Question

You have recently been hired to help with planning for a music festival in Sydney, Australia planned for late December 2020. Much still needs to be done in order for the event to go ahead. As the project manager working with the city, you are tasked with determining whether it is feasible to put on the event by the proposed date. The following activities would have to be undertaken before the festivities. Immediate Predecessor Activity A B С D E F G H Description Hire production manager Hire main entertainment act Hire promotor Find opening acts Select venue Find sponsors Sell tickets Sound check and rehearsal A A B D D, E CF Time (weeks) 5 3 7 6 7 3 10 8 The project network diagram is given on the next page.

Answer 1

(a)

Draw the table listing ES, LS, EF, LF and Slack time of each activity Earliest Start (ES) is calculated by forward pass method as latest of the predecessors Earliest Finish (EF). Latest Finish (LF) is calculated using backward pass method as earliest of the successors Latest Start (LS). Earliest Finish (EF) = Earliest Start (ES) + Activity's duration Latest Start (LS) = Latest Finish (LS) - Activity's duration Slack - Latest Finish - Earliest Finish Activity ES EF LS LF Slack Immediate Time Predecessor (weeks) 5 Successor Critical Activity Yes 5 0 0 5 C,D E 3 А B C D E F G 7 6 5 3 12 11 10 14 H F 5 0 2 2 0 2. 0 0 2 7 5 5 11 12 14 5 14 11 12 14 А А B D DE CF Yes слол 7 G H 3 Yes 3 11 11 14 21 22 1 10 8 H 22 22 0 Yes

.

(b)

Critical path is the longest path in the network. All the activities on critical path have 0 slack.

Critical path is:  A-D-F-H

Project length = Length of critical path = 5+6+3+8 = 22 weeks

.

(c)

For each activity, calculate the expected time, te =(optimistic + 4 * most likely + pessimistic)/6

Variance = (pessimistic - Optimistic)²/36

Activity	Predecessor	Optimistic	Most likely	Pessimistic	Expected Time, te	Variance (σ2)
A		3	5	7	5	0.44
B		3	3	3	3	0
C	A	7	7	7	7	0
D	A	2	6	10	6	1.78
E	B	4	7	10	7	1
F	D	1	3	5	3	0.44
G	D,E	10	10	10	10	0
H	C,F	8	8	8	8	0

We see that expected time remain same as deterministic time.

Project's expected completion time = 5+6+3+8 = 22

Critical path remains same, i.e. A-D-F-H

Project variance = SUM of variances of critical activities

= 0.44+1.78+0.44+0

= 2.67

.

Standard deviation = square root of variance

= sqrt(2.67)

= 1.63

Deadline = 25 weeks

z value = (25-22)/1.63

= 1.84

P(z) = NORMSDIST(1.84)

= 0.97

Probability of team failing to meet the deadline = 1 - P(z)

= 1 - 0.97

= 0.03

or, 3 %

.

(e)

For 90%, z value = NORMSINV(0.90)

= 1.28

Completion time = 22 + 1.28*1.63

= 24 weeks