Lead Time Under Load: What the Next Order Costs Every Other Order

How to read this sheet

Waiting is estimated with Kingman's approximation extended to parallel servers: the wait scales with the mean of the squared coefficients of variation, and with utilisation over one minus utilisation, which is what makes the last few points of loading so expensive. It is an approximation, it is accurate enough to plan with in the region factories run in, and it degrades near saturation - which matters less than it sounds, because near saturation the answer that matters is that there is no steady state rather than what the number is. Past 100% utilisation no lead time is reported at all, and backlog growth per week is reported instead. That is not a limitation being confessed, it is the correct answer: a saturated queue does not settle at a long lead time, it grows without bound, and a deterministic sheet reporting a slipped date at 104% load is describing something that does not happen. Two remedies are priced at whichever centre carries the most waiting - one more resource, or half the process variability - because they cost quite different money and the ranking between them changes with utilisation. Neither is recommended here; the sheet reports what each buys and the prices are yours. Several real effects are absent. Batching and transfer batch sizes, which often dominate real cut-to-pack times; blocking when there is nowhere to put finished work; priority rules and expediting, which shorten one order by lengthening others; and any correlation between arrivals, which is common when one buyer releases a season at once and makes the arrival variability entered here an understatement. Every centre is also treated as independent, which understates the wait when a slow centre feeds a fast one in bursts.