PERT/CPM Project Management

Introduction to PERT/CPM

• Program Evaluation and Review Technique (PERT) and Critical Path Method (CPM) are widely used in project management.
• Project management aims for on-time project completion within budget and according to specifications.
• A project is a human endeavor with a clear beginning and end.
• Project managers plan, schedule, and control work, detailing activities, resources, time, and inter-relationships.
• Scheduling involves setting start and end dates for activities.
• Project control requires status updates and trade-off analysis.
• Key project questions include completion time, impact of delays, resource allocation, and completion probability.
• Gantt charts were the popular scheduling technique, developed by Henry L. Gantt around 1900.
• Gantt charts graphically represent work vs. time, but struggle to show inter-dependencies.
• PERT and CPM were introduced in the late 1950s to overcome Gantt chart limitations.
• PERT and CPM were developed independently by the U.S. Navy and DuPont.
• PERT originated from the U.S. Navy's Polaris program; CPM was used in chemical plant construction.
• PERT was initially for research and development, while CPM was for construction.
• Both PERT and CPM use a critical path and network analysis to control critical activities for on-time completion.
• PERT suits non-repetitive, complex projects with uncertain time estimates.
• CPM is better for repetitive, non-complex projects with reliable time estimates.
• Technique selection depends on the certainty of time estimates and the consequences of delays.
• PERT focuses on time, whereas CPM includes time-cost trade-offs.

Network Analysis

• Network systems are fundamental to PERT and CPM.
• Networks graphically represent problems or proposed projects.
• Activity represents tasks requiring time and resources, depicted as arrows (arcs).
• Arrow length is for clarity, not time representation; arrowheads indicate flow.
• Activities cannot start before preceding activities finish.
• Clearly defined activities have identifiable start and end points.
• Events mark specific project accomplishments at a point in time, consuming no resources.
• Events are typically represented by circles (nodes).
• Events signify the end of one activity and the start of another.
• Activities represent the passage of time, whereas events are points in time.
• Activity arrows begin and end with event nodes.
• Predecessor activities must be completed before another activity starts.
• Successor activities cannot start until other activities finish.
• Concurrent activities can be done simultaneously.
• Activities can be predecessors, successors, or concurrent.
• Dummy activities address concurrent activities with the same start and end events, consuming no resources or time.
• Dummy activities are represented by dashed arrows.
• Dummy activities makes activities with common starting and finishing events distinguishable.

Guidelines for Constructing Network Diagrams

• Each activity has one arrow in the network.
• No two activities share the same beginning and end events; dummy activities are used to resolve such conflicts.
• Events are numbered so that higher numbers follow lower numbers.
• Dangling, which improperly identifies precedence and inter-relationships, must be avoided in network diagrams.
• Logical sequence and inter-relationships are ensured by answering questions about preceding, following, and concurrent activities.

Deterministic Time Estimates

• PERT/CPM analysis depends on whether activity time estimates are deterministic or probabilistic.
• Deterministic estimates are reliable, with minimal deviation.
• Probabilistic estimates vary, acknowledges these uncertainties.
• Network analysis is initially described with deterministic time estimates and, later, with probabilistic ones.

Developing a Project Network

• PERT/CPM networks contain activities and events.
• Networks illustrate activity sequence and relationships.
• Example: Activities A and B start immediately with no predecessors from event 1.
• Activity G has two predecessors, D and E, satisfying all relationships.

Project Duration and Critical Path

• The longest path in the network is the critical path, determining project duration.
• Delays on the critical path delay the entire project.
• Networks have at least one critical path, and sometimes multiple.
• Project duration and critical path can be identified.
• The critical path can be found by enumerating completion times.
• Activities on the critical path are critical, and cause overall project delays.
• Slack time defines how long an activity can be delayed.

Forward Pass (Earliest Expected Time)

• The forward pass calculates the earliest time an event can occur.
• The calculation depends on the latest completion time of activities ending at that event.
• The longest path is the earliest expected time for the event to occur.

Backward Pass (Latest Allowable Time)

• The backward pass calculates the latest time an event can be delayed.
• The time will not delay project completion.
• These calculations start from the end event, proceeding backward.
• The value for event is calculated by subtracting the duration times of all activities coming into the event.

Float

• Float is the time available for an activity beyond its duration, important for managers.
• As the start and end events of an activity have earliest and latest times, an activity has four associated times.

Probabilistic Time Estimates

• Activity times are often random variables, making PERT effective.
• PERT assumes activity times are statistically independent.
• Total activity times are normally distributed.
• Three time estimates can be obtained for each activity: optimistic (a), most likely (m), and pessimistic (b).
• The mean duration time (te) and variance (σ²) can be computed with those three time estimates.