The document describes the Modi method for solving transportation problems. It involves finding the unused route with the largest negative improvement index to determine the best way to ship units. The key steps are to construct a transportation table, find the initial basic feasible solution, identify occupied and unoccupied cells, calculate opportunity costs for unoccupied cells, select the cell with the largest negative opportunity cost, and assign units until reaching the optimal solution. The method is demonstrated on two example problems.

1. MODI METHOD

7. . PROBLEM1:Shipping costs are Rs. 10 per kilometer.. What shipping schedule should be used. if the matrix given below the kilometers from source to destination. Requirement 3 3 2 8 x 50 30 220 1 y 90 45 170 3 z 50 200 50 4 destination a b c availability

8. A B C X Y Z 30 220 50 90 45 170 50 200 50 30 220 1 2 3 2 2 2 2 3 P1 P2 P3 P4 20 20 20 20 45 45 45 _ 150 150 _ _ P1 40 15 120 P2 40 15 _ P3 40 15 _ IBFS BY USING VAM METHOD

9. 30 30 220 90 45 170 50 200 50 1 E 3 2 2 STONE SEQUARE =4 RIM REQUIREMENT =M+N-1=3+3-1=5 DEGENERACY NOW STONE SEQUARE =5 RIM REQUIREMENT =5 NON –DEGENERACY

10. 50 30 45 50 50 50 30 50 0 15 0 OCCUPIED MATRIX UNOCCUPIED MATRIX 105 25 170 50 65 30 65 170

11. OPTIMUL SOLUTION X A 50*1=50 X B 30*E=_ Y B 45*3=135 Z A 50*2=100 Z C 50*2=100 385 *10=3850

12. PROBLEM2:DETERMINE THE OPTIMUM SOLUTION FOR THE COMPANY OF TRASPOTATION PROBLEM(USING NWCM AND MODI METHOD) 8 8 15 15 10 17 3 9 10 REQUIREMENT 150 80 50 120 80 80 CAPACITY F1 F2 F3 W1 W2 W3 WAREHOUSE FACTORY

13. W1 W2 W3 F1 F2 F3 8 8 15 15 3 10 17 9 10 120 30 50 30 50 150 80 50 120 80 80 IBFS WITH NWCM

14. OCCUPIED MATRIX UNOCCUPIED MATRIX 8 15 10 9 10 15 10 11 -7 0 -1 15 10 11 -7 0 -1 5 11 6 -11 3 4 11 14

15. 15 8 8 15 10 17 3 9 10 10 120 30 50 30 50 + + _ _ 8 15 3 8 15 10 17 9 10 120 E 80 30 50 STONE SEQUARE=RIM REQUIREMENT DEGENERACY OCCUAR LOOP CONSTRUCT

16. OCCUPIED MATRIX UNOCCUPIED MATRIX 8 8 10 3 10 3 3 10 3 3 10 5 7 0 5 7 0 5 6 0 0 15 17 10 3

17. OPTIMUM SOLUTION F1 W1 8*120 =960 F1 W2 8*E = _ F2 W2 10*80 =800 F3 W1 3*30= 90 F3 W3 10*50 =500 2,350 RS