Question

The client of a project has requested the project team to crash 8 hours of time. The table below provides the necessary information about the possible project crashing.

(a) What is the crash cost for 8 hours of time-savings?

(b) Assume the team calls the client and asks for a project extension, reducing the amount of time they need to crash. The project team has a $20 crash budget. Is the budget sufficient to crash 4 hours of time?

Activity

Normal

Duration (hours)

Normal

Cost ($)

Crash

Duration (hours)

Crash

Cost (S)

Immediate

Predecessors

A

2

10

2

0

None

B

3

15

2

23

A

C

5

25

4

30

B

D

3

20

1

24

C

E

6

30

4

45

C

F

1

5

1

0

E

G

7

35

6

50

F

H

10

50

7

80

D, G

Answer 1

Activity	Normal	Normal	Crash	Crash	Immediate
	Duration (hours)	Cost ($)	Duration (hours)	Cost (S)	Predecessors
A	2	10	2	0	None
B	3	15	2	23	A
C	5	25	4	30	B
D	3	20	1	24	C
E	6	30	4	45	C
F	1	5	1	0	E
G	7	35	6	50	F
H	10	50	7	80	D, G

(a)

Initial codition (normal time estimates) D 3 A B с H 2 x 3 5 10 目一母母 Duration Project paths A-B-C-D-H A-B-C-E-F-G-H 23 34 Project duration 34

Activity	Normal	Normal	Crash	Crash	Slope
	Duration (hours)	Cost ($)	Duration (hours)	Cost ($)	$ / hr
A	2	10	2	0	-
B	3	15	2	23	8
C	5	25	4	30	5
D	3	20	1	24	2
E	6	30	4	45	7.5
F	1	5	1	0	-
G	7	35	6	50	15
H	10	50	7	80	10

Step-1: Crash 'C' by 1 hour. Total cost = $5

D 3 A H B 3 C 4X 2 x 10 E 6 G 7 Project paths |A-B-CD-H | A-B-C-E-F-G-H Duration 22 33 Project duration 33

Step-2: Crash 'E' by 2 hours. Total cost = 2 * $7.5 = $15

D 3 A B C H 2 x 3 4 x 10 E F G 中由电 = 4JX 1 X 7 Project paths | A-B-C-D-H | A-B-CE-F-G-H Duration 22 31 Project duration 31

Step-3: Crash 'B' by 1 hour. Total cost = $8

D 3 A H 一回一回 2|X 2 |x AIR 10 E F G 4TX 1 x Duration Project paths | A-B-C-D-H A-B-C-E-F-G-H 21 30 Project duration 30

Step-4: Crash 'H' by 2 hours. Total cost = 2 * $10 = $20

D 3 A H B 2 x 21X 4 x 8 E F G 4 x 11 7 Duration Project paths |A-B-C-D-H | A-B-C-E-F-G-H 19 28 Project duration 28

Note that the target of 8 hours reduction is achieved now (from 34 hrs initially to 28 hrs now). The total minimum cost of crashing = 5+15+8+20 = $48

(b)

A 4-hour reduction means the end of step-3 where the duration became 30 hours.

At this point, the total cost was 5+15+8 = $28. So, with only $20 in hand, it is not possible to achieve this target.