What are the major Safety Stock Calculation difference between Poisson and Negative Normal Distribution data types?

• Poisson assumes that the variance and mean are equal (Var=λ)
• Negative Binomial allows for overdispersion (Var>Mean), making it more flexible when data has high variability.

Application in Safety Stock Calculation

Safety stock helps prevent stockouts by considering demand and lead time variability. The choice of distribution depends on demand characteristics.

1. Poisson Distribution in Safety Stock

• Suitable when demand occurs in discrete units (counts) and is relatively stable.
• Used when demand follows a Poisson process (e.g., low-frequency orders).
• Safety Stock Formula: SS=z×Sqrt(λ*L)

where:

• z = service level factor
• lambda - λ = average demand per period
• L = lead time

Example: If an SKU has an average daily demand of 3 units (λ=3) and a lead time of 5 days, the safety stock at 95% service level (z=1.65) is:

SS = 1.65 sqrt{3 5} = 1.65 sqrt{15} = 6.39

2. Negative Binomial Distribution in Safety Stock

• Used when demand varies significantly (high variability).
• More suitable for highly uncertain or irregular demand.
• Safety stock is calculated using: SS=z×σD×Sqrt(L)

where:

• σD is the standard deviation of demand.

Example: If demand has a mean of 50 and a standard deviation of 20, with a lead time of 3 days:

SS=1.65×20×Sqrt(3)=57.15≈58?units

Which One to Use?

• Poisson → When demand variance ≈ mean (stable demand)
• Negative Binomial → When variance >> mean (highly uncertain demand)

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