PMGT3623 Scheduling - Week 4

PMGT3623 Scheduling - Week 4

• Topic: Probabilistic Approach to Project Network Diagram - Part I
• Probabilistic Approach: A project management approach needed for complex projects because task durations are often uncertain. Using a deterministic approach is appropriate for simple projects.
• Need for Probabilistic Approach: The previous week's deterministic approach to task duration is suitable for simple projects, but complex projects' uncertain task durations require a probabilistic approach.
• Topics Covered (Week 4, Part 1):
  • Why is a probabilistic approach needed in project network diagrams?
  • Probability and probability distributions
    • Expected Value
    • Beta Distribution
  • Program Evaluation and Review Technique (PERT)

Probability and Probability Theory

• Probability Definition: The probability of an event is a value between 0 and 1 representing the chance of the event occurring. It's calculated as the number of favorable outcomes divided by the total number of possible outcomes.
• Sums of Probabilities: The sum of probabilities of mutually exclusive and collectively exhaustive events equals 1.
• Sets and Probability:
  • A set is a collection of well-defined, distinct objects.
  • Subsets: If every member of set A is also a member of set B, then A is a subset of B.
  • Set Operations: ∪ (Union), ∩ (Intersection)
• Probability Examples:
  • Coin toss
  • Dice roll calculation

Probability Distribution: Beta Distribution

• Beta Distribution: A family of continuous probability distributions defined on the interval [0,1] parametrized by two positive shape parameters (α and β). It models variables with a constrained range, useful for projects with limited ranges/outcomes.
• Beta Distribution Usefulness: It's crucial for improved project estimation and more accurate task activity durations. Used to provide more reliable estimates of completion times when compared to approaches like the normal distribution, which don't account for the limited intervals of task durations.
• Beta Distribution Shape: The shape of the beta distribution is determined by the parameters α and β. When α and β are equal, the distribution is symmetric. Increasing the values of α and β reduces the variance.

Beta Distribution and PERT

• PERT (Program Evaluation and Review Technique): A network analysis technique for managing uncertainty in task durations. It is based on beta-distribution principles and used when task durations have high degrees of uncertainty.
• PERT Weighted Average: A formula (O + 4ML + P) / 6, where 'O' is an Optimistic estimate, 'ML' is a Most likely estimate, and 'P' is a Pessimistic estimate. It is used to calculate expected completion time.
• Standard Deviation: The standard deviation of a task estimate is calculated from PERT values, and its formula is (P-O)/6. The formula defines a relationship between project completion time and beta-distribution estimates.
• Expected Value Examples:
  • Various task duration estimations

Expected Value

• Expected Value: A calculation technique used to estimate the average outcome of various project stages, based on their probabilities and associated values.
• Expected Value Formula: The sum of the products of each possible outcome by its associated probability ( Σ xᵢ * P(xᵢ) )
• Expected Value Usefulness: Used in decision-making, project planning, and overall project outcomes, based on probability estimates and task durations.
• Expected Value Exercise: Given various project scenarios with different probabilities and durations, estimate the overall project completion time and standard deviation using PERT (Program Evaluation Review Technique).