North West Corner Method

Dr.D.B.Usharani
Vice Principal (Aided)
Associate Professor & Head
Department of Economics
Ethiraj College for Women
Chennai

1. NORTH WEST CORNER METHOD

2. NORTH WEST CORNER METHOD The North West corner rule is a method for computing a basic feasible solution of a transportation problem, where the basic variables are selected from the North – West corner ( i.e., top left corner ). Steps in North West Corner Rule: Select the upper left-hand corner cell of the transportation table and allocate as many units as possible equal to the minimum between available supply and demand. Adjust the supply and demand numbers in the respective rows and columns. If the demand or supply for the first cell is satisfied, then move horizontally or vertically to the next cell.

3. NORTH WEST CORNER METHOD Steps in North West Corner Rule (C ontd…) 4. If the supply for the first row is exhausted, then move down to the first cell in the second row. 5. If for any cell, supply equals demand, then the next allocation can be made in cell either in the next row or column. 6. Continue the process until all supply and demand values are exhausted.

4. TO → ↓SOURCE D 1 D2 D3 D4 SUPPLY F1 8 6 10 9 35 F2 9 12 13 7 50 F3 14 9 16 5 40 DEMAND 45 20 30 30 125 NORTH WEST CORNER METHOD -EXAMPLE 1

5. TO → ↓SOURCE D 1 D2 D3 D4 SUPPLY F1 35 8 6 10 9 35 F2 9 12 13 7 50 F3 14 9 16 5 40 DEMAND 45 20 30 30 NORTH WEST CORNER METHOD -EXAMPLE 1 STEP 1: Select the upper left-hand corner cell of the transportation table and allocate as many units as possible equal to the minimum between available supply and demand.

6. TO → ↓SOURCE D 1 D2 D3 D4 SUPPLY F1 35 8 6 10 9 35 F2 10 9 12 13 7 50 F3 14 9 16 5 40 DEMAND 45(10) 20 30 30 STEP 2: Adjust the supply and demand numbers in the respective rows and columns. NORTH WEST CORNER METHOD -EXAMPLE 1

7. TO → ↓SOURCE D 1 D2 D3 D4 SUPPLY F1 35 8 6 10 9 35 F2 10 9 20 12 13 7 50(40) F3 14 9 16 5 40 DEMAND 45 20 30 30 NORTH WEST CORNER METHOD -EXAMPLE 1 STEP 3: If the demand or supply for the first cell is satisfied, then move horizontally or vertically to the next cell.

8. TO → ↓SOURCE D 1 D2 D3 D4 SUPPLY F1 35 8 6 10 9 35 F2 10 9 20 12 20 13 7 50(20) F3 14 9 16 5 40 DEMAND 45 20 30 30 STEP 4: If for any cell, supply equals demand, then the next allocation can be made in cell either in the next row or column. NORTH WEST CORNER METHOD -EXAMPLE 1

9. TO → ↓SOURCE D 1 D2 D3 D4 SUPPLY F1 35 8 6 10 9 35 F2 10 9 20 12 20 13 7 50 F3 14 9 10 16 5 40 DEMAND 45 20 30(10) 30 NORTH WEST CORNER METHOD -EXAMPLE 1

10. TO → ↓SOURCE D 1 D2 D3 D4 SUPPLY F1 35 8 6 10 9 35 F2 10 9 20 12 20 13 7 50 F3 14 9 10 16 30 5 40(30) DEMAND 45 20 30 30 NORTH WEST CORNER METHOD -EXAMPLE 1

11. TO → ↓SOURCE D 1 D2 D3 D4 SUPPLY F1 35 8 6 10 9 35 F2 10 9 20 12 20 13 7 50 F3 14 9 10 16 30 5 40 DEMAND 45 20 30 30 STEP 5: Now the allocation obtained from north-west corner method is summarized to find the total cost. Total Cost = (35*8) + (10*9) + (20*12) + (20*13) + (10*16) + (30*5) = 1180

12. NORTH WEST CORNER METHOD -EXAMPLE 2 TO → ↓SOURCE D E F SUPPLY A 5 8 4 50 B 6 6 3 40 C 3 9 6 60 DEMAND 20 95 35 150 Solve the following using North West Corner Method.

13. NORTH WEST CORNER METHOD -EXAMPLE 2 TO → ↓SOURCE D E F SUPPLY A 20 5 8 4 50 B 6 6 3 40 C 3 9 6 60 DEMAND 20 95 35

14. NORTH WEST CORNER METHOD -EXAMPLE 2 TO → ↓SOURCE D E F SUPPLY A 20 5 30 8 4 50(30) B 6 6 3 40 C 3 9 6 60 DEMAND 20 95 35

15. NORTH WEST CORNER METHOD -EXAMPLE 2 TO → ↓SOURCE D E F SUPPLY A 20 5 30 8 4 50 B 6 40 6 3 40 C 3 9 6 60 DEMAND 20 95(65) 35

16. NORTH WEST CORNER METHOD -EXAMPLE 2 TO → ↓SOURCE D E F SUPPLY A 20 5 30 8 4 50 B 6 40 6 3 40 C 3 25 9 6 60 DEMAND 20 95(25) 35

17. NORTH WEST CORNER METHOD -EXAMPLE 2 TO → ↓SOURCE D E F SUPPLY A 20 5 30 8 4 50 B 6 40 6 3 40 C 3 25 9 6 60(35) DEMAND 20 95 35

18. NORTH WEST CORNER METHOD -EXAMPLE 2 TO → ↓SOURCE D E F SUPPLY A 20 5 30 8 4 50 B 6 40 6 3 40 C 3 25 9 35 6 60(35) DEMAND 20 95 35

19. TO → ↓SOURCE D E F SUPPLY A 20 5 30 8 4 50 B 6 40 6 3 40 C 3 25 9 35 6 60(35) DEMAND 20 95 35 150 Total Cost = (20*5) + (30*8) + (40*6) + (25*9) + (35*6) = 1015

20. TO → ↓SOURCE D 1 D2 D3 D4 SUPPLY F1 3 3 4 1 100 F2 4 2 4 2 125 F3 1 5 3 2 75 DEMAND 120 80 75 25 300 NORTH WEST CORNER METHOD -EXAMPLE 3 Solve the following Transportation Problem using North West Corner Method.

21. NORTH WEST CORNER METHOD -EXAMPLE 3 TO → ↓SOURCE D 1 D2 D3 D4 SUPPLY F1 100 3 3 4 1 100 F2 4 2 4 2 125 F3 1 5 3 2 75 DEMAND 120 80 75 25

22. NORTH WEST CORNER METHOD -EXAMPLE 3 TO → ↓SOURCE D 1 D2 D3 D4 SUPPLY F1 100 3 3 4 1 100 F2 20 4 2 4 2 125 F3 1 5 3 2 75 DEMAND 120(20) 80 75 25

23. NORTH WEST CORNER METHOD -EXAMPLE 3 TO → ↓SOURCE D 1 D2 D3 D4 SUPPLY F1 100 3 3 4 1 100 F2 20 4 80 2 4 2 125(105) F3 1 5 3 2 75 DEMAND 120 80 75 25

24. NORTH WEST CORNER METHOD -EXAMPLE 3 TO → ↓SOURCE D 1 D2 D3 D4 SUPPLY F1 100 3 3 4 1 100 F2 20 4 80 2 25 3 2 125(25) F3 1 5 3 2 75 DEMAND 120 80 75 25

25. NORTH WEST CORNER METHOD -EXAMPLE 3 TO → ↓SOURCE D 1 D2 D3 D4 SUPPLY F1 100 3 3 4 1 100 F2 20 4 80 2 25 4 2 125 F3 1 5 50 3 2 75 DEMAND 120 80 75(50) 25

26. NORTH WEST CORNER METHOD -EXAMPLE 3 TO → ↓SOURCE D 1 D2 D3 D4 SUPPLY F1 100 3 3 4 1 100 F2 20 4 80 2 25 4 2 125 F3 1 5 50 3 25 2 75(25) DEMAND 120 80 75 25

27. Total Cost = (100*3) + (20*4) + (80*2) + (25*4) + (50*3) + (25*2) = 840 TO → ↓SOURCE D 1 D2 D3 D4 SUPPLY F1 100 3 3 4 1 100 F2 20 4 80 2 25 4 2 125 F3 1 5 50 3 25 2 75 DEMAND 120 80 75 25 300