Safety Stock with a Fixed Lead Time

Why it matters

With a fixed lead time, safety stock covers the uncertainty about how much will be consumed until the moment the order is known to be ready for use. If the same quantity were consumed every day and replenishment really arrived in the same time, the average need would be enough. When daily demand varies, the average describes only the center point; in some replenishment periods higher consumption is seen. Safety stock is set aside for this difference. Putting the average demand back inside the safety stock counts the same need twice. Splitting the calculation first into average and uncertainty makes visible why the result arises and by which improvement it can be reduced.

If daily demands are independent and come from the same distribution, the variances of the days are added. Standard deviations are not added directly; the square root of the total variance is taken. As the lead time lengthens, the standard deviation of the uncertainty therefore grows with the square root of the time. This relation is not a law of nature to be applied to every demand series. If a product campaign raises several days together, if the days of the week differ markedly or if demand keeps growing, the simple assumption is questioned. The behavior of the data is examined before the calculation. A correct multiplication does not compensate for a wrong independence assumption; more records do not correct this error by themselves either.

The service factor z is related to the one-sided cycle service target chosen when the total demand of the replenishment period is represented by an approximately normal distribution. The given value z = 1.65 targets a cycle service of about 95%. This is not a promise that 95% of demand units will certainly be met or that exactly one shortage will occur in every twenty orders. The realized ratio varies with sampling. For the share of units filled, the size of the shortages is also needed. The coefficient of a two-sided confidence interval and the one-sided inventory protection factor do not serve the same purpose either; they are not used in place of each other by looking only at the similarity of the percentage.

In this lesson the lead time is exactly 4 days from the placing of the order to the usable acceptance of the material. A day means the working day on which demand data is kept. Mixing calendar days with working days distorts both the average and the protection period. If receiving inspection and internal transport are really inside this time, they are not added again; if they are outside, the scope is completed. Looking only at the time in the transport contract does not prove the fixed-replenishment assumption. The calculation result, together with the defined service target and the data conditions, is a policy input. To apply the ordering decision, inventory position, packaging and the movement record are also needed.

Formula