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.

 

 

Forecast Accuracy in a PUSH system

Since MRP works primarily as a push system, accuracy of the input data is the number one priority of the Planner. Forecasts that basically build and drive the Master Production Schedule, should depict the actual demand the closest possible. Inaccuracy will always lead to loss of money, either due to holding excessive stock or because of the lost sales.

The basic and most logical way to measure accuracy is by measuring the deviation between the forecasted demand and the actual demand. The difference between these two numbers, when is expressed as a percentage, is the actual forecast error.

 

	Sample SKU
Forecasted Demand	80
Actual Demand	75
Forecast Error (A-F/A)	-6,67%
Abs of Error	6,67%
Accuracy [1-abs(Error)]	93,33%

 

Most information I've found, propose to use the forecast error as an absolute number. I prefer to use as a signed percentage, because it clearly shows the direction of the deviation as well as the deviation itself. So, a negative forecast error shows clearly that the actual demand was less than what was forecasted and a positive forecast error would mean the opposite. Accuracy on the other hand is just 1 – the absolute value of the forecast error. In case that the forecast error is more than 100% then accuracy would just have a zero value, since there is no point showing negative accuracy.

 

Although the above calculations are pretty much straight forward, things are a little more complicate when it comes to measure the accuracy for many SKUs and thus the whole forecast. In order to achieve this, it is necessary to calculate what is called the Mean Absolute Percentage Error or else MAPE, which is basically the Average Absolute Error divided by the Average Actual Quantity.

 

	SKU A		SKU B	SKU C	SKU D	Total
Forecasted Demand		120	50	200	500	870
Actual Demand		100	40	51	450	641
Absolute Error		20	10	149	50	229
Average ABS Error (MAE)		57,25
Average Actual Demand		160,25
MAPE		35,73%
Forecast Accuracy (1-MAPE)		64,27%

 

 

From what I know, MAPE is the method most commonly used today. It is easy to calculate and self explicable. The only thing I don’t like about it is the use of the absolute values. I don’t know how long back in time MAPE can be traced but an engineer would definitely decide to solve the problem with a statistical approach. What else could it be better than trying to calculate the Standard Deviation of the Error? Well this approach is called RMSE, meaning the Root of the Mean Squared Error and has no difficulty at all, but still many people avoid it.

If you had a sample that you needed to find the standard deviation, you would simply calculate the mean, subtract the mean from each sample value and square the results. The square root of the average of the squared values would be the standard deviation. The same applies here but instead of calculating the mean of the samples we will use the Actual Demand as a reference point.

		SKU A	SKU B	SKU C	SKU D	Total
Forecasted Demand	120		50	200	500	870
Actual Demand	100		40	51	450	641
Squared Error	400		100	22201	2500	25201
Average of Squared Errors	6.300,25
RMSE	79,37

 

Although for me this makes much more sense well it misses something that most would ask for. This is the % sign. RMSE is an absolute number such as the standard deviation and that’s why many people choose MAPE.  I choose to calculate both MAPE and RMSE as accuracy indicators.

From this point you can do many more tricks. The cleverest one would be to use weights for the simple MAPE. If the weigh is the standard cost, then the most expensive SKU’s would weigh more and would adjust the MAPE to a more logical value. So, the accuracy error of the cheap SKU’s would be less significant than the error of the expensive SKU’s.

Once you automate the calculations in an Excel spreadsheet then there is even a better solution. Use all the above!