In: Advanced Math
You are responsible for developing a supervisory training programme for a company. The following table shows the relationships between the activities that must be completed, along with estimates of the durations in days.
Table 1: Activity Times and Predecessors
Activity | Immediate Predecessors | Optimistic Time (a) | Most Likely time (m) | Pessimistic Time (b) |
A | - | 3 | 7 | 13 |
B | - | 5 | 10 | 17 |
C | A,B | 3 | 5 | 8 |
D | C | 5 | 12 | 14 |
E | C | 2 | 5 | 9 |
F | E | 2 | 5 | 15 |
G | E,F | 5 | 8 | 12 |
H | D | 6 | 10 | 12 |
I | E,H | 3 | 4 | 8 |
J | G, I | 4 | 7 | 10 |
Required
(a) Draw the activity network for this problem (either AON or
AOA)
(b) Determine the Expected Time and Variance for each activity
(show in a table).
Round off times to two decimal places where fractional.
(c) Show the activity schedule (ES, EF, LS, LF) as well as slack
(in table).
(d) Determine and state the critical path for this project. This
must be based on
your work in c) and not by inspection.
(e) What are the expected time and the variance of the
project?
(f) What is the probability the project will be finished within 49
days?
(g) What time should be set such that there is a 99% chance of
completion?
(h) What is the probability the project will take between 45 and 50
days?