BM103

Exercise 11
1) Solve the ff. Modified Distribution (MODI) Warehouse
A1:V1+W1= 3, W1= 3
B1:V1+W2= 5, W2= 5
B2: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:

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 = 1
B3: 8 – 3 – 5 = 0

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
B2: 50 – 0 – 30 = 20
A3: 40 – 30 – 30 = -20
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
3)
OC
A1: V1+W1= 5, W1 = 5
A2: V1+W2= 7, W2 = 7
B2: V2+W2= 4, V2 = -3
C2: V2+W3= 10, W3 = 13
VC
A3: 7 – 0 – 13 = -6
B1: 8 + 3 – 5 = 6

A3: 7
7
4
10

Table 2
OC
A1: V1+W1 = 5, W1= 5
A3: V1+W3 = 7, W3= 7
B2: V2+W2 = 4, W2= 1
C2: V2+W3 = 10, V2= 3
VC CC = 100 + 70 + 140 + 50 =
A2: 7 – 1 – 0 = 6 = 360
B1: 8 – 5 – 3 = 0

4)
OC
A1: V1+W1 = 30, W1= 30
B1: 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
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
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?
OC
A1: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

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=-4
C3: 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 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

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