Concept

Lead time demand variability

Direct answer

When both demand and lead time vary, the standard deviation of demand during lead time combines them: sigma_DLT^2 = L * sigma_D^2 + d_bar^2 * sigma_LT^2. This is the correct input to safety-stock and ROP calculations^[1]. Using only one source of variance understates the required buffer.

sigma_DLT^2 = L * sigma_D^2 + d_bar^2 * sigma_LT^2

Combined demand-during-lead-time variance.

Concept

sigma_DLT (demand during lead time, std dev)

Combined uncertainty of demand and lead time, used to size safety stock.

sigma_DLT = sqrt(L * sigma_D^2 + d_bar^2 * sigma_LT^2)

When it matters: Use in place of sigma_LT when computing SS = Z * sigma_DLT. Particularly important for international sourcing with variable transit.

When lead-time variance dominates

For mean demand of 40 units/day with sigma_D = 10, mean lead time L = 20 days with sigma_LT = 5 days: the demand term L * sigma_D^2 = 2,000; the lead-time term d_bar^2 * sigma_LT^2 = 40,000. Lead-time variance is twenty times the demand variance. This is the typical case for offshore-sourced consumer goods^[2].

Measuring sigma_LT from PO history

Pull the last 24 to 36 PO receipts. Compute the per-PO lead time as receipt-date minus PO-date. Take the standard deviation. Exclude obvious outliers (port strikes, COVID delays) but document the exclusion. Result is your sigma_LT per supplier per category.

How dual-sourcing collapses sigma_LT

Adding a domestic backup supplier at higher unit cost but 7-day lead time vs 45-day offshore can cut blended sigma_LT by 60 to 80 percent. The carrying-cost saving from reduced safety stock often exceeds the unit-cost premium on the backup volume.

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