Optimising the placement of disaster evacuation shelters Using Monte Carlo Simulation

Project info

• Field of studyGeography and Disaster Studies
• LevelMaster's thesis (S2)
• Method typeOptimisation
• Estimated build time± 5 working days
• Toolsnumpy.random.default_rng, scipy.stats; matplotlib
• PriceUS$19 - US$128

Research goal

Find the best values of number of shelters and shelter capacity to optimise total evacuation travel time with Monte Carlo Simulation, then compare the resulting scenarios.

Variables

Example result

• 49.881Mean
• 8.503Std. deviation
• 37.527P5
• 64.613P95
• 0.3P(output > threshold)
• 0.085Standard error

A 10000-draw Monte Carlo run gives Total evacuation travel time a mean of 49.88 (SD 8.50), a P5-P95 range of 37.53 to 64.61, and a 30.0% chance of exceeding the threshold.

Computed from illustrative synthetic data, not from a real study.

About Monte Carlo Simulation

Monte Carlo simulation uses repeated random sampling to estimate the distribution of a model's output under uncertainty. It suits risk analysis, parameter uncertainty, and event probabilities that are hard to compute analytically.

Steps

1. 1Define the model and its uncertain inputs
2. 2Choose input distributions from data or literature
3. 3Draw N random samples with a fixed seed
4. 4Compute the model output for each sample
5. 5Summarise results: mean, percentiles, event probability
6. 6Check convergence and plot a histogram

Assumptions to check

• Input distributions reflect real uncertainty
• The number of runs is large enough for stable estimates
• Correlation among inputs is modelled when present

Reading and reporting the results

Report the mean, percentile interval (for example 5 to 95), event probability, and number of runs. Include a convergence plot to show results are stable.

Example Python code

A short starting script with this project's variable names. The delivered version is adapted to your data and fully commented.

import numpy as np
import matplotlib.pyplot as plt

rng = np.random.default_rng(30)
N = 20000

# Uncertain inputs: demand, unit price and unit cost
number_of_shelters = rng.normal(1000, 150, N)         # demand
shelter_capacity = rng.triangular(8, 10, 13, N)     # price
cost = rng.uniform(5, 8, N)
total_evacuation_travel_time = number_of_shelters * (shelter_capacity - cost) - 2000   # profit

print("Mean profit:", round(total_evacuation_travel_time.mean(), 1))
print("Std:", round(total_evacuation_travel_time.std(ddof=1), 1))
print("5th / 95th percentile:", np.percentile(total_evacuation_travel_time, [5, 95]).round(1))
print("P(profit < 0):", round((total_evacuation_travel_time < 0).mean(), 4))

running = np.cumsum(total_evacuation_travel_time) / np.arange(1, N + 1)
fig, ax = plt.subplots(1, 2, figsize=(10, 4))
ax[0].hist(total_evacuation_travel_time, bins=60)
ax[0].axvline(0, color="r"); ax[0].set_xlabel("Profit")
ax[1].plot(running); ax[1].set_xlabel("Runs"); ax[1].set_ylabel("Running mean")
plt.tight_layout()
plt.show()

Packages and prices

Choose how much help you need. Each higher package includes everything in the lower ones. Prices exclude 11% VAT.

• Payment: 50% down payment before work starts, balance after the deliverables are handed over
• Tax: Prices exclude 11% VAT
• Data and academic integrity: Results are computed from your own research data; you write and stand behind your manuscript, we help with the analysis and your understanding of it
• Revisions: Up to 2 revisions are included in the price (Package 3: 3 rounds)

Frequently asked questions