Question

1. Consider a project that requires the completion of 7 tasks, as follows:

   o Tasks A and B can begin simultaneously at the beginning (“time zero”).

   o Task C can only begin after task B is completed.

   o Task D can only begin after task A is completed.

   o Task E can only begin after task A is completed.

   o Task F can only begin after task E is completed.

   o Task G can only begin after tasks C and D are completed.

   The expected durations (in days) of each task are as follows: A=15; B=20; C=10; D=10; E=30; F=20; G=40.

   What is the expected completion of the whole project?

   		50 days
   		60 days
   		70 days
   		75 days

2.Consider the project from the previous question with the added complexity that the actual completion time of each task will be:

Task	Completion Time
A	15+RANDBETWEEN(-8,8)
B	20+RANDBETWEEN(-8,8)
C	10+RANDBETWEEN(-8,8)
D	10+RANDBETWEEN(-8,8)
E	30+RANDBETWEEN(-8,8)
F	20+RANDBETWEEN(-8,8)
G	40+RANDBETWEEN(-8,8)

Using PERT, what is the expected completion time of the project?

		50
		60
		70
		75

Answer 1

1. A network diagram is drawn satisfying all precedence relationships. Then earliest start time(ES), earliest finish time(EF) , latest start time(LS), latest finish time(LF) for each activities are calculated. Here ES & EF are calculated through a forward pass on the diagram by adding up the expected durations for each activities then LS & LF are calculated through a backward pass and reversing the activity completion times. Critical path is the path which one's delay will leads to delay in the whole project. The duration of critical path will give us expected duration of whole project.

Here expected project duration is found out as 70 days.

2. Here, while estimating the time for a PERT network , we have considered the distribution as beta distribution. and accordingly standard deviation is also calculated. Here as expected durations of each activities are found out to be sames as the values in the previous questions, the overall expected project completion time is also equal that is 70 days with a standard deviation of 7.04 days.

All steps and calculations are given below :

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