Question

Table below contains information about an environmental clean-up project in the township of Hiles. Shorten the project three weeks by finding the minimum-cost schedule. Assume that project indirect costs and penalty costs are negligible. Identify activities to crash while minimizing the additional crash costs.

Table 1 - Environmental Project Data

Activity	Normal Time (weeks)	Crash Time (weeks)	Cost to Crash ($ per week)	Immediate Predecessor(s)
A	7	6	200	None
B	12	9	250	None
C	7	6	250	A
D	6	5	300	A
E	1	1	-	B
F	1	1	-	C, D
G	3	1	200	D, E
H	3	2	350	F
I	2	2	-	G

Answer 1

Network Diagram:

Activity	Normal Time	Crash time	Time can be decreased	Cost to crash per week
A	7	6	1	200
B	12	9	3	250
C	7	6	1	250
D	6	5	1	300
E	1	1	0	--
F	1	1	0	--
G	3	1	2	200
H	3	2	1	350
I	2	2	0	--

In this project, there are two critical paths. So to shorten the project by three weeks we need to crash the activities on both paths simultaneously.

Step 1:

On Path A-C-F-H, min crashing cost is for A, while on path B-E-G-I min crashing cost is for G.

So we can crash the both activity A and G by 1 week.

Crashing Cost = 200 +200 = 400

Step 2:

Now, D is also become a critical activity.

Further, we can crash Activity G by 1 week, and simultaneously we can crash activity H by 1 wee.

Crashing Cost = 200 +350 = 550

Step 3:

Further, we can crash Activity B by 1 week, and simultaneously we need to crash Activity C and D (because both are on the critical path) by 1 week.

Crashing Cost = 250+ 250 +300 =800

Total Crashing Cost = 400 + 550 +800 = 1750