Graphene Sheet Demand Forecast Using Normal Distribution

Assume Graphene Sheet Demand for last 100 days as Table 1 below.

Demand analysis and forecast for the graphene sheet based on the last 100 days of data:

🔹 Given:

• Mean daily demand, $\mu = 100.01$

• Standard deviation, $\sigma = 20.01$

• Desired service level = 95%
  → which means the warehouse wants only a 5% risk of shortage.

---

🔹 Formula:

For a normal demand distribution, the required stock (safety stock included) for a given service level is:

                                                        Q = μ + z × σ

Where:

• $z$ = z-score corresponding to the desired service level

• For 95% service level → $z = 1.645$ (one-sided)

---

🔹 Calculation:

$$Q=100.01+1.645\times 20.01$$ $$Q = 100.01 + 32.82 = 132.83$$

✅ Answer:

The warehouse should prepare ≈ 133 graphene sheets to achieve a 95% service level (only 5% chance of shortage).

                                        Table 1: Graphene Sheet Demand for last 100 days

Code from ChatGPT

import numpy as np

import matplotlib.pyplot as plt

from scipy.stats import norm

# Given parameters

mean_demand = 100.01

std_demand = 20.01

service_level = 0.95

z_value = 1.645  # z-score for 95% service level

# Calculate the stock level for 95% service level

Q = mean_demand + z_value * std_demand

# Create range of possible demand values

x = np.linspace(mean_demand - 4*std_demand, mean_demand + 4*std_demand, 500)

y = norm.pdf(x, mean_demand, std_demand)

# Plot the normal distribution

plt.figure(figsize=(8, 5))

plt.plot(x, y, label='Demand Distribution', linewidth=2)

plt.fill_between(x, y, 0, where=(x <= Q), color='skyblue', alpha=0.4, label='95% Service Area')

plt.axvline(Q, color='red', linestyle='--', linewidth=2, label=f'95% Service Level = {Q:.1f} sheets')

# Labels and title

plt.title("Graphene Sheet Demand Forecast (95% Service Level)")

plt.xlabel("Daily Demand (Sheets)")

plt.ylabel("Probability Density")

plt.legend()

plt.grid(alpha=0.3)

# Show plot

plt.show()