Find out the time required to complete the following project and the critical activities:

**Determination of Project
Completion Time in PERT**

**Problem 2**

Find out
the time required to complete the following project and the critical
activities:

Using the
single time estimates of the activities, we get the following network diagram
for the project.

Consider the paths, beginning with the start node
and stopping with the end node. There are four such paths for the given
project. They are as follows:

Time for the path: 4+10+9+ 6+3 = 32 days. Compare the times for the four paths. Maximum of {48, 31, 49, 32} = 49. We see that Path III has the maximum time. Therefore the critical path is Path III. i.e., The critical activities are A, C, E, F and H. The non-critical activities are B, D, G and I. Project time (Also called project length) = 49
days. **Problem 3**

Find out
the time, variance and standard deviation of the project with the following
time estimates in weeks:

From
the three time estimates *t*_{p} , *t*_{m} and *t*_{o} , calculate *t*_{e} for each activity.
We obtain the following table:

With
the single time estimates of the activities, we get the following network
diagram for the project.

Consider
the paths, beginning with the start node and stopping with the end node. There
are three such paths for the given project. They are as follows:

**Calculation ****of Standard ****Deviation and Variance for the Critical Activities:**

Variance of | | project time (Also called
Variance of | project length) = | | |

Sum of the variances for the critical activities
= 1+4+1+ 4/9 = 58/9 Weeks. |

Standard deviation of project time = √Variance =
√58/9 = 2.54 weeks.

**Problem 4** A project consists of seven activities with the
following time estimates. Find the probability that the project will be completed
in 30 weeks or less.

**Solution**

From the three time estimates
, and , calculate for each activity. The results are furnished in the
following table:

With the
single time estimates of the activities, the following network diagram is
constructed for the project.

Consider the paths, beginning with the start node
and stopping with the end node. There are three such paths for the given
project. They are as follows:

**Calculation of Standard Deviation and
Variance for the ****Critical
Activities:**

We refer
to the Normal Probability Distribution Table.

Corresponding to Z = 1.414, we
obtain the value of 0.4207

We get 0.5 + 0.4207 = 0. 9207 Therefore the required
probability is 0.92 i.e.,
There is 92% chance that the project will be completed before 30 weeks. In
other words, the chance that it will be delayed beyond 30 weeks is 8%

Tags : Operations Management - Network Problems

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