•A graphical display of project activities.

•An estimate of how long the project will take.

•An indication of which activities are the most critical to timely project completion. •An indication of how long any activity can be delayed without delaying the project.

The Network Diagram

Network (precedence) diagram

-Diagram of project activities that shows sequential relationships by the use of arrows and nodes. 2 Different Conventions:

1.Activity-on-arrow ( AOA)

-Network diagram convention in which arrows designate activities. 2.Activity-on-node (AON)

-Network diagram convention in which nodes designate activities.

Activities

-Project steps that consume resources and/or time.

Events

-The starting and finishing of activities, designated by nodes in the AOA convention.

Deterministic time estimates

The main determinant of the way PERT and CPM networks are analyzed and interpreted is whether activity time estimates are PROBABILISATIC or DETERMINISTIC.

PROBABILISATIC

Estimates of time that allow for variation.

DETERMINISTIC

Time estimates that are fairly certain.

PROBABILISTIC TIME ESTIMATES

Three Time Estimates:

1.Optimistic Time ( to ) – the length of time required under optimum conditions 2.Pessimistic Time ( tp ) – the length of time required under the worst conditions 3.Most likely time ( tm* ) –the most probable amount of time required

Beta Distribution

•used to describe probabilistic time estimates.

In special interest in network analysis is the average or expected time for each activity and the variance of each activity time. The expected time of analysis is a weighted average of the three estimates:

te- expexted time∂2 - variance of each activity time

ta + 4tm +tp

te= -----------------------

6

The expected duration of a path is equal to the sum of the expected times of the activities on that path:

∂path = √ ∑ (variance of activities on path)

EXAMPLE:

The network diagram for a project in the figure, with three time estimates for each activity . Activities are in weeks..

STEPS:

a.Compute the expected time for each activity and the expected duration for each path. b.Identify the critical path.

•The path that has the longest expected duration is the critical path. Because path d-e-f has the largest path total, it is the critical path. c.Compute the variance of each activity and the variance and standard deviation of each path. Manager enables to compute probabilistic estimates of the project completion time, such as… oThe probability that the project will be completed by a specified time. oThe probability that the project will take longer than its scheduled completion time. Activity times are represented by a beta distribution, the path distribution is represented by a normal distribution. The rationale for using a normal distribution is that sums of random variables (activity times) will tend to be normally distributed, regardless of the distribution of the variables. The normal tendency improves as the number random variable increase.

DETERMINATION PATH PROBABILITIES

The probability that a given path will be completed in a specified length of time can be determined using the following formula:

Specied time – Path Mean

z = ---------------------------------------

Path standard deviation

The resulting value of z indicates how many standard deviation of the path distribution the better.

A project is not completed untl all of its acitivities have been completed, not only those on the critical path.

Determine the probability that all paths will finish by a specified time. Independence

•Assumption that path duration times are independent of each other: requiring that activity times be independent, and that each activity is on only one path.

•The assumption of independent...