Question

The city of Bloomington is about to build a new water treatment plant. Once the plant is designed (D) we can select the site (S), the building contractor (C and the operating personnel (P). Once the site is selected we may erect the building (B). We can order the water treatment machine (W) and prepare the operations manual (M) only after the contractor is selected. We can begin training the operators (T) when both the operations manual and operating personnel selected are completed.  When the water treatment and building are finished, we can install the treatment machine (I). Once the treatment machine is installed and the operators are trained, we can obtain an operating license (L). The time to complete each activity is assumed to be a normal distribution and the estimated mean and standard deviation of the time (in months) needed to complete each activity is defined below:

ACTIVITY	DESCRIPTION	MEAN	STANDARD DEVIATION
D	Design plant	6	1.5
S	Select site	2	0.3
C	Select Building Contractor	4	1.0
P	Select Operating Personnel	3	1.0
B	Erect Building	24	0.6
W	Order Water Treatment machinery	14	4.0
M	Prepare Operations Manual	3	0.4
T	Train Operators	4	1.0
I	Install Treatment Machine	6	1.0
L	Obtain Operator License	3	6.0

1. Draw the PERT network for the project
2. Calculate the critical path and estimated completion time of the project
3. Using this estimated completion time, determine the probability of completing the project in (1) under 50 months and (2) over 55 months
4. Use simulation to calculate the estimated completion time and to determine the probability of completing the project in (1) under 50 months and (2) over 55 months (use a monte carlo simulation of 200 repetitions)
5. Explain why the answers to questions (b) and (c ) may differ to that determined in question (d).
6. Use simulation to estimate the probability that B, I and T are critical activities

Answer 1

We will use the provided information to decide the predecessor for our PERT network construction. We will define the mean expected time for the activities to calculate the critical path. After that, we will find all the paths to complete the project. Finally, we will calculate the required probabilities from the critical path obtained.