) Find the total transportation cost using Vogel’s Approximation Method when the unit transportation costs, demands and supplies are as given below:
Destination
Origins D1 D2 D3 D4 Supply
O1 6 1 9 3 70
O2 11 5 2 8 55
O3 10 12 4 7 70
Demand 85 35 50 45
To find the total transportation cost using Vogel's Approximation Method, follow these steps:
Step 1: Create a table to represent the transportation costs between origins (O1, O2, O3) and destinations (D1, D2, D3, D4):
Destination
Origins D1 D2 D3 D4
O1 6 1 9 3
O2 11 5 2 8
O3 10 12 4 7
Step 2: Find the difference between the two smallest transportation costs in each row and each column:
Destination
Origins D1 D2 D3 D4 Difference
O1 6 1 9 3 5
O2 11 5 2 8 3
O3 10 12 4 7 3
Step 3: Select the row or column with the largest difference. In this case, it is the row for O1.
Step 4: Identify the smallest transportation cost in the selected row. In this case, it is 1.
Step 5: Allocate the maximum possible quantity (demand or supply) to the cell with the smallest transportation cost. In this case, we can allocate 35 (demand for D2) to the cell (O1, D2).
Destination
Origins D1 D2 D3 D4 Difference
O1 6 0 9 3 5
O2 11 5 2 8 3
O3 10 12 4 7 3
Step 6: Update the remaining demand and supply quantities:
Destination
Origins D1 D2 D3 D4 Difference
O1 6 0 9 3 5
O2 11 0 2 8 3
O3 10 12 4 7 3
Demand 85 0 50 45
Step 7: Repeat Steps 2 to 6 until all demand and supply quantities are zero.
Destination
Origins D1 D2 D3 D4 Difference
O1 0 0 9 3 5
O2 11 0 2 8 3
O3 10 12 0 7 3
Destination
Origins D1 D2 D3 D4 Difference
O1 0 0 0 3 2
O2 9 0 2 8 3
O3 7 10 0 7 3
Demand 76 0 41 42
Destination
Origins D1 D2 D3 D4 Difference
O1 0 0 0 0 1
O2 9 0 2 7 1
O3 5 9 0 6 3
Demand 65 0 40 36
Step 8: Calculate the total transportation cost by multiplying the allocated quantities with the corresponding transportation costs and summing them up:
Total transportation cost = (35 x 1) + (35 x 2) + (15 x 3) + (15 x 7) + (35 x 9) + (15 x 5) = 35 + 70 + 45 + 105 + 315 + 75 = 645
Therefore, the total transportation cost using Vogel's Approximation Method is 645.