Question

At the Hard Rock Café, like many organizations, project management is a key planning tool. Tomasso is in charge of the Rockfest event, which is attended by well over 100,000 enthusiastic fans. The challenge is pulling it off within 5-month planning horizon. Tomasso identifies activities, their immediate predecessors and time estimates as shown in the table below. As a chief project manager, you have been asked to prepare a report for your company. This report needs to address the concerns of the following: (a) Introduction (b) An explanation of the model and the methodology used (i.e. CPM and PERT). (c) Display your estimated outputs using tables and graphs as well as network diagram. (d) A discussion of the results estimated. (e) Any other comments you feel relevant to the issues being addressed. (f) Conclusion and recommendations. HINT: 1) Determine the project network, critical path, expected time duration. 2) What is the probability that the project can be completed within 5 months? . Table1: Managing Hard Rock’s Rockfest Activity Activity Description Immediate Predecessor Duration (days) o- m- p a Finalize site and building contracts - 1-10-15 b Set police and fire security plan a 1-5-8 c Hire director a 3-5-7 d Develop site plan c 10-14-21 e Set venue capacity d 5-10-12 f Set TV deal c 1-2-4 g Plan for TV camera placement f 3-5-7 h Select local promoter a 6-14-20 i Passes and stage credentials h 3-6-10 j Sound and staging h 15-22-30 k Power, plumbing, AC, toilet services a 3-10-15 l Hire operations manager h 14-25-40 m Hire production manager l 7-12-20 n Hire sponsor coordinator m 10-15-25 o Finalize sponsors n 30-45-60 p Target headline entertainers l 3-7-10 q Target support entertainers p 2-5-8 r Travel accommodations for talent q 10-12-16 s Define signage for sponsors r,o 2-4-7 t Ticketmaster contract p 10-18-21 u Travel accommodations for staff p 1-2-3 v On-site ticketing k,b,g,e,i,j 0.5-0.5-0.5 w Final control s,t,u,v 0.5-0.5-0.5 son - w

Answer 1

Project scheduling with uncertain activity times (Optimistic, Most likely, Pessimistic)

a	-	1	10	15
b	a	1	5	8
c	a	3	5	7
d	c	10	14	21
e	d	5	10	12
f	c	1	2	4
g	f	3	5	7
h	a	6	14	20
i	h	3	6	10
j	h	15	22	30
k	a	3	10	15
l	h	14	25	40
m	l	7	12	20
n	m	10	15	25
o	n	30	45	60
p	l	3	7	10
q	p	2	5	8
r	q	10	12	16
s	r,o	2	4	7
t	p	10	18	21
u	p	1	2	3
v	k,b,g,e,l,j	0.5	0.5	0.5
w	s,t,u,v	0.5	0.5	0.5
son	w	0	0	0

Expected time of each activity,

Activity	to	tm	tp	te=(to+4⋅tm+tp)/6	σ2=(tp-to/6)2
a	1	10	15	9.33	5.44
b	1	5	8	4.83	1.36
c	3	5	7	5	0.44
d	10	14	21	14.5	3.36
e	5	10	12	9.5	1.36
f	1	2	4	2.17	0.25
g	3	5	7	5	0.44
h	6	14	20	13.67	5.44
i	3	6	10	6.17	1.36
j	15	22	30	22.17	6.25
k	3	10	15	9.67	4
l	14	25	40	25.67	18.78
m	7	12	20	12.5	4.69
n	10	15	25	15.83	6.25
o	30	45	60	45	25
p	3	7	10	6.83	1.36
q	2	5	8	5	1
r	10	12	16	12.33	1
s	2	4	7	4.17	0.69
t	10	18	21	17.17	3.36
u	1	2	3	2	0.11
v	0.5	0.5	0.5	0.5	0
w	0.5	0.5	0.5	0.5	0
son	0	0	0	0	0

The earliest and latest expected time for each activity is calculated by considering the expected time te

Activity	Immediate Predecessors	Duration
a	-	9.33
b	a	4.83
c	a	5
d	c	14.5
e	d	9.5
f	c	2.17
g	f	5
h	a	13.67
i	h	6.17
j	h	22.17
k	a	9.67
l	h	25.67
m	l	12.5
n	m	15.83
o	n	45
p	l	6.83
q	p	5
r	q	12.33
s	r,o	4.17
t	p	17.17
u	p	2
v	k,b,g,e,l,j	0.5
w	s,t,u,v	0.5
son	w	0

Edge and it's preceded and succeeded node

Edge	Node1 → Node2
a	1→2
c	2→3
h	2→7
k	2→9
b	2→19
d	3→4
f	3→6
e	4→5
d	5→10
d	5→19
g	6→19
j	7→8
l	7→10
i	7→19
v	8→17
d	9→19
d	10→8
m	10→11
p	10→14
n	11→12
o	12→13
s	13→16
q	14→15
t	14→16
u	14→17
r	15→13
d	16→17
w	17→18
son	18→19

The critical path of the project is: 1-2-7-10-11-12-13-16-17-18-19 and critical activities are a,h,l,m,n,o,s,d,w,son.
The total project time is 126.67

The probability that the project would be completed in 5 months i.e. 5*30 = 150 days

The project duration required is 126.67 = Summation of Mean

Summation of Variance = 91.94, Summation of Std. Deviation = Square root of Variance = 9.588

In this case, there is 99.25% chance that the project will be over in 150 days.