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Solving Transportation Problem in Operations Research
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Transcript of Solving Transportation Problem in Operations Research
Presentation on Transportation
Problem
Presented By:- Group A1
Nikita Bali (11004)Neethi Nair (11044)Ranjini Nair (11045)Chandan Pahelwani (11047)Himani Parihar (11049)Sonia Dadlani (10022)
• QUESTION:A company has three production facilities P1, P2 and P3 with production capacity of 7, 10 and 18 units per week of a product, respectively. These units are 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 unit between factories to warehouses are given in the table below.
D1 D2 D3 D4 Capacity
P1 20 30 50 15 7
P2 70 35 40 60 10
P3 40 12 60 25 18
Demand 5 8 7 15 35
Step 1: Using Vogel’s Approximation Method (VAM) method to find out the initial basic feasible solution.
D2
20)5
7040
3035
D3
5040)7
D4
15)2
60)3
P1
P2
P312)8 60 25)10
Supply
7/2/0
10/7/3
18/10/0
5/0demand 8/0 7/0 15/13/3 35
20
Pena
lty
18 10 101010
Penalties
5513
15513
352035
D1
-
2035
18 1010
20 35
So the feasible solution is:
D1 D2 D3 D4
P1 20)5 - - 15) 2
P2 - - 40)7 60) 3
P3 - 12) 8 - 25) 10
Test for Optimality
Step 2:MODI Method
D1 D2 D3 D4
P1 U1=0
P2 U2=-45
P3 U3=-10
V1=-20
V2=-2V3=
5V4=-15
20
40
12
15
60
25
D1 D2 D3 D4
P1 2830
5550
U1=0
P2 570
-1235
U2=-45
P3 1040
5560
U3=-10
V1=-20
V2=-2
V3=5
V4=-15
20
12
40
25
60
1530-2 50+5
35-45-270-20-45
60-10+540-20-10
D1 D2 D3 D4
P1
P2
P3
0+X
8-X 10+X
3-X
• Improvisations of Solution
D1 D2 D3 D4
P1 20)5 - - 15)2
P2 - 35)3 40)7 -
P3 - 12)5 - 25)13
Take x = min {nos. with –x} = min {3,8} = 3
D1 D2 D3 D4
P1 U1 = 0
P2
U2 = -33
P3
U3 = -10
V1 = -20 V2 = -2 V3 = -7 V4 = -15
20 15
25
40
12
35
D1 D2 D3 D4
P1 28) 30 [30-2]
43) 50 [50-7]
U1 = 0
P2 17) 70[70-20-33]
12) 60[60-15-33]
U2 = -33
P3 10) 40[40-20-10]
43) 60[60-7-10]
U3=-10
V1 = -20 V2 = -2 V3 = -7 V4 = -15
20 15
25
40
12
35
Total transportation cost
20 * 5 = 100 35 * 3 = 10512 * 5 = 6040 * 7 = 280 15 * 2 = 30 25 * 13 = 325Total = Rs.900