Stockout-Censored Demand

A size that sells 12 of 12 units records the same 12 sales whether 13 customers wanted it or 40. Once M reaches zero, every later request for M disappears from the sales record. A six-size curve can therefore sell through while concealing the demand needed to build its replacement.

How sales lose the signal

Let (D) be demand during a period and (Q) the stock available:

[ S = \min(D,Q) ]

If sales (S<Q), demand is observed: (D=S). If (S=Q), all the data says is (D\geq Q). Treating (S) as demand turns the inventory ceiling into a forecast.

The distortion spreads when customers substitute. A shopper who cannot find M may buy L, choose another style, or leave. The missing M demand then appears as an L sale, a different product sale, or nothing.

Anupindi, Dada, and Gupta formalised this problem in 1998: stocked-out products have censored sales, while available substitutes can have inflated sales. The transaction log records choices under constraint, not unconstrained preference.

What can recover the missing demand

Evidence	What it reveals	What it cannot settle
Stockout timestamp	How quickly (Q) units sold	Arrivals after stockout
Size requests or searches	Interest without availability	Purchase intent
Substitution path	Where blocked demand moved	Customers who left
Repeated stores and weeks	Variation across availability states	Bad inventory records
Returns and fit reasons	Whether the label matched the body	Demand from non-buyers

Timing carries more information than a binary stockout flag. Jain, Rudi, and Wang reported in 2015 that stockout timing removed an average 76.1% of the expected-profit loss caused by learning from the stockout event alone in their numerical study. For fashion, the useful clock is often not “sold out this week” but “M vanished on day 3 while XL survived until day 19.”

What is contested

The censoring itself is settled. The disputed part is how to infer what happened after the shelf emptied.

Poisson arrival models can estimate a latent demand rate from sales timing, linking this problem to concept poisson process. Choice models can estimate substitution, but their answer depends on which alternatives the model assumes the shopper considered. Inventory errors add another ambiguity: a system may report one M while the garment sits in a fitting room, carries the wrong tag, or is absent from the rail.

No method can identify unlimited lost demand from one clean sell-through. It needs variation, such as the same size remaining available elsewhere, direct request data, or a prior informed by concept size curve.

Why this crosses realms

This is an concept information theory problem hiding inside a garment rack. Once stock reaches zero, demand states of 13, 20, and 40 customers all compress into the same observation: 12 sales. Information destroyed by the availability constraint cannot be recovered from sales alone.

It also changes the operating case for concept inditex playbook and concept open to buy. Faster replenishment does more than capture revenue. It creates another observation window in which demand becomes visible again.

An open question

If searches, fitting-room requests, substitutions, and walkaways were recorded beside sales, would “sell-through” remain the buying floor’s preferred measure, or would it become merely the lower bound?

Key Sources

Anupindi, Dada, and Gupta, “Estimation of Consumer Demand with Stock-Out Based Substitution” (1998) - the canonical model of censored sales, substitution, and lost demand.
Conlon and Mortimer, “Demand Estimation under Incomplete Product Availability” (2013) - evidence from vending-machine availability observed every four hours.
Jain, Rudi, and Wang, “Demand Estimation and Ordering Under Censoring” (2015) - shows why the stockout timestamp carries much of the missing information.
Mersereau, “Demand Estimation from Censored Observations with Inventory Record Inaccuracy” (2015) - separates demand censoring from unreliable stock records.

Abhishek's take

I distrust a clean sell-through when the winning size disappeared early. The neat number can be evidence of underbuying, not accuracy. I treat stock as an observation limit: the floor can reveal demand only while the requested garment remains available.

Where I've used this

I use this on the buying floor when rebuilding a size curve from weekly sales. A zero closing balance is not a completed demand observation; it is a warning that the customer signal ended before the week did.

Abhishek