Simulating Project Estimated Costs with Monte Carlo in Python

Monte Carlo simulation is a powerful tool to analyze project costs by considering uncertainty and generating multiple possible outcomes. Here's how to use it in Python:

1. Define the Variables:

• Project Activities: Break down your project into individual activities.
• Cost Estimates: For each activity, define a range of possible costs.
• Probability Distributions: Specify how likely each cost within the range is. Common distributions include:
  • Normal Distribution: For activities with symmetrical cost variations.
  • Triangular Distribution: For activities with a most likely cost, and a minimum and maximum.
  • Uniform Distribution: For activities with an equal chance of any cost within the range.

2. Python Code Implementation:

python import numpy as np import matplotlib.pyplot as plt

Define project activities and their cost details

activities = { 

    "Activity A": {"distribution": "normal", "mean": 1000, "std": 100}, 
    "Activity B": {"distribution": "triangular", "min": 500, "mode": 600, "max": 700}, 
    "Activity C": {"distribution": "uniform", "low": 800, "high": 1200} 

  }

Number of simulations

num_simulations = 10000

Initialize array to store simulated project costs

simulated_costs = []

Perform Monte Carlo simulation

for _ in range(numsimulations): 

   totalcost = 0 

   for activity, details in activities.items(): 

     if details["distribution"] == "normal": 
        cost = np.random.normal(details["mean"], 
        details["std"]) 

     elif details["distribution"] == "triangular": 
        cost = np.random.triangular(details["min"], 
        details["mode"], 
        details["max"]) 

     elif details["distribution"] == "uniform": 
        cost = np.random.uniform(details["low"], 
        details["high"]) 

     else: 
       raise ValueError("Invalid distribution type") 
       totalcost += cost simulatedcosts.append(total_cost)

Analyze and visualize results

plt.hist(simulated_costs, bins=50) 
plt.xlabel("Project Cost") 
plt.ylabel("Frequency") 
plt.title("Monte Carlo Simulation of Project Costs") 
plt.show()

print(f"Mean Project Cost: {np.mean(simulatedcosts)}") 
print(f"Standard Deviation: {np.std(simulatedcosts)}") 
print(f"5th Percentile: {np.percentile(simulatedcosts, 5)}") 
print(f"95th Percentile: {np.percentile(simulatedcosts, 95)}")

3. Interpretation:

• Histogram: The histogram shows the distribution of simulated project costs, providing insights into the likelihood of different outcomes.
• Mean Project Cost: The average cost across all simulations.
• Standard Deviation: Measures the spread or variability of the cost distribution.
• Percentiles: The 5th and 95th percentiles indicate the range within which 90% of the simulated costs fall.

Explanation of Code:

• The code first defines a dictionary activities containing details about each project activity, including its cost distribution type and parameters.
• It then sets the number of simulations to run (num_simulations).
• Inside the loop, for each simulation, the code iterates through the activities, generating a random cost for each based on its specified distribution.
• The total cost is calculated by summing the costs of all activities.
• After all simulations are complete, the code analyzes the results using statistical functions like mean, std, and percentile.
• Finally, it plots a histogram of the simulated costs for visual representation.

Benefits of Monte Carlo Simulation:

• Uncertainty Analysis: Captures the uncertainty inherent in cost estimates.
• Risk Assessment: Identifies potential cost overruns and helps prioritize mitigation strategies.
• Decision Making: Provides a more informed basis for project decisions by considering multiple scenarios.

Key Considerations:

• Accurate Input Data: Ensure the cost estimates and distributions reflect realistic possibilities.
• Independence of Activities: Ensure costs of different activities are independent.
• Number of Simulations: Increase the number of simulations for a more accurate and reliable analysis.

By implementing Monte Carlo simulation, you can gain valuable insights into the potential costs of your project and make more informed decisions.

answer July 28, 2024, 2:33 p.m.

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