Module 2 Portfolio Project – Monte Carlo Simulation
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Module 2 Portfolio Project - Monte Carlo Simulation
Objective: In this assignment, you will apply Monte Carlo simulation techniques and probability distributions to estimate project completion time and total project costs. You will use a mix of historical data to fit distributions for some tasks and predefined parameters for others, reflecting real-world project management.
Business Case Overview:
You are a project manager at a logistics company overseeing the expansion of a distribution center. The project involves several sequential tasks, each with an uncertain duration and cost. Your goal is to estimate the total project completion time and total project cost using a Monte Carlo simulation. You will be provided with historical data on task durations and costs, and your task is to run simulations to predict potential outcomes and evaluate risks.
Project Tasks:
|
Task |
Distribution Type |
Parameters or Historical Data |
Description |
|
Task 1: Site Preparation |
Uniform |
Historical data provided |
Prepare the site for expansion. |
|
Task 2: Equipment Setup |
Uniform |
Predefined (duration: 10 to 20 days; cost: $20,000 to $40,000) |
Install necessary equipment for operations. |
|
Task 3: Staff Training |
Normal |
Historical data provided |
Train the staff for new operations. |
|
Task 4: Test Operations |
Normal |
Predefined (duration: mean 7 days, std dev 1 day; mean $5,000, std dev $500) |
Test operations before the full roll-out. |
Below is a flow diagram for the activities involved in the project:
Steps to perform:
1. Fit the distribution for Task 1 (Uniform) using the provided historical data for durations and costs.
2. Fit the distribution for Task 3 (Normal) using the provided historical data for durations and costs.
3. Use predefined distributions for Task 2 and Task 4
4. Perform Monte Carlo simulations. Hints for setting up the simulation:
o Using Excel, set up a Monte Carlo simulation model for the project. For each task, use the appropriate probability distribution (normal or uniform) to simulate the duration and cost of the tasks.
o Generate 1,000 iterations (trials) to estimate the total project completion time and total cost.
o Use Excel functions such as =NORMINV() for normal distributions and =RAND() for uniform distributions.
5. Analyze the results to answer the following questions.
Questions:
1. Based on your simulation, what is the mean and standard deviation of the total project duration?
2. Based on your simulation, what is the mean and standard deviation of the total project cost?
3. What is the probability that the total project duration will be less than 40 days? Less than 45 days?
4. What is the probability that the total project cost will be between $60,000 and $65,000?
5. What is the joint probability that the project will take more than 50 days and cost more than $75,000?
6. What is the IQR for the total project cost?
7. Which task is most likely to cause a delay of the project? Explain why.
8. What is the probability that Task 2 will take less than 12 days?
9. What is the probability that Task 4 will cost more than $6,000?
10 What is the probability that the total project cost will exceed $80,000?
11. If the project takes more than 55 days, what is the probability that the cost will exceed $75,000?
12. If the project is strictly required to finish within 48 days, what is the probability of completing on time?
13. What is the expected penalty cost if the project exceeds 50 days, assuming a penalty of $1,000/day?
14a. We consider this project successful if its total cost doesn’t exceed $80,000 and if it is completed within 48 days. Create a random variable in Excel named “Success” and assign to it 1 every trial in which both conditions for a successful project are satisfied, 0 otherwise.
14b. Which named probability distribution can we use to model the random variable defined in 14a? Please explain your logic.
15. How does increasing the variability (standard deviation) of Task 3: Staff Training impact the total project duration and cost?
16. Based on the simulation results, if you had to allocate additional resources to reduce variability in one task, which task would you choose and why?
17. The project team is planning to run 10 similar projects, each with the same success criteria: a project is considered successful if it is completed within 48 days and costs less than $80,000. Based on your Monte Carlo simulation results, you estimate that each project has a 70% chance of being successful.
What is the probability that at least 8 out of the 10 projects will be successful?
Submission:
Submit a PDF document with your answers. Each answer needs to have the supported analysis, such us screenshots of charts and calculations performed on your Excel file.
2025-02-22