Question

Consider the following project activities:

Activity A 8 с D E F G H Duration (weeks) Predecessor Optimistic Most Likely Pessimistic 1 2 A 2 7 A 1 3 5 B 3 6 9 C 2 3 7 A 5 7 EF 4 8 D 1 3 GH 2 6 MIN AN -

1. Calculate the expected time (t_e) for each activity.
2. Draw an Activity on Node (AON) diagram to reflect the flow of these activities.
3. Calculate the Early Start (ES), Early Finish (EF), Late Start (LS), and Late Finish (LF) for each activity.
4. Calculate the slack for each activity.
5. Identify all activities on the Critical Path.
6. Use the data to calculate the probability the project will finish in 20 weeks (Hint: z-score).

Answer 1

a.

Activity	Optimistic time-a	Expected completion time-m	Pessimistic time-b	Expected time= (a+4*m+ b)/6
A	1	2	4	2.17
B	2	3	7	3.50
C	1	3	5	3.00
D	3	6	9	6.00
E	2	3	7	3.50
F	4	5	7	5.17
G	3	4	8	4.50
H	1	2	3	2.00
I	2	4	6	4.00

b.

AON >H A 1 ' CE 'F

c & d

step 1	find early start, and early finish from the start of the project for each activity
step 2	Find Maximum EF and keep it as the LF of last activities. Max of EF's is 17.67
step 3	calculate LS for each activity after calculating its EF

Activity	Duration, D	Early start, ES=Max of early finish of preceding activities	Early finish, EF = ES + D	Late finish, LF= Min of LS of successor activities	Late start, LS= LF - D	Total slack= LF-EF
A	2.17	0.00	2.17	2.17	0.00	0.00
B	3.50	2.17	5.67	5.67	2.17	0.00
C	3.00	2.17	5.17	5.67	2.67	0.50
D	6.00	5.67	11.67	11.67	5.67	0.00
E	3.50	5.17	8.67	9.17	5.67	0.50
F	5.17	2.17	7.33	9.17	4.00	1.83
G	4.50	8.67	13.17	13.67	9.17	0.50
H	2.00	11.67	13.67	13.67	11.67	0.00
I	4.00	13.67	17.67	17.67	13.67	0.00