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7/30/2019 BM 103 Exersice 11
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Exercise 11
1) Solve the ff. Modified Distribution (MODI) Warehouse
A1:V1+W1= 3, W1= 3
B1:V1+W2= 5, W2= 5B2:V2+W2= 8, V2= 3
C2:V2+W3= 4, W3= 1
C3:V3+W3= 4, V3= 3
VC
C1: 3 0 1 = 2
A2: 4 3 3 = -2
A3: 3 3 3 = -3
B3: 8 3 5 = 0
A3:
A B C
1 3 5 3 30
2 4 8 4 30
3 3 8 4 25
20 35 30 8585
W1=3 W2=5 W3=1
V1=0 3 5 3 30
V2=3 4 8 4 30
V3=3 3 8 4 25
20 35 30 8585
- 3 5
- 8 4
3 - 4
- 3 5
- 8 4
3 - 4
20
10
255
25
20
10
25
5
25
10
20
25
5
25
20
30
5 25
5
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Table 2:
OC
B1: V1+W2= 5, W2 = 5
B2: V2+W2= 8, V2 = 3
C2: V2+W3= 4, W3 = 1
A3: V3+W1= 3, W1 = 0
C3: V3+W3= 4, V3 = 3
VC CC
A1: 3 0 0 = 3 150 + 40 + 100 + 60 + 20
C1: 3 0 0 = 3 = 370
A2: 4 3 0 = 1B3: 8 3 5 = 0
W1=0 W2=5 W3=1
V1=0 3 5 3 30
V2=3 4 8 4 30
V3=3 3 8 4 25
20 35 30 8585
20
25
5
30
5
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2)
OC
A1: V1+W1 = 30, W1 = 30
A2: V2+W1 = 30, V2 = 0
B2: V2+W2 = 50, W2 = 50
B3: V3+W2 = 60, V3 = 10
VC
B1: 30 0 50 = -20
A3: 40 10 30 = 0
B1:
- 30 30
30 - 50
Table 2:
OC
A1: V1+W1= 30, W1 = 30
B1: V1+W2= 30, W2 = 30
A2: V2+W1= 30, V2 = 0
B3: V3+W2= 60, V3 = 30
VC
A B
1 30 30 25
2 30 50 15
3 40 60 30
30 40 7070
W1 = 30 W2 = 50
V1 = 0 30 30 25
V2= 0 30 50 15
V3= 10 40 60 30
30 40 7070
- 30 30
30 - 50
W1 = 30 W2 = 30
V1 = 0 30 30 25
V2= 0 30 50 15
V3= 30 40 60 38
30 40 7070
2
51
05 3
0
2
5
1
053
0
2
5
51
0
1
5
1
5
1
0
1
5
1
0
1
5 3
0
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B2: 50 0 30 = 20
A3: 40 30 30 = -20
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A3:
Table 3:
OC
B1: V1+W2= 30, W2= 30
A2: V2+W1= 30, V2= 20
A3: V3+W1= 40,W1= 10
B3: V3+W2= 60, V3= 30
VC: CC
A1: 30 0 10 = 20 B1: 750
B2: 50 20 30 = 0 A2: 450
A3: 1200
B3: 1800
4200
- 30 + 30
+ 40 - 60
- 30 + 30
+ 40 - 60
W1 = 10 W2 = 30
V1 = 0 30 30 25
V2= 20 30 50 15
V3= 30 40 60 38
30 40 7070
15
30
10 25
15
15
15
2
5
1
5 3
0
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4)
OC
A1: V1+W1 = 30, W1= 30B1: V1+W2 = 30, W2= 30
B2: V2+W2 = 50, V2= 20
B3: V3+W2 = 60, V3= 30
VC
A2: 25 20 30 = -25
A3: 30 30 30 = -30
A3:
Table 2
OC
A1: V1+W1= 30, W1 = 30
B1: V1+W2= 30, W2 = 30
B2: V2+W2= 50, V2 = 20
A3: V3+W1= 30, V3 = 0
VC
A2: 25 20 30 = -25
B3: 60 0 30 = 30
A B
1 30 30 35
2 25 50 19
3 30 60 16
30 40 7070
- 30 + 30
+ 30 - 60
- 30 + 30
+ 30 - 60
W1 = 30 W2 = 30
V1= 0 30 30 35
V2= 20 25 50 19
V3= 30 30 60 16
30 40 7070
W1 = 30 W2 = 30
V1= 0 30 30 35
V2= 20 25 50 19
V3= 0 30 60 16
30 40 7070
3
01
9
5
1
6
3
05
1
6
1
4
2
1
1
6
3
01
9
5
1
6
1
41
9
2
1
1
6
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A2:
30 30
25 50
Table 3
OC
B1: V1+W2= 30, W2= 30
A2: V2+W1= 25, W1= 5
B2: V2+W2= 50, V2= 20
A3: V3+W1= 30, V3= 25
VC CC
A1: 30 0 5 = 25 B1: 1050
B3: 60 25 30 = 5 A2: 350
B2: 250
A3: 480
2130
30 30
25 50
W1 = 5 W2 = 30
V1= 0 30 30 35
V2= 20 25 50 19
V3= 25 30 60 16
30 40 7070
1
4
2
1
1
9
1
4
3
5
5
1
4
5
3
5
1
6
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5) Aling Milling, a fruit trader, sells fruits to shoppers in Manila, Quezon City, and
Caloocan City, the monthly demand is 5000 kilos in Metro Manila, 3000 kilos in Quezon
City, and 2000 kilos in Caloocan City. The fruits are shipped from Laguna, Batangas, and
Mindoro. The monthly supply offered in Laguna is 4000 kilos, in Batangas, is 3500 kilos,
and 2500 kilos in Mindoro.
The shipping cost per kilos is shown below
To Manila Caloocan City Quezon City
From
LAGUNA 5 55 60
BATANGAS 64 66 60
MINDORO 74 75 80
What is the lowest transportation cost?
OCA1:V1+W1 = 5, W1 = 5
A2:V2+W1 = 64, V2 = 59
B2:V2+W2 = 66, W2 = 7
C2:V2+W3 = 60, W3 = 1
C3:V3+W3 = 80, V3 = 79
VC
B1: 55 7 0 = 48 A3: 74 79 5 = -10
C1: 60 0 1 = 59 B3: 75 79 7 = -11
B3:
66 60
75 80
Manila, 5 Caloocan, 7 Quezon, 1Laguna, 0 5 55 60 4000
Batangas, 59 64 66 60 3500
Mindoro, 79 74 75 80 2500
5000 2000 300010000
10000
66 60
75 80
400
0
100
0
200
0500
250
0
200
0500
250
0
200
0
250
0
500
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Table 2:
OC
A1: V1+W1=5,W1=5
A2: V2+W1=64,V2=59
C2: V2+W3=60,W3=1
B3: V3+W2=75, W2=-4C3: V3+W3=80, V3=79
VC
B1: 55 + 4 0 = 59 B2: 66 + 4 - 59 = 11
C1: 60 0 1 = 59 A3: 74 5 79 = -10
A3:
Table 3:
CC
A1: 20000
A2: 32000
C2: 180000
A3: 37000
B3: 150000
419000
OC
A1: V1+W1=5, W1=5 A3: V3+W1=74, V3= 69
B2:V2+W1=64, V2=59 B3: V3+W2=75, W2= 6
C2:V2+W3=60, W3=1
VC
B1: 55 0 1 = 49 B2: 66 59 6 = 1
C1: 60 0 1 = 59 C3: 80 69 1 = 10
Manila 5 Caloocan -4 Quezon 1Laguna 0 5 55 60 4000
Batangas 59 64 66 60
3500Mindoro 79 74 75 80 2500
5000 2000 3000 1000010000
64 60
74 80
64 60
74 80
Manila 5 Caloocan 6 Quezon 1Laguna 0 5 55 60 4000
Batangas 59 64 66 60 3500
Mindoro 69 74 75 80 2500
5000 2000 3000 1000010000
400
0
100
0
200
0
250
0
500
100
0
250
0
500
500300
0
500
400
0
500
200
0
300
0
500
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6) Using the MODI, find the minimum cost by filling up the following Tables:
Table I
W1 = 3 W2 = 1
A B
V1= 0 1 3 1 10
V2= 2 2 5 3 12
V3= 3 3 2 4 8
17 13 30
CC OC VC
A1: 30 A1: V1+W1 = 3 B1: 1 1 0 = 0
A2: 35 A2: V2+W1 = 5 A3: 2 3 3 = -4
B2: 15 B2: V2+W2 = 3
B3: 32 B3: V3+W2 = 4
Table II
W1 = 3 W2 = 5
A B
V1= 0 1 3 1 10
V2= -2 2 5 3 12
V3= -1 3 2 4 8
17 13 30
CC OC VC
A1: 30 A1: V1+W1 = 3 B1: 1 5 0 = -5
B2: 36 B2: V2+W2 = 3 A2: 5 + 2 3 = 4
A3: 14 A3: V3+W1 = 2
B3: 4 B3: V3+W2 = 4
10
75
8
10
7
12
1
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Table III
W1 = 3 W2 = 1
A B
V1= 0 1 3 1 10
V2= 2 2 5 3 12
V3= -1 3 2 4 8
17 13 30
CC OC VC
A1: 27 A1: V1+W1 = 3 A2: 5 2 3 = 0
B1: 1 B1: V1+W2 = 1 B3: 4 + 1 1 = 3
B2: 36 B2: V2+W2 = 3
A3: 16 A3: V3+W1 = 2
80
9
8
12
1