Question

In a probabilistic inventory model, which distribution is commonly used to model demand?

• A. Uniform distribution
• B. Normal distribution
• C. Exponential distribution
• D. Binomial distribution

Hint:

The Normal distribution is symmetrical, which simplifies the calculation of safety stock for both over-demand and under-demand scenarios.
Always look for the standard normal distribution tables ($z$-tables) to quickly find the service factor $z$ associated with a given service level.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
This question concerns probabilistic inventory control models in production planning and control.
We need to identify the statistical probability distribution that is most widely used to represent uncertain demand.

Step 2: Key Formula or Approach:
In probabilistic models (such as the continuous review system or the single-period newsboy model), the demand during lead time is treated as a random variable.
The safety stock ($SS$) is typically computed using the standard deviation of demand and a service level factor ($z$):
\[ SS = z \cdot \sigma_d \]
This approach assumes a specific probability distribution for demand to determine the corresponding $z$-score.

Step 3: Detailed Explanation:

• Real-world customer demand is composed of many independent, individual buying decisions.

• According to the Central Limit Theorem, the sum of a large number of independent random variables tends toward a normal distribution, regardless of the shape of the underlying individual distributions.

• Therefore, aggregate demand over a given period (such as lead time) is most accurately and practically modeled using a continuous Normal distribution.

• The Normal distribution is highly favored in industry because it is completely defined by two easily calculated parameters: the mean ($\mu$) and the standard deviation ($\sigma$).

• This enables straightforward calculations for service levels, stockout probabilities, and safety stock requirements.

Step 4: Final Answer:
The Normal distribution is the most commonly used distribution to model demand in probabilistic inventory models.