CPM or  "Critical Path Method":

  • 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.

Two types:

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.

      inserted into the network to show a precedence relationship, but it does not represent any actual passage of time.

Activity Slack

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

Activity Scheduling

Earliest Start time (ES):

      the earliest time an activity can start

Forward pass:

      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

Beta distribution:
  • 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.

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