Bullwhip effect · Lee, Padmanabhan & Whang

NOBODY PANICKED. IT AMPLIFIED ANYWAY.

Var(q)Var(d)  ≥  1 + 2Lp + 2L2p2

Every stage forecasts from what it was ordered, not what was sold, and adds cover for its lead time. Do that four times and a gentle ripple at the shelf becomes a whipsaw at the plant. The inequality is the floor, not the ceiling — and notice what is in it: only lead time L and forecast window p. No one has to behave badly. Shorten the lead time or lengthen the window and the whip shortens with it.