or column with the largest penalty. Find the first basic variable which has the smallest shipping cost in that row or column. Then assign the highest possible value to that variable, and cross-out the row or column which is exhausted. Step-III: Compute new penalties and repeat the same procedure until all the rim requirements are satisfied.

2. An example for Vogel’s Method Find the IBFS of the following transportation problem by using Penalty Method. O1 O2 Demand

3. Step 1: Compute the penalties in each row and each column .

4. Step 2: Identify the largest penalty and choose least cost cell to corresponding this penalty

5. Step-3: Allocate the amount 5 which is minimum of corresponding row supply and column demand and then cross out column2

6. Step-4: Recalculate the penalties

7. Step-5: Identify the largest penalty and choose least cost cell to corresponding this penalty

8. Step-6: Allocate the amount 5 which is minimum of corresponding row supply and column demand, then cross out column3

9. Step-7: Finally allocate the values 0 and 15 to corresponding cells and cross out column 1

10. Solution of the problem Now the Initial Basic Feasible Solution of the transportation problem is X 11 =0, X 12 =5, X 13 =5, and X 21 =15 and Total transportation cost = (0x6)+(5x7)+(5x8)+(15x15) = 0+35+40+225 = 300.