Project Management Techniques: PERT and CPM Analysis

Project Management Fundamentals: PERT and CPM

HL (Total Slack) is the time that can delay the completion of an activity without affecting the start of another and the final term. HM (Marginal Slack) refers to the most unfavorable slack case in the book.

The Critical Path

The Critical Path is the longest and most winding route. It defines the sequence that marks the current and critical events in a double-arrow network. An activity is considered critical when it has zero slack time. An event is critical when its TE (Earliest Time) and TL (Latest Time) are equal. It is essential to pay attention to critical paths, as any delay can affect the entire project. Both initial and final events are critical.

PERT: Probabilistic System

PERT is a probabilistic system that assigns three possible durations to each activity: pessimistic (b), most likely (m), and optimistic (a). The expected duration is calculated using the following formula: d = (a + 4m + b) / 6.

For the total time calculation, it is important to know that each task has a probability. To calculate the probability factor (Z) for reaching a stage, we use the formula: z = (ts - t) / √Σσ², where:

• ts: Target time or earliest start.
• t: Expected time.
• √Σσ²: Square root of the critical path variance (independence factor).

The project is more feasible if there is at least a 25% probability of completion, while statistical certainty is reached at a 97% probability.

CPM: Critical Path Method

CPM is one of the planning and programming methods represented by a graphic arrow network to establish the critical path. As a deterministic method, CPM develops each activity based on a fixed duration according to available resources, performance, and experience. CPM establishes two time limits: the maximum length an activity can take and the minimum selected.

These corresponding times influence activity costs and the final event time.

Data and Duration

Each activity is allocated a duration depending on experience, resource estimations, and performance. Activity and event times include:

• Event Times: Each event is assigned two times: TE (Earliest) and TL (Limit/Latest).
• Event Slack: The difference between the latest time and the earliest time of an event.
• Activity Slack: The differences existing between the maximum time available and the time necessary for execution.
• HT (Total Slack): The time an activity can be delayed without affecting the fixed termination date.