tool to analyze project and determine duration, based on identification of "critical path" through an activity network. Knowledge of the critical path can permit management of the project to change duration. A single estimate for activity time was used that did not allow for variation in activity times Activity times are assumed to be known or predictable ("deterministic") Activities are represented as nodes or circles
PERT or "Project Evaluation and Review Technique":
Another derivative of the GANTT chart Multiple time estimates were used for each activity that allowed for variation in activity times Activity times are assumed to be random, with assumed probability distribution ("probabilistic") Activities are represented by arrowed lines between the nodes or circles
Over time, CPM and PERT merged into one technique referred to as "CPM/PERT".
Visually easier to see precedence relationships Ideal for large projects with many activities They consist of a network of branches and nodes.
Activity-on-node (AON) -- nodes represent activities and arrows show precedence relationships. Activity-on-arrow (AOA) -- arrows represent activities and nodes are events for points in time.
Dummy inserted into the network to show a precedence relationship, but it does not represent any actual passage of time.
Slack is computed by:
Sij = LSij - ES ij
Sij = LFij - EF ij
Slack enables resources to be temporarily diverted other activities to:
avoid delays compensate for an inaccurate time estimate
Most network activities are estimates
project uniqueness means little historical basis subject to a lot of uncertainty Using probabilistic methods rather than deterministic to minimize uncertainty
Earliest Start time (ES):
the earliest time an activity can start
start at the first node and move forward through the network to determine the earliest start time for an activity
Earliest Finish time (EF):
the earliest start time plus the activity time
EFij = ESij + t ij
Latest Start time (LS):
the latest time an activity can start without delaying the completion of the project beyond the critical path time
LSij = LFij - tij
Latest Finish time (LF):
the latest time an activity can be completed and still maintain the critical path time
Probabilistic Time Estimates
PERT-type approach uses 3 time estimates for each activity
most likely time (m) subjective estimate of most frequent time optimistic time (a) shortest possible time (ideally) pessimistic time (b) longest time possible if everything went wrong
Estimate the mean and variance of a beta distribution of the activity times. continuous w/ no predetermined shape others types of distribution are no more or less accurate
Human judgment element
Process no better than network and resource estimates Project teams make these subjective estimates Knowledgeable people must determine which events must precede others and how long activities will take.