Optimal Harvest Timing: What a Simple Growth Model Reveals

Simplified Model

Define the following variables:

t: time.

r: regeneration (growth) rate of the plant (length per unit time).

T: harvest interval.

H: plant height at each harvest.

Y: total harvested length over a given period.

Assumptions:

The growth rate r is constant during the study period.

After each harvest the plant regrows from ground level.

Maximum height is unbounded.

Environmental factors remain unchanged.

The growth can be expressed by a linear equation L(t)=r·t. The harvest amount per cut is H = r·T, and with N = 365/T cuts per year the total yield is Y = N·H = r·365, which shows that total yield depends only on the growth rate, not on the interval.

Improved Model

Real plant growth is not strictly linear; different stages have different rates. Observations for chives indicate:

First harvest possible after about 1.5 months; first year 3‑4 cuts, later about monthly.

Maturity around 20‑30 cm height, with flower buds and darker leaf color as indicators.

Ideal conditions: 6‑8 h sunlight, well‑drained neutral‑pH soil, regular watering, fertilizer every 2‑3 weeks.

Growth phases: 7‑14 days germination, 2‑4 weeks seedling, 4‑6 weeks vegetative, 8‑12 weeks flowering.

To capture this, a piecewise function can be used. For example, let r₁ be the growth rate for the first 30 days and r₂ for later days. The height at time t is:

L(t)= r₁·t   (0 ≤ t ≤ 30)

L(t)= r₁·30 + r₂·(t‑30)   (t > 30)

With observed rates of 0.3 cm/day initially and 0.5 cm/day afterwards, the model predicts higher yields when accounting for the increased later rate.

In short, although short‑term harvest intervals seem important, long‑term total yield is governed mainly by the plant’s growth rate and its continuity.