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.
An example for Vogel’s Method
Find the IBFS of the following transportation problem by using Penalty Method.
O1 O2 Demand
Step 1: Compute the penalties in each row and each column .
Step 2: Identify the largest penalty and choose least cost cell to corresponding this penalty
Step-3: Allocate the amount 5 which is minimum of corresponding row supply and column demand and then cross out column2
Step-4: Recalculate the penalties
Step-5: Identify the largest penalty and choose least cost cell to corresponding this penalty
Step-6: Allocate the amount 5 which is minimum of corresponding row supply and column demand, then cross out column3
Step-7: Finally allocate the values 0 and 15 to corresponding cells and cross out column 1
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)