Question

Pirmin's bike shop is behind on a custom bike and needs to crash 8 hours of time from the 8-step project. Suppose Pirmin calls the customer and asks for a project extension, reducing the amount of time he needs to crash.

Activity	Normal Duration (hr)	Normal Cost ($)	Crash Duration (hr)	Crash Cost ($)	Immediate Predecessors
A	2	10	2	N/A	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	N/A	C,E
G	7	35	6	50	F
H	10	50	7	80	D,G

A. Draw (with a computer application) the network diagram.

B. Calculate the maximum time-savings available on a $25 crash budget.

C. Calculate the cost to crash four hours of savings.

Answer 1

The project network is as follows:

The network consists of 3 paths as follows:

A-B-C-D-H, duration is 23 days

A-B-C-F-G-H, duration is 28 days

A-B-C-E-F-G-H, duration is 34 days

Determine crashing cost per hour as follows:

	Normal Duration (Hr.)	Normal Cost	Crash Duration	Crash Cost		Allowable crashing	Crashing cost per hour
Activity	NT	NC	CT	CC	CC - NC	NT - CT	(CC - NC)/(NT - CT)
A	2	$10	2	NA	$0	0	$0
B	3	$15	2	$23	$8	1	$8
C	5	$25	4	$30	$5	1	$5
D	3	$20	1	$24	$4	2	$2
E	6	$30	4	$45	$15	2	$7.5
F	1	$5	1	NA	$0	0	$0
G	7	$35	6	$50	$15	1	$15
H	10	$50	7	$80	$30	3	$10
TOTALS		$190

Crashing Sequence:

According to crashing principle, crash only critical path and crash the critical activities with lowest crashing cost per hour.

Crashing Sequence	0	1	2	3	4
Critical Paths		A-B-C-E-F-G-H	A-B-C-E-F-G-H	A-B-C-E-F-G-H	A-B-C-E-F-G-H
Lowest crashing cost per week activity (crashing cost)		C ($5/ hour)	E ($7.5/ hr)	E ($7.5/ hr)	B ($8/ hr)
Activity Crashed	None	C	E	E	B
Crashing Duration	0	1	1	1	1
Project duration	34	33	32	31	30
A-B-C-D-H	23	22	22	22	21
A-B-C-F-G-H	28	27	28	28	27
A-B-C-E-F-G-H	34	33	32	31	30
Crash cost	$0	$5	$7.5	$7.5	$8
Cum. Crash cost	$0	$5	$12.5	$20	$28

b.

Crashing activity B by 1 hour, the cumulative crashing cost is increases to $28. To obtain duration for $25 cumulative crashing cost, crash the activity B by fraction of hour. For $25 cost, crash duration = $5/$8 = 0.625 hours.

Thus, if the activity B is crashed by 0.625 hours the cost will increase by $5.

Total project duration will be 30.625 hours.

Maximum time saved for $25 crash budget = 34 hours – 30.625 hours = 3.375 hours

c.

To save four hours or to complete the project in 34 – 4 = 30 hours, the cumulative crash cost is $28. It requires to crash activities C, E, and B by 1, 2 and 1 hours respectively.