Decay Rate: Modeling Spoilage and Shrinkage

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 explains why perishable and shrink-prone inventory often disappears faster than sales data alone can explain.

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

How to pick a starting decay rate

If you do not have enough cycle-count history yet, use a conservative starting point and replace it with measured data as soon as possible:

The starting number should be treated as a hypothesis. After two or three count cycles, the actual variance between expected and counted inventory should begin replacing the default.

How LineNow estimates decay automatically

You do not need to start by setting every decay rate by hand. LineNow estimates them from cycle data:

1. At each manual count, the system records the difference between expected (I + receipts − sales) and actual inventory.
2. The cumulative loss percentage f = min(Δ/S, 0.9) is computed for the cycle.
3. The implied daily rate is d = 1 − (1−f)^(1/L) where L is cycle length in days.
4. 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.

Decay rate governs how much to order; FIFO, FEFO, and LIFO picking policies govern which physical lot to use or ship first once inventory is on hand. For perishables, the two work together: decay rate sets the replenishment urgency, and FEFO picking (first-expiry-first-out) ensures the lot with the shortest remaining shelf life exits inventory before it contributes to that decay loss.

Decay rate vs safety stock

Decay rate and safety stock solve different problems:

For perishables, increasing safety stock without modeling decay can make the problem worse. You buffer against stockouts by buying more, but the extra inventory may spoil before it is used. A good reorder model separates "we need more because demand is volatile" from "we need more because some stock will become unusable."

The operational question is: does the item disappear because customers bought it, because the supplier shipped late, or because it decayed? The procurement response is different in each case.

Decay rate vs shrinkage vs spoilage

Operators often use these words interchangeably, but they are useful in different ways:

Decay rate is the term that belongs in replenishment math. Spoilage and shrinkage explain why the decay exists. A cafe with berries spoiling after five days has a different problem than a bar losing bottles to over-pour or breakage, but both show up as inventory that disappears faster than sales explain.

How to audit decay in a small business

Use a short audit before trusting the number:

1. Pick 10 high-risk items: fresh produce, proteins, flowers, cannabis lots, fragile retail goods, or bar inventory.
2. Record starting quantity, receipts, POS sales, transfers, and ending count for one cycle.
3. Calculate expected ending inventory: starting + receipts - sales.
4. Compare expected to actual.
5. Separate known waste from unexplained shrink.
6. Convert the loss into an implied daily rate.

The point is not to build a perfect academic model on day one. The point is to stop treating perishable and shrink-prone items like shelf-stable goods. Once a category has a measured decay rate, the buying plan can order enough to cover real usable demand instead of idealized demand.

Decay-rate mistakes that create bad purchase orders

The common mistakes:

1. Using recipe usage as the only demand signal. Recipe usage tells you what should have been consumed. Counts reveal what actually disappeared.
2. Ignoring receiving quality. A case of produce arriving half-ripe has a higher effective decay rate than a fresh case.
3. Treating all suppliers the same. Two suppliers can sell the same item with different shelf life on arrival.
4. Using one decay rate per category forever. Berries in July and berries in December behave differently.
5. Not separating waste from theft or counting error. A high decay rate can be a storage problem, a process problem, or a control problem. The math surfaces the gap; operators still need to interpret it.
6. Over-correcting with bigger orders. If a high decay rate comes from poor rotation, bigger orders add more waste.

Decay-aware procurement is not a license to overbuy perishables. It is a way to make the tradeoff explicit: what stockout risk are we accepting, and what waste risk are we creating?

When decay should change the order

Decay should affect a purchase order when:

• the item regularly spoils before the next order cycle
• the supplier sells in packs larger than weekly demand
• the item is required for high-margin recipes or bundles
• the item has a regulatory expiration or FEFO requirement
• the revenue lost from stockout is greater than the waste risk

That last point is important. A zero-waste order is not always the best order. A restaurant may accept some herb waste if the alternative is running out of a high-margin dish on Friday night. Decay-aware procurement makes that tradeoff explicit.

How LineNow uses decay-rate inputs

LineNow has inventory metadata for manual and recommended decay rates, plus cycle data that can support decay estimates. In the buying workflow, decay rate is an input to perishable PAR and replenishment math, not a generic AI claim. The system can show estimated daily loss, apply decay-aware order math, and let operators override the rate when their domain knowledge beats the current data.

The strongest use case is not academic forecasting. It is owner-operator control:

• a cafe can stop treating milk, berries, flour, and cups as if they age the same way
• a restaurant can separate recipe demand from waste
• a florist can order stems with shelf life in mind
• a regulated retailer can pair expiry-aware inventory with FEFO discipline
• a bar can distinguish sales from over-pour, breakage, and shrink

Decay rate is the bridge between inventory math and the physical reality of goods that age, break, leak, spoil, or disappear.