Question

The ABC Manufacturing Co. has made a decision to replace an existing production line with new equipment. This project will require several tasks (jobs) with precedence relationships and duration (days) as shown in the following table. The project will be finished when activities A-J are all finished.

Activity	predecessor	Optimistic	Most likely	Pessimistic	Expected
A	-	4	5	12
B	A	3	4.5	15
C	A	2	3	4
D	C	6	8	22
E	B	4	6	8
F	C	3	4	5
G	D,E	1.5	3	4.5
H	B	5	7	15
I	H	3	4	5
J	G, I	2	4	6

1. Calculate the expected time for each activity

Expected times (t) = a + 4m + b) / 6

a = Optimistic time, m= most likely, b= pessimistic time

2. Create an Activity-On-Arrow network diagram for this Project.
3. Sketch Gantt chart for this project
4. Construct the PERT Network for this using this legend (you need to calculate the earliest start (ES) and finish (EF) times and latest start (LS) and finish (LF) times, the slack (S) for each of the activities in the network).

ES	D	EF
Activity name
LS	S	LF

ES: Early start, EF: early finish, LS: Late start, LF: late finish

D: Duration or Expected time

S: Slack

5. Identify the critical path(s).
6. What is the project completion duration?

Answer 1

1	B	C	D	E	F	G
2	Activity	predecessor	Optimistic	Most likely	Pessimistic	Expected
3	A	-	4	5	12	6
4	B	A	3	4.5	15	6
5	C	A	2	3	4	3
6	D	C	6	8	22	10
7	E	B	4	6	8	6
8	F	C	3	4	5	4
9	G	D,E	1.5	3	4.5	3
10	H	B	5	7	15	8
11	I	H	3	4	5	4
12	J	G, I	2	4	6	4

Formula

1	B	C	D	E	F	G
2	Activity	predecessor	Optimistic	Most likely	Pessimistic	Expected
3	A	-	4	5	12	=(D3+(4*E3)+F3)/6
4	B	A	3	4.5	15	=(D4+(4*E4)+F4)/6
5	C	A	2	3	4	=(D5+(4*E5)+F5)/6
6	D	C	6	8	22	=(D6+(4*E6)+F6)/6
7	E	B	4	6	8	=(D7+(4*E7)+F7)/6
8	F	C	3	4	5	=(D8+(4*E8)+F8)/6
9	G	D,E	1.5	3	4.5	=(D9+(4*E9)+F9)/6
10	H	B	5	7	15	=(D10+(4*E10)+F10)/6
11	I	H	3	4	5	=(D11+(4*E11)+F11)/6
12	J	G, I	2	4	6	=(D12+(4*E12)+F12)/6

From the Network diagram, It can be concluded that Critical Path is A– B –H - I - J and it is shown with Bold Line, again Project Need at least 28 Days to finish,

Activity	ES	LS	EF	LF	Slack	Critical Path activity Yes or No
A	0	0	6	6	0	Yes
B	6	6	12	12	0	Yes
C	6	8	9	11	2	No
D	9	11	19	21	2	No
E	12	15	18	21	3	No
F	9	24	13	28	15	No
G	19	21	22	24	2	No
H	12	12	20	20	0	Yes
I	20	20	24	24	0	Yes
J	24	24	28	28	0	Yes