A Partially Solved PERT Problem Is Detailed in the Table

question 10

Essay

A partially solved PERT problem is detailed in the table below. Times are given in weeks.
$\begin{array}{|c|c|c|c|c|c|l|}\hline\text { Activity } & \text { Preceding } & \begin{array}{c}\text { Optimistic } \\\text { Time }\end{array} & \begin{array}{c}\text { Probable } \\\text { Time }\end{array} & \begin{array}{c}\text { Pessimistic }\\\text { Time }\end{array} & \begin{array}{c}\text { Expected } \\\text { Time }\end{array} & \text { Variance } \\\hline \mathrm{A} & -- & 7 & 9 & 14 & & 1.361 \\\hline \mathrm{B} & \mathrm{A} & 2 & 2 & 8 & & 0 \\\hline \mathrm{C} & \mathrm{A} & 8 & 12 & 16 & & 0 \\\hline \mathrm{D} & \mathrm{A} & 3 & 5 & 10 & & 1.361 \\\hline \mathrm{E} & \mathrm{B} & 4 & 6 & 8 & & 0 \\\hline \mathrm{F} & \mathrm{B} & 6 & 8 & 10 & & 0 \\\hline \mathrm{G} & \mathrm{C}, \mathrm{F} & 2 & 3 & 4 & & 0 \\\hline \mathrm{H} & \mathrm{D} & 2 & 2 & 8 & & 1.000 \\\hline \mathrm{I} & \mathrm{H} & 6 & 8 & 16 & & 2.778 \\\hline \mathrm{J} & \mathrm{G}, \mathrm{I} & 4 & 6 & 14 & & 2.778 \\\hline \mathrm{K} & \mathrm{E}, \mathrm{J} & 2 & 2 & 5 & & 0.250 \\\hline\end{array}$
a. Calculate the expected time for each activity. Enter these values in the appropriate column in the table above.
b. Which activities form the critical path?
c. What is the estimated time of the critical path?
d. What are the project variance and the project standard deviation?
e. What is the probability of completion of the project after week 40?

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Definitions:

Normal Production

The standard or average level of production volume that a company expects to achieve under normal operating conditions.

Direct Labour Rate Variance

A financial measure that calculates the difference between the actual cost of direct labor and the estimated (or standard) cost.

Actual Production

The total count or volume of units produced by a manufacturing or production process in a specific period.

Normal Production

The expected production capacity or output level under standard operating conditions, without factoring in extraordinary circumstances.