Operation Research
CS355-A
Assignment# 02
Name: Areeb Arshad
Roll No. 181400149
Submitted Date:
February 28th, 2021
Question No. 1:
3
2
7
2
40
4
10
11
1
6
6
1
20
9
8
8
5
40
14
18
9
8
3
16
6
20
30
15
13
4
10
11
1
6
6
1
20
9
8
8
5
40
14
18
9
8
3
16
6
20  0
30
15
13
4
6
10
(6)
11
1
60
1
8
5
40
14
18
9
8
3
16
6
0
30  4 0
15
13
4
6
10
(6)
11
1
0
1
8
5
9
8
3
16
6
0
0
4
6
10
1
9
8
3
0
0
0
13  6 0
Answer:
3
(20)
2
7
2
40 20
3
2
(20)
(20)
7
2
20 0
3
2
(20)
(20)
7
2
0
3
2
7
2
0
(20)
(20)
(6)
11
1
0
(4)
20
9
84
(4)
20
(4)
9
4 0
(4)
(4)
20
9
0
40
(11)
14
18 7
8
5
40
(11)
14
(7)
70
16
(6)
6 0
15  11 0
13
= 3*20 + 2*20 + 10*6 + 1*4 + 20*4 + 40*11 + 14*7 + 16*6
= 60 + 20 + 60 + 4 + 80 + 484 + 98 + 96
 = 902 Ans.
Question No. 2:
14
65
35
4
25
25
3
7
45
35
65
6
5
55
15
13
6
8
16
45
35
65
6
5
55
15
13
62 0
8
16
45
5
55
15
13
0
83 0
16
35
5
55
65
15
0
0
16  13 0
45
5
55
Answer:
14
(4)
65
35
4 0
25
14
(4)
65
35
0
25
3
5 0
65
6 3
14
(4)
65
35
0
25
45
14
25
(4)
65
35
0
(2)
25
3
7 5
25
25
(2)
(5)
(2)
(5)
3
0
25
3
0
(2)
(5)
35
(3)
(3)
(3)
3 0
35
65
0
(3)
(3)
(13)
13 0
15
(13)
0
= 14*4 + 25*2 + 25*5 + 35*3 + 65*3 + 15*13
0
0
0
= 56 + 50 + 125 + 105 + 195 + 195  = 686 Ans.
Question No. 3:
2
3
5
1
7
7
3
4
6
9
4
1
7
2
18
5
8
7
14
Answer:
a) Minimum Cost Method
2
3
5
1
7
7
3
4
6
9
4
2
3
5
7
3
4
6
9
4
4
0
7
3
4
6
9
2
3
7
3
4
1
(7)
7 0
2
3
5
1
(7)
1
(8)
7
2
18 10
1
(8)
7
2
10
1
(8)
7
2
(7)
10 3
1
(8)
5
80
7
14
5
0
7
14

5
0
7
70
5
0
7
4
5
1
(7)
0
2
3
5
1
0
1
7
3
4
(7)
6
2
(2)
4
(7)
2
3
5
7
4
4
0
6
0
(7)
52
0
0
0
20
0
0
0
0
1
(7)
(3)
(8)
7
2
3
(7)
4
6
2 0
(2)
(3)
(8)
7
2 (7)
3 0
1
(7)
(7)
70
0
3
1
3
0
1
2
7
2
3
5
7
6
9 2
4
(7)
(7)
(3)
(8)
7
2
(7)
0
0
0
0
0
= 1*8 + 1*7 + 2*7 + 4*7 + 4*3 + 7*2
= 8 + 7 + 14 + 28 + 12 + 14  = 83 Ans.
---------------------------------------------------------------------------------------------------b) North-West Method
2
(5)
3
5
1
7 2
7
3
4
6
9
4
1
7
2
18
50
8
7
14
2
3
(5)
(2)
7
3
(6)
5
1
2 0
4
6
9 3
2
7
3
(5)
(2)
5
1
0
2
3
(5)
(2)
5
1
0
2
3
5
1
0
(5)
(2)
3
(6)
4
(3)
6
3 0
7
3
(6)
4
(3)
6
0
7
3
(6)
4
(3)
6
0
4
1
7
2
18
0
86 0
7
14
4
1
0
0
74 0
14
7
(4)
2
18 14
4
1
7
(4)
(14)
14 0
2
4
1
7
2
(4)
(14)
0
0
0
14  0
0
0
0
0
0
= 2*5 + 3*2 + 3*6 + 4*3 + 7*4 + 2*14
= 10 + 6 + 18 + 12 + 28 + 28  = 102 Ans.
We got 83 value from minimum cost method and got 102 from north-west
method, then as it is clear that Minimum cost Method is better.
Question No. 4:
19
70
40
5
30
30
8
8
50
40
70
7
10
60
20
14
7
9
18
Answer:
W1
19
70
40
5
W2
30
30
8
(8)
8 0
F1
F2
F3
Req.
Penalty 40-19=21 30-8=22
W1
19
(5)
70
40
5 0
W2
30
30
8
(8)
0
F1
F2
F3
Req.
Penalty 40-19=21 --W1
19
(5)
70
40
0
F1
F2
F3
Req.
Penalty ---
F1
F2
F3
W1
19
(5)
70
40
W3
50
40
70
7
W4
10
60
20
14
Cap
7
9
18  10
Penalty
Cap
72
9
10
Penalty
Cap
2
9
10  0
Penalty
Cap
20
9
0
Penalty
19-10=9
40-30=10
20-8=12
50-40=10 20-10=10
W3
50
40
70
7
W4
10
60
20
14
19-10=9
40-30=10
40-20=20
50-40=10 20-10=10
W2
30
30
8
(8)
0
W3
50
40
70
7
W4
10
60
20
(10)
14 4
---
50-40=10 20-10=10
W2
30
30
8
(8)
W3
50
40
70
W4
10
(2)
60
20
(10)
30-10=20
40-30=10
70-20=50
30-10=20
40-30=10
---
Req.
0
Penalty --W1
19
(5)
70
40
0
F1
F2
F3
Req.
Penalty ---
W1
19
(5)
70
40
0
F1
F2
F3
Req.
Penalty ---
W1
19
(5)
70
40
0
F1
F2
F3
Req.
Penalty ---
0
7
4 2
---
50-40=10 20-10=10
W2
30
30
8
(8)
0
W3
50
40
70
7
---
50-40=10 60
W2
30
30
8
(8)
0
W3
50
40
(7)
70
7 0
---
50-40=10 ---
W2
30
30
8
(8)
0
W3
50
40
(7)
70
0
W4
10
(2)
60
(2)
20
(10)
0
---
---
---
W4
10
(2)
60
(2)
20
(10)
2 0
W4
10
(2)
60
(2)
20
(10)
0
Cap
0
97
0
Penalty
Cap
0
70
0
Penalty
Cap
0
0
0
Penalty
--40-30=10
---
--40-30=10
---
-------
= 19*5 + 10*2 + 8*8 + 40*7 + 60*2 + 20*10
= 95 + 20 + 64 + 280 + 120 + 200  = 779 Ans.
__________________________________________________________________
Question No. 5:
2
1
3
3
11
4
9
3
10
7
4
4
3
2
8
5
7
1
12
6
4
8
9
10
7
4
4
3
2
8
5
7
1
12
6
4
8
9
10
7
(4)
3
7
1
0
862
0
9
Answer:
a) North-West Method:
2
(3)
11
(1)
1
3
3 0
4
9
3 2
2
11
(3)
(1)
(2)
1
4
3
0
9
2 0
4
4 0
8
5 3
12
6
11
10
7
(4)
4
0
3
7
1
10
7
(4)
4
0
3
2
(3)
4
1
3
0
2
1
3
0
(1)
(2)
9
0
(3)
11
4
9
0
(1)
(2)
2
(2)
2
(2)
8
(3)
3 0
2
8
(2)
(3)
0
= 2*3 + 11*1 + 4*2 + 7*4 + 2*2 + 8*3 + 12*6
= 6 + 11 + 8 + 28 + 4 + 24 + 72  = 153
12
(6)
6 0
7
1
12
(6)

1 0
0
0
96 0
0
0
0
---------------------------------------------------------------------------------------------------b) Vogel’s Approximation Method:
2
1
3
3
11
4
9
3
10
7
4
4
3
2
8
5
7
1
12
6
4
8
9
Origin
A
B
C
Demand
Penalty
A1
2
1
3
3
2-1=1
B1
11
4
9
3
9-4=5
C1
10
7
4
4
7-4=3
D1
3
2
8
5
3-2=1
E1
7
1
(6)
12
6 0
7-1=6
Supply
4
82
9
Penalty
3-2=1
2-1=1
4-3=1
Origin
A
B
C
Demand
Penalty
A1
2
1
3
3
2-1=1
B1
11
4
(2)
9
3 1
9-4=5
C1
10
7
4
4
7-4=3
D1
3
2
8
5
3-2=1
E1
7
1
(6)
12
0
---
Supply
4
20
9
Penalty
3-2=1
2-1=1
4-3=1
Origin
A
B
C
Demand
Penalty
A1
2
1
3
3
3-2=1
B1
11
4
(2)
9
1
11-9=2
C1
10
7
4
(4)
4 0
10-4=6
D1
3
2
8
5
8-3=5
E1
7
1
(6)
12
0
---
Supply
4
0
95
Penalty
3-2=1
--4-3=1
Origin
A
A1
2
B1
11
C1
10
D1
3
(4)
E1
7
Supply Penalty
4  0 3-2=1
B
C
Demand
Penalty
1
3
3
3-2=1
4
1
4
9
(4)
1
0
11-9=2 ---
2
8
5 1
8-3=5
(6)
12
0
---
0
5
--8-3=5
Origin
A
B
C
Demand
Penalty
A1
2
1
3
3
3
B1
11
4
(2)
9
(1)
1 0
9
C1
10
7
4
(4)
0
---
D1
3
(4)
2
8
1
8
E1
7
1
(6)
12
0
---
Supply
0
0
54
Penalty
----8-3=5
Origin
A
B
C
Demand
Penalty
A1
2
1
3
3
3
B1
11
4
(2)
9
(1)
0
---
C1
10
7
4
(4)
0
---
D1
3
(4)
2
8
(1)
1 0
8
E1
7
1
(6)
12
0
---
Supply
0
0
4 3
Penalty
----8-3=5
Origin
A
B
C
Demand
Penalty
A1
2
1
3
(3)
3 0
3
B1
11
4
(2)
9
(1)
0
---
C1
10
7
4
(4)
0
---
D1
3
(4)
2
8
(1)
0
---
E1
7
1
(6)
12
0
---
Supply
0
0
30
Penalty
----3
Origin
A
A1
2
B1
11
C1
10
D1
3
(4)
E1
7
Supply Penalty
0
---
(2)
7
B
1
3
C
(3)
Demand 0
Penalty ---
4
9
(2)
(1)
0
---
7
4
1
2
(4)
0
---
8
(1)
0
---
(6)
12
0
---
0
0
= 3*4 + 3*3 + 4*2 + 1*6 + 9*1 + 4*4 + 8*1
= 12 + 9 + 8 + 6 + 9 + 16 + 8  = 68
Origin
A
B
C
D
Req.
1
7
4
5
4
20
2
2
4
5
5
2
2
15
Avail.
30
15
10
20
Origin
A
B
C
D
Req.
Penalty
1
7
4
5
4
20
5-4=1
2
3
(25)
5
4
6
3
3
-1
4
25 0
15
2-(-1)=3 4-3=1
4
5
5
2
2
15
5-2=3
Avail.
30  5
15
10
20
Penalty
5-2=3
5-4=1
3-2=1
2-(-1)=3
Origin
A
B
C
D
Req.
Penalty
1
7
4
5
4
20
5-4=1
2
4
5
5
Avail.
5
15
10  0
20
Penalty
7-5=2
5-4=1
3-2=1
4-2=2
4
3
-1
25
3
5
6
3
4
15
2
2
(25)
4
3
-1
0
---
3
5
6
3
4
15
4-3=1
2
(10)
2
15 5
5-2=3
-----
Origin
A
B
C
D
Req.
Penalty
1
7
4
5
4
20
5-4=1
2
Origin
A
B
C
D
Req.
Penalty
1
7
2
Origin
A
B
C
D
Req.
Penalty
1
7
Origin
A
B
C
D
Req.
Penalty
1
7
4
(15)
4
5
5
4
3
-1
0
---
3
5
6
3
4
15
5-4=1
4
5
5
2
3
2
5
4
5
5
(25)
4
3
-1
0
---
(25)
4
3
-1
0
---
2
(15)
4
(5)
5 0
7-4=3
(15)
5
4
3
5
6
3
4
15
5-4=1
2
2
5
4
4
5
5
2
5
4
20 5
7-4=3
4
3
5
6
3
4
15
4-3=1
(5)
0
---
(25)
(25)
4
3
-1
0
---
(5)
6
3
4
15 10
5-4=1
2
(10)
2
(5)
5 0
5-2=3
2
2
(10)
(5)
Avail.
5
15
0
20  15
Penalty
7-5=2
5-4=1
5-3=2
4-2=2
Avail.
5
15  0
0
15
Penalty
7-5=2
6-4=2
--4-4=0
0
---
2
2
(10)
(5)
Avail.
5
0
0
15  10
Penalty
7-5=2
----4-4=0
0
---
2
2
(10)
(5)
0
---
Avail.
50
0
0
10
Penalty
5
----4
Origin
A
B
C
D
Req.
Penalty
1
7
Origin
A
B
C
D
Req.
Penalty
1
7
4
2
2
(15)
5
4
(5)
0
---
4
(15)
5
4
(5)
0
---
3
(25)
5
(5)
4
5
5
4
3
-1
0
---
6
3
(10)
10 0
4
2
2
3
2
5
4
5
5
(25)
4
3
-1
0
---
2
4
(5)
6
3
4
0
---
Penalty
------4
Avail.
0
0
0
0
Penalty
---------
0
---
2
(10)
(10)
(5)
Avail.
0
0
0
10  0
2
(10)
(5)
0
---
= 2*25 + 4*15 + 5*5 + 2*10 + 4*5 + 4*10 + 2*5
= 50 + 60 + 25 + 20 + 20 + 40 + 10  = 225 Ans.
__________________________________________________________________
THE END