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Project scheduling is the time phased processing of operations subject to precedence interactions, time constraints, and resource constraints in order to achieve particular goals.

Projects were planned utilizing bar charts until around 1960.

When it comes to the techniques of network analysis for project scheduling, two different forms were developed. The first one is called as critical path method (CPM), and the other one is called as program evaluation and review technique (PERT).

The fundamental network assessment of the project is typically carried out in three stages: stage of network planning, stage of network scheduling, and stage of network control.

All of them are among the components of network.

A burst point occurs when there is a prevalent predecessor for two or more operations.

It is not AOA, it is AON that can be drawn and read more readily

The estimation equation for mean is distributed in six standard deviations in PERT.

The major steps in PERT analysis can be summarized as follows:

1. Determine three estimates; optimistic “a”modal “m”, and pessimistic “b” durations for each activity.

2. Calculate the expected value for each activity by using a, m, and b.

3. Compute the variance of each activity by using the formula for.

4. Calculate the expected project duration, Tx.

CPM is activity-oriented and not time-related, not PERT

Project scheduling is the time-phased processing of operations subject to precedence interactions, time constraints, and resource constraints in order to achieve particular goals.

The components of the network are described below:
• Node

• Arrow
• Activity
• Restriction
• Dummy
• Predecessor activity
• Successor activity
• Descendent activity 
• Antecedent activity
• Merge point
• Burst point
• Precedence diagram

To describe a project, three kinds of data are required:
• Activity information: Divide the project (at the required point of detail) into its
individual operations.
• Precedence relationships: Define the predecessor(s) for each activity.
• Time information: Forecast each activity’s duration

Some principles to adopt, when creating an AOA network diagram, are as follows:
• Each activity must have a distinctive number such as i and j, where j is greater than i (number at the arrow’s tail ).
• A gap between numbers is suggested. This will enable missed operations to be accommodated.
• Keep away from back arrows
• Use dummy activities when more than one arrow exits the same node and enters at another node

It is possible to use both networks to represent a project network. However, there are some differencesbetween them:
• The dummy activities in AON representation are not necessary.
• AON can be drawn and read more readily.
• In AOA, the activity can only begin once all of its predecessors have been completed.
• AON enables the depiction of overlap /lag.
• AON enables four kinds of relationships to be represented while AOA enables only to finish to start relationship.

Program Evaluation and Review Technique (PERT) and Critical Path Method (CPM) can be applied to various types of projects, including but not limited to the following types:
• New plant construction
• New product research and development 

• Space projects
• Aircraft production
• Development of new missile systems
• Nuclear reactor maintenance
• Management information systems applications, etc.

The major steps in PERT analysis can be summarized as follows (Badiru, 2011):
1. Determine three estimates; optimistic “a” modal “m”, and pessimistic “b” durations for each activity.
2. Calculate the expected value for each activity by using a, m, and b.
3. Compute the variance of each activity by using the formula.

4. Calculate the expected project duration, Tx. Similar to CPM, the duration of the project is calculated by summing up the expected modal time of critical activities.
5. Similar to the expected duration, calculate the variance of the project as the sum of individual variance of activities on the critical path.

6. In addition to the expected project duration, the probability of finishing the project within specified time limits can be calculated, which does not exist in CPM.

The most important inputs of the PERT are the three estimates: optimistic, pessimistic and the modal duration of each activity in the project network diagram( shown as a, b, and m, respectively). It is possible to use several approaches to determine the duration estimates necessary for PERT. The following are some of the strategies:
• Predictions provided by an experienced person
• Estimates derived from historical data
• Estimates obtained from statistical methods such as regression
• Estimates provided by the results of simulation scenarios
• Approximations obtained from heuristic assumptions
• Customer requirements

PERT derives the following advantages:
• Allows managers to analytically plan their projects and evaluate all the factors that affect the progress of the project. The network analysis process involves project planning to be carried out from start to finish in considerable detail.
• Provides management with a tool to predict the effect of schedule changes and be prepared to resolve such circumstances. The likely trouble areas are placed earlier which gives enough time to apply some preventive or corrective steps.
• Task relationships are represented visually for easier assessment, and individuals can logically deduce their role in the overall task requirements at various steps.
• The PERT time is based on three estimates, and therefore, it is the most objective prediction under the uncertainties and results in a higher degree of forecast accuracy.
• PERT provides improved communication results. The network diagram provides a mutual interest for different stakeholders such as project managers, customers, contractors, etc., and they all understand the role and contributions of each other.
• The network will illustrate situations that require higher priority attention whereas intention can be applied to key activities without overlooking the lower priority tasks. This provides management a chance to shift focus to any critical activity in order to finish the entire project on time.

CPM vs. PERT
While both strategies enable you to predict which series of activities (or paths) will take the longest time to finish in a project, there are some differences between PERT and CPM. These differences are shown as a comparison table below.