Safety Stock & Service Level

As formerly stated, Safety Stock is used to absorb the error of the estimation of the demand. In its simplest form is expressed as:

Safety Stock= Lead Time x Estimation Error

When a company has set a service level goal, safety stock must be calculated in a way of satisfying this goal. For instance, if the service level is set on 95%, then the company should hold enough stock, so there is equal or less than 5% chance, of not satisfying an order due to stock out.

Under the assumption that our estimation error is following a normal distribution curve, it is possible to perform this calculation using the following formula.

SS= Z-statistic x Sqrt (Leadtime) x Std Deviation of Estimation (1)

To demystify this equation I’ll quickly explain it. 

We know that any sample value that follows a normal distribution will lie in μ σ x Z. Since we are looking for extra stock we actually calculate only for μ+σ x Z (2). In addition, we know our estimation’s variance per period but we need to calculate the variance for the lead time. Since it is known that the sum of the variance of two independent variables is equal to the sum of their variances, then

 

 

 

From (2), (3) we can get the formula (1).

Now let’s make an actual computation. The following table holds the data of a real SKU for 2011. The forecast accuracy is 80,1% and the RMSE is 372.

SKU X	1	2	3	4	5	6	7	8	9	10	11	12	Total
Actual Demand (Linear Meters)	508	884	1.024	1.458	2.433	3.523	2.322	818	1.753	889	438	283	16.333
Forecast (Linear Meters)	533	867	1.234	1.523	2.763	2.707	1.998	444	1.015	767	509	440	14.801
Error	-4,89%	1,88%	-20,55%	-4,46%	-13,58%	23,16%	13,95%	45,72%	42,08%	13,76%	-16,25%	-55,34%
Absolute Error	25	17	210	65	330	816	324	374	738	122	71	157
Squared Error	617	277	44.281	4.232	109.170	665.589	104.860	139.846	544.096	14.955	5.065	24.523

 

Average Absolute Error	271
Average Demand	1.361
MAPE	19,89%
RMSE	372
Accuracy	80,1%
Service Level	95,0%
Lead Time (Days)	5
Z Statistic	1,645
Sqrt(Lead Time)	2,24
Working Days per Month	22
Sqrt(W.D.p.M)	4,69
Safety Stock	291

 

 

For a 95% Service Level the safety stock should be:

 

 

 

 

 

 

 

 

 

 

 

 

 

Thus the average Daily Safety Stock should not be less than 291 units, in order to satisfy a 95% service level. Now, can we go wrong with this calculation? The answer is YES, if our data do not follow a normal distribution curve.
I’ve also seen some implementations of the above formula using t-statistic instead of Z. The value of the T-Statistic for a 95% Service Level, would be 2.18 ,thus , increasing more the safety stock.