Chapter 7, Problem 18P

Summary Introduction

Interpretation: The expected time and variance in task A is to be calculated.

Concept Introduction:

PERT diagram is a graphical project management tool used to organize and analyze project and it’s activity. It defines time duration for a project and also for each activity in a project.

Explanation of Solution

The estimated task time can be computed by adding optimistic time, mostly likely time multiplied by 4, and pessimistic time. Then, divide the attained value with 6. The optimistic time is 3 days, mostly likely time is 4 days, and pessimistic time is 10 days of task A.

  $\begin{array}{l}\text{Variance}\text{in}\text{task}\text{time}\text{=}{\left(\frac{\text{7days}}{\text{6}}\right)}^{\text{2}}\\ \\ \text{=}{\text{(1}}^{\text{.1667}}\\ \text{=}\text{1}\text{.36}\text{days}\end{array}$

  $\text{Estimated}\text{time}\text{=}\text{4}\text{.8}\text{days}$

  $\text{Estimated}\text{time}\text{=}\frac{\text{3}\text{days+16}\text{days+10}\text{days}}{\text{6}}$

  $\text{Estimated}\text{time}\text{=}\frac{29\text{days}}{\text{6}}$

  $\text{Estimated}\text{time}\text{=}\text{4}\text{.8}\text{days}$

Hence, the estimated time in task A is 4.8 days

Variance in task time:

The variance in task time computed by deducting optimistic time from pessimistic time and divided by six. Then, completely square the attained value. The optimistic time is 3 days, and pessimistic time is 10 days of task A.

  $\text{Variance}\text{in}\text{task}\text{time}\text{=}{\left(\frac{\text{Pessimistic}\text{time}\text{-}\text{Optimistic}\text{time}}{\text{6}}\right)}^{\text{2}}$

  $\text{Variance}\text{in}\text{task}\text{time}\text{=}{\left(\frac{\text{10}\text{days}\text{-}\text{3}\text{days}}{\text{6}}\right)}^{\text{2}}$

  $\begin{array}{l}\text{Variance}\text{in}\text{task}\text{time}\text{=}{\left(\frac{\text{7days}}{\text{6}}\right)}^{\text{2}}\\ \\ \text{=}{\text{(1}}^{\text{.1667}}\\ \text{=}\text{1}\text{.36}\text{days}\end{array}$

Hence, the variance in task A time is 1.36 days.

The project management has two techniques that is critical path method and program Evaluation Review technique. In program evaluation review technique the project’s optimistic time, mostly likely time, and pessimistic time are combined together in to single expected value. This expected value signifies expected time of project’s task.