Your company is in the process of planning a project that is to be undertaken for an

external client. The project consists of nine activities as follows $($see next page$)$:

$1$

I strongly recommend that each group member downloads and installs the add$-$in so that everybody is

familiar with using the triangular and PERT distributions in Excel.

Due to a possible delay in statutory approvals, there is a $25\%$ chance that the branch

leading to Activity $2$ must be taken before Activity $3$ can be started and a $75\%$

probability that the branch to Activity $3$ can be followed. The rest of the network

should be interpreted in the normal way: Activities $4$ and $5$ can only be started when

Activity $3$ has been completed and Activities $6,7$ and $8$ are dependent on the

completion of both Activities $4$ and $5.$ Likewise, the final activity can only start once

the preceding three parallel activities have been completed.

Activity $1$ consists of a well$-$known design process and will take $2$ weeks $(10$ days$)$ to

complete. However, previous experience with similar projects has shown that the

duration of all the other activities should be considered a random variable. Historical

data and inputs from the various project members have been collected in the

following table to reflect the uncertainty:

Activity no Distribution Parameters

$2$ Uniform a$=6,$ b$=12$

$3$ Triangular $10,12,22$

$4$ PERT $15,18,30$

$5$ Normal mean$=16,$ sd$=6$

$6$ Poisson lambda$=20$

$7$ Triangular $18,24,38$

$8$ Triangular $16,19,45$

$9$ PERT $7,10,17$

All distributions model duration in days.

$2\mathrm{.}1$ Use Excel to simulate the distribution and CDF for the network completion time.

Perform the simulation with integer numbers only $($i$.$e$.$ whole days, not

fractions$).$ Also make sure that no negative durations are produced in your

simulation, as this is clearly not possible.

$2\mathrm{.}2$ Provide a table with the descriptive statistics. Clearly highlight the mean and

standard deviation of the completion time. What are your observations, insights

and conclusions?

$2\mathrm{.}3$ Company policy states that the project duration quoted for clients should have

at least a $85\%$ chance of achieving. What is the duration time that should be

quoted for this project