Most reorder math treats lead time as a single number: “this supplier takes 21 days.” That number is a fiction. Real lead time is a stack of variable stages, transit, customs, dock and put-away, each with its own spread, and collapsing them to an average is one of the most common reasons a reorder fires “on time” and still stocks out.
Lead time is a sum of variable stages
A replenishment lead time is really:
lead_time = order_processing + production + transit + customs + port_dwell + dock_to_stockEach term has a mean and a variance. Customs in particular is not Gaussian: most shipments clear quickly, but a few get held for days or weeks, a long right tail. Transit has weather and carrier variance. Dock-to-stock depends on your own labour. The total is a compound distribution, the sum of these component random variables.
Why the average under-provisions you
Safety stock covers variability over the lead time. If you feed it only the mean lead time, you ignore lead-time variance entirely, and you systematically hold too little buffer. The reorder point should use the variance of demand over lead time, which combines demand variability and lead-time variability:
# illustrative: variance of demand over a variable lead time
var_DLT = E[LT] * var_demand + (mean_demand ** 2) * var_LT
sigma_DLT = sqrt(var_DLT)
# safety stock from sigma_DLT, NOT from demand variance aloneThat var_LT term is exactly what the “lead time is 21 days” model throws away, and it is often the
larger contributor for items with long, customs-exposed supply chains.
How to model the compound distribution
- Collect stage-level data, not just door-to-door totals. You usually have purchase-order, ship, customs-clear, and receipt timestamps; the gaps between them are your component samples.
- Fit or bootstrap each stage, then convolve (sum) them, by simulation if the shapes are awkward. The customs tail matters, so do not force a normal fit on it.
- Use the resulting distribution, not its mean, to size safety stock, exactly the non-normal buffer argument from why your safety stock formula breaks.
The takeaway
A single lead-time number hides the variance that actually causes stockouts. Treat lead time as the sum of its stages, capture the spread of each (especially the fat customs tail), and size replenishment buffers against the variability of demand over a variable lead time. The reorder point built that way fires early enough to survive the slow shipment, not just the average one.
Implementing this at your scale?
The walkthrough above comes from production work. AvanSaber’s inventory practice has implemented variations of this pattern across multiple customer engagements.
If you are building this and want expert review of your design, or would rather have the team that built this build yours, book a discovery conversation or describe your situation at [email protected].