Question

Case Study: Westin Contractors

William Purvis looked across his desk at the company’s latest management recruit and said, ‘Welcome to Westin Contractors. This is a good company to work for and I hope you settle in and will be very happy here. Everyone working for Westin has to be familiar with our basic tools, so you should start by looking at network analysis.

Here is a small project we have just costed – I have to give the customer some details about schedules, workloads and budgets by the end of the week. I would like a couple of alternative views with your recommendation of the best. Everything you need is available in the office so don’t be afraid to ask for help and advice.’ William Purvis supplied the following data and said that there is a penalty cost of BD 3,500 for every week the project finished after week 28.

Activity	Preceding Activity	Times of Completion (in weeks)
		Optimistic	Most Likely	Pessimistic
A	-	1	3	4
B	-	3	5.5	9
C	-	4	7	8
D	A	4	8.5	10
E	C	2	3.5	9
F	B,E	2	3	5
G	C	6	9	16
H	D, F,G	2	3	5

Q1.If you were the recruit, how would you set about this job and what would you say in your report?

Answer 1

The calculations for this project are:

Activity	Optimistic	Likely	Pessimistic	Mean	Std dev	Variance
A	1	3	4		2.833333	0.5	0.25
B	3	5.5	9		5.666667	1	1
C	4	7	8		6.666667	0.666667	0.444444
D	4	8.5	10		8	1	1
E	2	3.5	9		4.166667	1.166667	1.361111
F	2	3	5		3.166667	0.5	0.25
G	6	9	16		9.666667	1.666667	2.777778
H	2	3	5		3.166667	0.5	0.25
Precedences
Activity	Time	Pred 1	Pred 2	Pred 3
A	2.833333
B	5.666667
C	6.666667
D	8	A
E	4.166667	C
F	3.166667	B	E
G	9.666667	C
H	3.166667	D	F	G
Results
Activity	Early Start	Early Finish	Late Start	Late Finish	Slack		Variance	Critical Variance
A	0	2.833333	5.5	8.333333	5.5		0.25
B	0	5.666667	7.5	13.16667	7.5		1
C	0	6.666667	0	6.666667	0		0.444444	0.444444
D	2.833333	10.83333	8.333333	16.33333	5.5		1
E	6.666667	10.83333	9	13.16667	2.333333		1.361111
F	10.83333	14	13.16667	16.33333	2.333333		0.25
G	6.666667	16.33333	6.666667	16.33333	0		2.777778	2.777778
H	16.33333	19.5	16.33333	19.5	0		0.25	0.25
	Project	19.5					Project	3.472222
							Std.dev	1.86339

The optimal assignment of the project acitivities should be:

C-G-H.

The expected duration of finishing the project is 19.5 weeks.

The probability of finishing the project after 28 weeks is:

z = (28 - 19.5)/1.86339 = 4.56

P (z > 4.56) = 0.0000

The probability of finishing the project after 28 weeks is 0.0000.

Thus, the company does not have to worry about the penalty cost of BD 3,500 for every week the project finished after week 28 because the probability of finishing the project after 28 weeks is 0.0000.

In short, I would report that the jobs assignment should be C-G-H and the project would be finished within 28 weeks with a 100% probability.