What is the Gompertz Curve in NPI Ramp-up forecasting?

Created by Shyam Sayana, Modified on Fri, 10 Apr at 2:30 AM by Shyam Sayana

The Gompertz curve is a classic S-shaped growth model widely used in demand planning for New Product Introduction (NPI) ramp-up forecasting. Here's a comprehensive breakdown:

What is the Gompertz Curve?

The Gompertz curve is a sigmoid (S-shaped) mathematical function that models growth processes where:

Growth starts slowly
Accelerates through a rapid adoption phase
Then decelerates asymptotically toward a ceiling (saturation point)

It differs from a symmetric S-curve (like the logistic curve) in that the inflection point is skewed earlier — meaning the growth phase arrives faster, but the tail-off is longer and more gradual.

The Formula

$$F(t) = L \cdot e^{-b \cdot e^{-c \cdot t}}$$

Parameter	Meaning	Planning Interpretation
L	Upper asymptote (ceiling)	Maximum achievable demand/market saturation level
b	Displacement parameter	Controls where on the time axis growth begins (initial delay)
c	Growth rate parameter	How fast adoption accelerates — higher c = steeper ramp
t	Time	Weeks or months post-launch
e	Euler's number (~2.718)	Mathematical constant

How It Behaves Across the Ramp-Up Lifecycle

Demand

▲

L |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ← Saturation ceiling

| ___-------

| _____/

| ____/ ← Inflection point (peak growth rate)

| ___/

|___/ ← Slow start (lag phase)

─────────────────────────────────► Time (weeks/months post-launch)

Phase 1 — Lag Phase (slow start)

Demand is near zero — the market is unaware or trialing
Controlled by the b parameter (displacement)
In planning terms: safety stock must be pre-positioned *before* this phase ends
Risk: under-stocking at breakout point if the ramp is faster than anticipated

Phase 2 — Growth Phase (acceleration)

Demand accelerates rapidly — this is the critical replenishment window
The c parameter governs how steep this climb is
In planning, procurement lead times must align to this acceleration — if your lead time is 8 weeks and the ramp hits week 6, you will be out of stock at launch peak
Inflection point = the moment of maximum growth rate (not maximum demand)

Phase 3 — Deceleration Phase (approaching ceiling)

Growth continues, but at a declining rate
The curve approaches L asymptotically — never quite reaching it
In planning, this is where forecast overruns become excess inventory risk if planners don't adjust down

Gompertz vs Logistic (Bass) — Key Difference

Feature	Gompertz	Logistic (Bass)
Shape	Asymmetric S	Symmetric S
Inflection point	Earlier (~37% of L)	Middle (50% of L)
Tail behaviour	Longer, gradual tail	Faster saturation
Best fit for	Technology products, consumer electronics (fast adoption, long tail)	Products with more symmetric adoption
Planning implication	Don't plan linearly — ramp hits hard early, then fades slowly

How It's Used in Demand Planning

1. NPI Ramp-Up Curve Fitting

When launching a new product, you fit the Gompertz curve to:

Analogous product launch history (similar SKUs launched previously)
Market research on adoption speed
Sales team's estimates of ramp duration

The curve then generates a monthly forecast profile for the new product from zero to full run-rate demand.

2. Proportional Ramp Factors

The Gompertz output is often converted into ramp index multipliers:

Month Post-Launch	Gompertz Value	Ramp Index
Month 1	50	0.1
Month 2	180	0.36
Month 3	350	0.7
Month 4	450	0.9
Month 5	490	0.98
Month 6+	500 (L)	1

These multipliers are applied to the **steady-state demand forecast** to generate the NPI ramp plan.

3. Safety Stock During Ramp

Because the Gompertz inflection arrives early and sharply, safety stock calculations must be dynamic:

Standard safety stock = `Z × σ × √(Lead Time)` — but σ is artificially high during ramp due to velocity change
Best practice: use a ramp-adjusted safety stock that accounts for the rate-of-change in demand, not just variability

4. Supplier Ramp Synchronization

The Gompertz curve must be shared with suppliers so they can pre-ramp their own capacity:

If the curve shows a steep c value → supplier needs early build authorization
Purchase orders should be **front-loaded** ahead of the inflection point
A mismatch between the Gompertz demand ramp and supplier capacity ramp = the most common NPI stockout scenario

Common Planning Pitfalls with Gompertz

Pitfall	Why It Happens	How to Avoid
Misjudging L (ceiling)	Analogous products are in different markets	Use 2-3 analogues + confidence interval on L
Underestimating c (growth rate)	Viral adoption faster than expected	Monitor week-1 sell-through vs curve — trigger re-fit early
Ignoring the long tail	Planners cut safety stock too soon	Keep elevated cover until the curve slope < 5% per month
Flat ordering pattern vs curved demand	Procurement buys in equal buckets	Convert Gompertz to time-phased PO quantities
Using a symmetric logistic when Gompertz fits better	Model selection not validated	Back-test on 3+ analogs, choose the lowest MAPE

Key Takeaway for Planners

The Gompertz curve tells you two critical things:

When to have inventory ready — the inflection point is earlier than intuition suggests
When to stop building safety stock — the long asymptotic tail means demand stabilizes gradually, not suddenly

The most actionable use: fit the curve to an analogous SKU's first 12 months of data, extract the L, b, and c parameters, apply those multipliers to your new SKU's run-rate forecast, and build your time-phased procurement plan from that — not from a straight-line ramp assumption.