How this calculation works
Apply the entered factor to the modeled lead-time demand standard deviation. Retain independent demand/lead assumptions and display the exact rounding convention for whole-unit buffers and the combined cutoff.
Fixed lead SD = demand SD × √L; variable lead variance ≈ Lσd² + meanDemand²σL²; buffer = z × lead SDA worked example
Mean demand 100 per period, demand SD 20, four fixed independent periods and z = 1.645 give lead-time SD 40 and a buffer of 65.8 units. The mean-plus-buffer cutoff is 465.8 units, rounded up once to 466.
Good to know
A normal-approximation scenario, not an achieved service or fill-rate guarantee. Variable mode assumes independent stationary demand and lead time. Skew, intermittency, seasonality and correlation are not modeled. Buffer-first ERP rounding can differ from the stated combined-cutoff rounding.
Reference: Reference: model definitions and scope (opens in a new tab) ↗
Lead-time variability changes the uncertainty being buffered
For mean demand 100 per base period, demand standard deviation 20 and four fixed independent periods, lead-time demand has modeled standard deviation 20√4 = 40. Multiplying by the entered factor 1.645 gives a buffer of 65.8 units. Mean demand over the four periods is 400 units.
In variable-lead mode, a lead-time standard deviation of one period adds the mean-demand-squared term to the variance. The resulting deviation is √(4 × 20² + 100² × 1²), about 107.703296 units, and the same factor gives a buffer about 177.171922 units. That larger number follows the supplied independent-variability model; it is not a measured shortage outcome.
The reorder point and inventory position calculator can compare a supplied buffer with counted commitments; it does not choose a distribution model on your behalf.
Rounding rules can change a whole-unit cutoff
This page displays the buffer rounded up separately, but its combined cutoff rounds mean-plus-unrounded-buffer once. With mean 10.2, SD 0.2, one fixed period and factor 1.645, the buffer is 0.329 and the combined cutoff is 10.529, rounded up to 11.
An ERP that first rounds the buffer to one, adds mean demand 10.2, and then rounds again would return 12. Both calculations follow different stated conventions. The linked reference describes its own buffer-first process; this tool is an explicit arithmetic scenario rather than a reproduction of every ERP preference.
A normal factor is not a fill-rate guarantee
The factor is supplied directly. The approximation assumes stationary independent demand, with independent lead time when that mode is selected. Correlation, intermittency, promotion effects, strong skew or a low mean can make the normal model inappropriate. No service target is inferred from a pasted history and no achieved service is measured.
The reorder point and inventory position calculator can compare a buffer from your chosen method with current stock commitments. The economic order quantity calculator addresses a separate ordering/holding-cost tradeoff. This page does not choose an order lot, model receipt dates, or turn a theoretical distribution cutoff into a guarantee that every customer order is filled.
A few questions, answered
Can fixed lead time use a fractional number of base periods?
This fixed independent-period model requires whole periods. Choose an appropriate smaller base period and compatible demand statistics when needed. Variable mode uses a supplied mean lead time.
Does variable mode include demand/lead correlation?
No. It uses the stated independent-moment approximation and does not infer covariance.
Is the entered factor a measured fill rate?
No. It is a standard-normal model factor. Cycle-service concepts and quantity fill rates are different, and actual service is not measured here.
Why might an ERP return a different whole cutoff?
It may use different demand definitions, variability models, service factors or rounding order. This page explicitly rounds the combined mean-plus-buffer once.