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Advanced PERT Simulator - Project Management Tool

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Advanced PERT Simulator
PERT Project Simulator

PERT Project Simulator

Created By: Ir. MD Nursyazwi

Instructions on How To Use

Welcome to the Project Evaluation and Review Technique (PERT) simulator. This tool helps you estimate project time and cost with greater accuracy by accounting for uncertainty.

  1. Enter Task Details: Fill out the form with your task's name, its dependencies (by task ID, comma-separated), and three time and cost estimates for each:
    • Optimistic: The best-case scenario.
    • Most Likely: The most probable scenario.
    • Pessimistic: The worst-case scenario.
  2. Add Task: Click "Add Task" to add your task to the table.
  3. Review Results: The simulator will instantly calculate the **expected time** and **cost** for each task. It also finds the **critical path**, which is the sequence of tasks that determines the total project duration.
  4. Use Probabilities: Use the "Calculate Probability" sections to determine the likelihood of finishing your project on or before a specific date or within a specific budget.
  5. Visualize: The **PERT Diagram**, **Cost/Time Graph**, and **Monte Carlo Histograms** provide a clear visual overview of your project's plan and resource allocation.

Data Input

Use the form below to add and manage your project tasks.

Data Output

The table below shows all your project tasks and their calculated values. You can double-click on a cell to edit it.

ID Task Name Dependencies Optimistic Time Most Likely Time Pessimistic Time Expected Time Time Std Dev Optimistic Cost Most Likely Cost Pessimistic Cost Expected Cost Cost Std Dev ES EF LS LF Slack Action

Project Summary

Total Expected Time: 0.00

Total Time Standard Deviation: 0.00

Total Expected Cost: 0.00

Total Cost Standard Deviation: 0.00

Critical Path

Tasks on the critical path have zero slack and determine the project's total duration.

    Calculate Probability of Completion (Time)

    Based on the total project time and standard deviation, you can find the probability of completing the project by a specific deadline.

    Calculate Probability of Completion (Cost)

    Find the probability of completing the project within a specific budget.

    Chart and Diagram

    These visuals help you understand the relationships and scale of your project tasks at a glance.

    Task Expected Cost vs. Expected Time

    PERT Diagram

    Monte Carlo Simulation

    Run a simulation to generate a probability distribution of possible project outcomes.

    Science Explanation

    What is PERT?

    PERT, or **Project Evaluation and Review Technique**, is a statistical method used in project management to analyze and represent the tasks involved in a project. It helps in planning and scheduling projects by estimating the time and cost required to complete each task.

    Unlike simple project management methods that use a single estimate, PERT considers three time estimates for each task to account for uncertainty:

    • Optimistic Time: The minimum possible time a task is expected to take, assuming everything goes perfectly.
    • Most Likely Time: The most probable time a task will take.
    • Pessimistic Time: The maximum possible time, assuming significant setbacks.

    The PERT Formulas

    The core of PERT is the calculation of a **weighted average** for the expected time and the **variance** for each task. The most likely time is given a weight of four, while the optimistic and pessimistic times have a weight of one, reflecting the higher probability of the most likely scenario.

    To find the expected time for a task, you use a weighted average. The formula gives four times the weight to the most likely time, adding it to the optimistic and pessimistic times, and then dividing by six.

    The time standard deviation, which measures the uncertainty of the estimate, is calculated by taking the difference between the pessimistic and optimistic times and dividing it by six.

    A similar set of calculations is used for cost, replacing the time variables with their cost counterparts.

    The Critical Path

    The **critical path** is the longest sequence of tasks that must be completed on time for the entire project to be completed on time. Any delay on a task on the critical path will delay the entire project. Tasks not on the critical path have **slack**, meaning they can be delayed without affecting the project's overall completion date.

    Probability Calculation (Z-score)

    The probability calculation uses the **Standard Normal Distribution** (also known as the Z-distribution) to determine the likelihood of finishing by a target time. We calculate a **Z-score** for the target time, which tells us how many standard deviations away the target is from the expected completion time.

    A higher Z-score indicates a higher probability of completion.

    Monte Carlo Simulation

    While the standard PERT method gives a single expected value, the **Monte Carlo Simulation** provides a more robust analysis of risk. It works by running a large number of trials (simulations) to model the outcomes. For each trial, a random value for each task's duration and cost is selected from a normal distribution based on the task's expected value and standard deviation. The project's total time and cost are calculated for each trial, and the results are compiled into a distribution (a histogram). This gives you a clear visual of the most probable range of project completion times and costs, as well as the likelihood of extreme scenarios.

    References

    To learn more about project management and the techniques used in this simulator, check out these excellent books:

    Other Simulators

    While PERT is a powerful tool for projects with uncertain timelines, other simulators and project management techniques exist that serve different purposes:

    Location: Sandakan, Sabah, Malaysia

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