The project network is a visual flow diagram of the sequence, and dependencies of all the activities that must be accomplished to complete the project. One or more work packages can for an activity. Networks identify dependencies, sequence, and timing of activities which will be used to define the project schedule.

Activities

Activities are described using a verb/noun format – for example, wait for approvals, develop product specifications, etc. If two or more activities can take place at the same time, they are a called parallel activities. An activity that is preceded by two or more activities is call merge activity. An activity that is followed by two or more activities is called burst activity. Dependent activities form a sequence called path. The path with the longest duration through the network is called critical path. Looping or recycling through a set of activities must be avoided.

Network

In a network, activities are represented by boxes and the dependency is shown as a arrow. Arrows can cross each other. The network must start and end with only one node. The networks can be developed using of two methods, either activity-on-node, the most popular, or activity-on-arrow. The network is constructed by identifying the activities that precede or follow each activity.

The network can be further enhanced by adding the duration (TE) and timing of the activities. The time estimates can be found in the work packages but for proper scheduling of these activities a forward and backward pass is to be performed. The forward pass starts with the first activity and traces each path through the network to the last project activity, and for each activity, it identifies the early start (ES) and end times (EF). The start time will coincide with the end time of the preceding activity. If an activity is preceded by two or more activities, the largest early finish is being selected. The backward pass starts with the last project activity and trace backward on each path subtracting activity duration  to find the late start (LS) and late finish (LF) times for each activity. If a deadline for the completion of the project is given, then that twill be the date used for the late finish of the the last activity. If an activity is followed by two or more activities, use the smallest late start of all its immediate successor activities to establish its late finish.

Slack

Slack, or float, refers to the amount of time an activity can be delayed without delaying the completion of the project. It is simply calculate as the difference between the late start and early start (SL = LS – ES), or between the late finish and early finish (SL = LF – EF). The critical path has the least slack.

Lag

So far it has been assumed that all immediate preceding activities must be 100 percent complete before starting the following activities, known as finish-to-start relationship. In practice , this may be unrealistic, and lags have been used to increase flexibility of the network construction. A lag is the minimum amount of time a dependent activity must be delayed to begin or end. It is a useful technique to employ when dealing with long activities performed in parallel by segmenting the the long activity in smaller ones separated by lags. An alternative to segmenting the activities is to use a start-to-start relation, which helps compressing the critical path, or finish-to-finish relationship, or start-to-finish relationship depending on the scope of the connected activities.