D Calculations 43 for total 21 Consider the project describe

D. Calculations. (43 for total) 21) Consider the project described by the table where all durations are in days and the costs in dollars. What is the minimum cost of completing this project in 150 days? Activi Predecesso Normal Minimum Time Time Normal Cost Crash Cost 100 30 22 2.5004100 C A 1,000 15,000 ,000 3,000 41,000 30,000 0,000 ,500 6,500 14,400 3,000 ,300 15,500 6,000 E po 145 37,500 40 15 30 5,000 200 19,400 18,600 7.500 13 26 2015,250 23,500 5,000 5,000

Solution

The crash cost per day has been added to the table. Possible routes through the network are:

ABFGKLM=175

ABFGKNQ=55

ABFJHPQ=155

ACDEHPQ=160

and the initial project cost is $227,450.

Activity

Predecessor

Normal Time

Minimum Time

Normal Cost

Crash cost

$/day

A

15

12

800

1,100

100

B

A

30

22

2,500

4,100

200

C

A

45

37

21,000

31,000

1500

D

C

20

17

15,000

22,000

2333

E

D

5

4

3,000

3,300

300

F

B

10

7

13,000

15,500

833

G

F

30

25

41,000

46,000

1000

H

J, E

50

45

30,000

37,500

1500

J

F

25

20

20,000

25,000

1000

K

G

35

33

6,500

7,200

350

L

K

40

33

16,500

19,400

414

M

L

15

13

14,400

18,600

2100

N

K

30

26

23,500

27,500

1000

P

H

20

15

15,250

23,500

1650

Q

N, P

5

5

5,000

5,000

Purchasing critical activities from least expensive to most expensive without switching critical paths proceeds as follows:

Purchase

Activity

# Days

Path Lengths

Extra Cost

1

A

3

ABFGKLM=172

ABFGKNQ=152

ABFJHPQ=152

ACDEHPQ=157

300

2

B

8

ABFGKLM=164

ABFGKNQ=144

ABFJHPQ=144

ACDEHPQ=157

1,600

3

K

2

ABFGKLM=162

ABFGKNQ=142

ABFJHPQ=144

ACDEHPQ=157

700

4

L

5

ABFGKLM=157

ABFGKNQ=142

ABFJHPQ=144

ACDEHPQ=157

2,071

5

L

E

1

1

ABFGKLM=157

ABFGKNQ=142

ABFJHPQ=144

ACDEHPQ=157

414.30

300

6

L

C

1

1

ABFGKLM=156

ABFGKNQ=142

ABFJHPQ=144

ACDEHPQ=156

414.30

1,250

7

F

C

3

3

ABFGKLM=153

ABFGKNQ=139

ABFJHPQ=141

ACDEHPQ=153

2,500

3,750

8

G

C

3

3

ABFGKLM=150

ABFGKNQ=136

ABFJHPQ=144

ACDEHPQ=150

3,000

3,750

Total reduction is 25 days at an additional cost of $20,050, for a total project cost of $247,500.

3A\'s = 300

8B\'s = 1600

7C\'s = 8750

1E = 300

3F\'s = 2500

3G\'s = 3000

2K\'s = 700

7L\'s = 2900

Activity	Predecessor	Normal Time	Minimum Time	Normal Cost	Crash cost	$/day
A		15	12	800	1,100	100
B	A	30	22	2,500	4,100	200
C	A	45	37	21,000	31,000	1500
D	C	20	17	15,000	22,000	2333
E	D	5	4	3,000	3,300	300
F	B	10	7	13,000	15,500	833
G	F	30	25	41,000	46,000	1000
H	J, E	50	45	30,000	37,500	1500
J	F	25	20	20,000	25,000	1000
K	G	35	33	6,500	7,200	350
L	K	40	33	16,500	19,400	414
M	L	15	13	14,400	18,600	2100
N	K	30	26	23,500	27,500	1000
P	H	20	15	15,250	23,500	1650
Q	N, P	5	5	5,000	5,000