Monte Carlo Simulation

Step 1: Define the Problem

Problem: We need to estimate the total completion time for a project with multiple tasks, where each task duration is uncertain.

Variables: Task durations with different probability distributions representing uncertainty in estimates.

Task 1: Minimum Duration (days)

Task 1: Maximum Duration (days)

Task 2: Minimum Duration (days)

Task 2: Maximum Duration (days)

Task 3: Minimum Duration (days)

Task 3: Maximum Duration (days)

Distribution Used: Uniform distribution for each task - assumes all durations within the range are equally likely.

Step 2: Develop a Model

Our mathematical model represents the relationship between individual task durations and total project completion time.

Model:
Total_Project_Time = Task1_Duration + Task2_Duration + Task3_Duration

Where each Task_Duration ~ Uniform(min_duration, max_duration)

This model assumes tasks are performed sequentially. In real scenarios, parallel tasks and dependencies could be incorporated for more complex modeling.

Step 3: Generate Random Samples

We generate random samples for each task duration based on their defined probability distributions.

Number of Simulations

Step 4: Run Simulations

Execute the model for each sampled scenario to generate a range of possible project completion times.

Business Insights: