Project Management

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Path: A sequence of activities that leads from the start node to the end node.

Critical path: The longest path from start to end; determines the expected project duration

Critical activities: Activities on the critical path

Path slack time: Allowable slippage for a path, the difference between the length of the path and the length of the critical path.

Large networks are analyzed by a computer program and a solution technique that develops four values for each activity

- ES: the earliest time the activity can start

- EF: the earliest time the activity can finish

- LS: latest time the activity can start and not delay the project

- LF: the latest time the activity can finish and not delay the project

EF = ES + t

- ES for an activity with on immediate predecessor is equal to the EF of that node. ES for an activity with multiple immediate predecessors is equal to the largest EF of those nodes. Let ES of the start node be zero.

LS = LF – t

- For a node with one immediate successor, LF equals the Ls of that node. For a node with multiple immediate successors, F equals the smallest LS of those nodes. Let LF of the end node equal its EF.

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ES # EF

LS Dur. LF

Project crashing: In many situations, it is impossible to reduce the length of a project by using additional resources. The impetus to shorten projects may reflect efforts to avoid late penalties, to take advantage of monetary incentives for timely or early completion of a project, or to free resources for use on other projects.

Only activities on the critical path are potential candidates for crashing because shortening non-critical activities would not have an impact on the project duration. From an economic standpoint, critical activities should be crashed according to crashing cost per periods (lowest).

Crashing continues as long as the cot to crash is less than the benefits derives from crashing.