Transportation Problems
Assignment II (Part – A)
Q1. Solve the following Transportation Problem
by NWCM and test its optimality by Stepping Stone Method. The Shipping
Costs are given in the table.
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Plants
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Projects
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||||
|
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A
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B
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C
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Supply
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|
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W
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4
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8
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8
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56
|
|
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X
|
16
|
24
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16
|
82
|
|
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Y
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8
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16
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24
|
77
|
|
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Demand
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72
|
102
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41
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215
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Answer: WB=56, XB=41, XC=41, YA=72,
YB=05. Total Cost= 2744
Q2. Solve the following Transportation Problem
whose cost matrix, availability at each plant & requirement at each
warehouse are given. Apply Stepping Stone Method for optimal solution The Shipping Costs are
given in the table.
|
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W1
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W2
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W3
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W4
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Supply
|
|
P1
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15
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24
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11
|
12
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5000
|
|
P2
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25
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20
|
14
|
16
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4000
|
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P3
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12
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12
|
22
|
13
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7000
|
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Demand
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3000
|
2500
|
3500
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4000
|
16000
13000
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Answer: P1W3=2500,
P1W4=2500, P2W3=1000, P2W5=3000.P3W1=3000P3W2=2500P3W4=1500 Total Cost= 1,57,000
Q3. Given below is a table. Solve it as
transportation problems & test it optimality. Apply stepping stone method
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Factories
|
|
Centers
|
||||
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C1
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C2
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C3
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C4
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Supply
|
||
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A
|
10
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8
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7
|
12
|
500
|
|
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B
|
12
|
13
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6
|
10
|
500
|
|
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C
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8
|
10
|
12
|
14
|
900
|
|
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Demand
|
700
|
550
|
450
|
300
|
1900
2000
|
|
Answer: AC2=350, AC3=150,
BC3=300, BC4=200, CC1=700, CC2=200,
DC4=100 Total Cost= 15,250
Q4. A cement factory manager is considering
the least way transport cement from his three manufacturing centers P, Q & R to depots A, B, C, D & E. The weekly production
and demands along with transportation costs are given below. Apply stepping stone method.
|
|
A
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B
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C
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D
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E
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Supply
|
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P
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4
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1
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3
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4
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4
|
60
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Q
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2
|
3
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2
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2
|
3
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35
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R
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3
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5
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2
|
4
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4
|
40
|
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Demand
|
22
|
45
|
20
|
18
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30
|
135
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Answer: PB=45, PE=15, QA=2, QD=18,
QE=15, RA=20, RC=20, Total Cost =290
Q5. Consider the following transportation
problem and solve by applying VAM &
test it optimality. Apply stepping stone method
|
|
X
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Y
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Z
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Supply
|
|
A
|
4
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3
|
2
|
10
|
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B
|
5
|
6
|
1
|
8
|
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C
|
6
|
4
|
3
|
5
|
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D
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3
|
5
|
4
|
6
|
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Demand
|
7
|
12
|
5
|
|
Answer: Total Cost =66
Q6. Given below is a table. Solve it as
transportation problems & test it optimality. Apply VAM and stepping stone
method
|
Factories
|
|
Centers
|
||||
|
1
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2
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3
|
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Supply
|
||
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P
|
16
|
19
|
12
|
|
14
|
|
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Q
|
22
|
13
|
19
|
|
16
|
|
|
R
|
14
|
28
|
8
|
|
12
|
|
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Demand
|
10
|
15
|
17
|
|
1900
2000
|
|
Answer: P1=9, P3=5, Q1=1, Q2=15, R3=12 Total Cost= 517
Q7. Given below is a table. Solve it as
transportation problems & test it optimality. Apply NWCM and stepping stone
method
|
|
W1
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W2
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W3
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W4
|
Supply
|
|
F1
|
21
|
16
|
25
|
13
|
11
|
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F2
|
17
|
18
|
14
|
23
|
13
|
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F3
|
32
|
27
|
18
|
41
|
19
|
|
Demand
|
6
|
10
|
12
|
15
|
43
|
Answer: F1W4=11, F2W1=6, F2W2=3,
F2W4=4, F3W2=7, F3W3=12 Total
Cost= 796
can u please solve q3......
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