When I first learned inventory planning the math was rather simple. On top of the cycle stock (expected demand during lead time) I would add a percentage or a number of days (or more likely weeks). If the lead time was 2 weeks I might carry 3 or 4 weeks. I soon learned that demand for some inventory items is more volatile than for others, and some suppliers less reliable than others. I’d rather have too much then not enough, and I’d never gotten in trouble for having a little too much.

So since all items and situations are different I started using some statistics; **(average demand * lead time) + ( one sided Z factor * demand standard deviation) **for the target inventory level; a little better approach.

Here’s another formula from Inventory Management Review;

Safety Stock:

**{Z * SQRT (Avg. Lead Time * Standard Deviation of Demand ^2 + Avg. Demand ^2 * Standard Deviation of Lead Time ^2)}**.

(note ^2 means ‘square’)

Reorder Point:

**Average Lead Time*Average Demand + Safety Stock***.*

Over at QuickMBA ; To calculate the safety stock, first calculate the standard loss function, designated as L(z). This function is dependent on the values of the desired fill rate *f*, the demand μ and its standard deviation σ , the time between orders *p*, and the replenishment lead time *l* : L(z) = ( 1 – *f* ) *µ p* / *σ* ( *p *+ *l* )^{1/2}. Once L(z) is known, z can be found in a look-up table and the safety stock can be calculated by:

**Safety Stock = z σ ( p + l )^{1/2}**

Here’s a new one recently published by Kent Linford in the APICS Magazine Nov/Dec 2006.

SS = √ [( σFE)^{2} x (LTI/FI)^{beta} + ( σLT)^{2} x D^{2}] x Z x (FI/OCI)^{beta}

Where:

SS = safety stock

FE = forecast error

LT = lead time interval

FI = forecast interval (pick a beta between 0.5 and 0.7)

D = average demand during lead time

Z = normal distribution service factor based on desired service level

OCI = order cycle interval

Dave Piasecki at InventoryOps.com uses;

**safety stock = (standard deviation)*(service factor)*(lead-time factor)*(order cycle factor)*(forecast-to-mean-demand factor)**

And so too does Joannès Vermorel, and a nice spreadsheet example.

Michel Baudin makes an interesting comment on safety stock in an article titled Beware of Formulas.

Accounting Explained has this one …

**Safety Stock = (Maximum Daily Usage − Average Daily Usage) × Lead Time**

Any questions? Got any other versions? What formula do you use?

Larry Loucka

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