Decay Rate: Modeling Spoilage and Shrinkage
Decay rate is the daily fraction of inventory lost to spoilage, shrinkage, or other non-sales consumption. Formula: I(t) = I₀ × (1−d)^t. With recommended values per category.The decay rate is the daily fraction of inventory that becomes unusable due to spoilage, shrinkage, theft, breakage, or any other loss not captured by sales. It is the silent destroyer of margin in food service and the long-tail killer of stock accuracy in retail.
The formula
Inventory under decay follows exponential decay:
I(t) = I₀ × (1 − d)^t
where:
- I₀ is starting inventory
- d is the daily decay rate (e.g. 0.02 = 2%)
- t is days elapsed
For a 5% daily decay rate, after 7 days, only (1−0.05)^7 ≈ 70% of the original inventory remains usable.
Typical decay rates by category
| Category | Daily decay | Notes |
|---|---|---|
| Berries, leafy greens, fresh herbs | 5–15% | Days-to-spoil < 7 |
| Stone fruit, soft fruit | 3–8% | Days-to-spoil 7–14 |
| Hard produce (potatoes, onions, citrus) | 0.5–2% | Days-to-spoil > 30 |
| Fresh proteins (fish, ground beef) | 10–20% | Highly perishable |
| Dairy, eggs | 2–5% | Sealed, cold-stored |
| Dry goods (flour, rice, beans) | 0–0.1% | Effectively zero, except for pests |
| Apparel, accessories (retail) | 0.01–0.05% | Mostly shrinkage / theft |
| Bar inventory (over-pour, breakage) | 0.5–2% | Highly venue-dependent |
How LineNow estimates decay automatically
You don't need to set decay rates by hand. LineNow estimates them from cycle data:
- At each manual count, the system records the difference between expected (I + receipts − sales) and actual inventory.
- The cumulative loss percentage
f = min(Δ/S, 0.9)is computed for the cycle. - The implied daily rate is
d = 1 − (1−f)^(1/L)where L is cycle length in days. - The recommended decay rate is the median of the last 3 cycles. As more cycles accumulate, the estimate stabilizes.
You can override this with a manual entry, or use the recommendation. High decay rates — above 5% — are a flag that something else is going on (recipe miscalculation, inventory leakage, theft).
Why decay matters for PAR and reorder math
If decay is non-zero and you ignore it, your PAR level is too low. Some inventory will be lost before it can be sold, so you need to order more aggressively to maintain the same effective coverage.
The base demand integral with decay is:
baseDemand = (s/d) × (s^(−T) − 1) × c
where s = 1 − d, T = order frequency days, c = consumption rate
For a 7-day cycle with 5% daily decay and 18 lbs/day consumption, baseDemand ≈ 147 lbs vs 126 lbs without decay handling — a 17% upward adjustment to PAR.