jump to navigation

Safety Stock Calculations January 29, 2007

Posted by Lawrence Loucka in : Definitions, Lean Sigma, Logistics, Sigma, Supply Chain , trackback

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.  Here’s a web app that uses this percentage approach.  If the lead time was 2 weeks I  might carry 3 or 4.  I soon learned that demand for some inventory items is more volatile than others, and some suppliers less reliable than others.  I’d either have too much or not enough, and I’d never get in trouble for having a little too much.  So I started using (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}.

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 D2] 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)
Jon Schreibfeder has anoher approach.

Got any other versions?

Comments»

1. Artem.Kalitin - May 21, 2007

Lawrence,
could you please check the source of APICS formula, it seems that standart demand(D) should be squared.
Thank you.

2. Lawrence Loucka - May 27, 2007

Thanks Artem.