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# Solving Transportation Problem in Operations Research

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### Solving Transportation Problem in Operations Research

1. 1. Presentation onTransportation Problem
2. 2. Nikita Bali (11004)Neethi Nair (11044)Ranjini Nair (11045)Chandan Pahelwani (11047)Himani Parihar (11049)Sonia Dadlani (10022)
3. 3. • QUESTION:A company has three productionfacilities P1, P2 and P3 with productioncapacity of 7, 10 and 18 units per weekof a product, respectively. These unitsare to be shipped to four warehouses D1,D2, D3 and D4 with requirement of 5, 8,7 and 15 units per week, respectively.The transportation cost per unitbetween factories to warehouses aregiven in the table below.
4. 4. D1 D2 D3 D4 CapacityP1 20 30 50 15 7P2 70 35 40 60 10P3 40 12 60 25 18Demand 5 8 7 15 35
5. 5. Step 1: Using Vogel’sApproximationMethod (VAM)method to find outthe initial basicfeasible solution.
6. 6. D1 D2 D3 D4 Supply PenaltiesP1 20)5 30 50 15)2 7/2/0 5 15 35 -P2 70 35 40)7 60)3 10/7/3 5 5 20 20P3 40 12)8 60 25)10 18/10/0 13 13 35 35demand 5/0 8/0 7/0 15/13/3 35 20 18 10 10 Penalty 18 10 10 10 10 20 35
7. 7. So the feasible solution is: D1 D2 D3 D4P1 20)5 - - 15) 2P2 - - 40)7 60) 3P3 - 12) 8 - 25) 10
8. 8. Step 2:MODI Method Test for Optimality
9. 9. D1 D2 D3 D4P1 U1= 20 15 0P2 60 U2= 40 -45P3 12 25 U3= -10 V1= V2= V3= V4= -20 -2 5 -15
10. 10. D1 D2 D3 D4P1 28 55 50+5 U1= 20 30-2 15 30 50 0P2 5 70-20-45 -12 35-45-2 40 60 U2= 70 35 -45P3 1040-20-10 12 55 60-10+5 25 U3= 40 60 -10 V1= V2= V3= V4= -20 -2 5 -15
11. 11. • Improvisations of Solution D1 D2 D3 D4P1 0+X 3-XP2P3 8-X 10+X
12. 12. Take x = min {nos. with –x} = min {3,8} =3 D1 D2 D3 D4 P1 20)5 - - 15)2 P2 - 35)3 40)7 - P3 - 12)5 - 25)13
13. 13. D1 D2 D3 D4P1 U1 = 0 20 15 U2 = -33 35 40P2 U3 = -10P3 12 25 V1 = -20 V2 = -2 V3 = -7 V4 = -15
14. 14. D1 D2 D3 D4P1 28) 43) U1 = 0 30 50 20 [30-2] [50-7] 15P2 17) 12) U2 = -33 70 60 [70-20-33] 35 40 [60-15-33]P3 10) 43) 40 12 60 25 U3=-10 [40-20-10] [60-7-10] V1 = -20 V2 = -2 V3 = -7 V4 = -15
15. 15. Total transportation cost 20 * 5 = 100 35 * 3 = 105 12 * 5 = 60 40 * 7 = 280 15 * 2 = 30 25 * 13 = 325 Total = Rs.900