Question

Project management

Expediting a Project

Task	Predecessor	Normal Time Weeks	Normal Cost	Crash Time	Crash Cost
A	-	4	$2000	4	-
B	A	4	$1500	2	4500
C	A	6	5000	4	8000
D	B	2	1000	2	-
E	B	6	8000	3	10000
F	C	10	10000	7	14000
G	D	7	3500	4	5000
H	E	4	2500	2	5000
I	G,H	3	2000	2	3500
J	I,F	3	3000	1	4500

Consider the project shown above.

a)Draw the network diagram and find the critical path, time and cost for an all-normal level of project activity.

b)Calculate the crash cost-per-week assuming that all activities may be partially crashed.

c)Which tasks should be crashed to do the project in 21 weeks? What is the project cost?

d)Calculate the shortest delivery time for the project. What is the cost?

Answer 1

(i)

Critical path is ABEHIJ with duration 24 weeks.

cost for nromal time =38500

(ii)

Activity	slope	Max crash
A	None	0
B	1500	2
C	1500	2
D	None	0
E	666.66	3
F	1333.33	3
G	500	3
H	1250	2
I	1500	1
J	750	2

crashing schedule

(i) E is the cheapest activity which can be crashed for a week at 666 per week. Duration is 23 and cost is 38500+666 =39166

Now ABDGIJ, ABEHIJ and ACFJ are critical paths.

(ii) J can be crashed for 2 weeks at a total cost of 1500. Duration is now 21 weeks and cost is 40666

The cost for crashing the project to 21 days is 2166. Total cost is 40666.

(iii) G, E and F can be crashed at a total cost of 2500. Duration is 20

Total cost is 43166

(iv) G, E and F can be again crashed at a total cost of 2500. Duration is 19

Total cost is 45666

(v) B and f can be crashed for 1 day each at a total cost of 2833, Duration is 18

Total cost is 48000

(vi) B and C can be crashed for 1 day at a cost of 3000. Duration is 17

Total cost is 51000.

(vii) C and I can be crashed at a total cost of 3000. Duration is 16

Cost is 54000.

No more crashing is possible.