Size-Curve Economics
A style can reach 80% sell-through and still fail. If its remaining units sit in unwanted sizes while the demanded sizes sold out in week 2, the headline percentage hides both dead stock and lost sales. The concept size curve turns assortment planning from a taste decision into a constrained allocation problem.
The constraint inside the style
For size (s), let (q_s) be units bought, (D_s) demand, and (m_s) unit margin. The contribution captured before substitution or markdown is:
[ \text{Contribution}=\sum_s m_s\min(q_s,D_s), \qquad \sum_s q_s=Q ]
The second equation is the trap. Increasing M requires removing units from another size unless the total buy (Q) changes. Minimum order quantities, carton ratios, store packs, budgets, and display rules narrow the feasible choices further.
A worked example makes the accounting visible. A 1,000-unit style sells 800 units, leaving 200 units in XS and XXL. After M and L stock out, another 150 customers seek those sizes. Reported sell-through is 80%; demand was at least 950 units. The same style produced shortage and surplus at once.
What aggregate sell-through misses
Sales are censored by availability. A size that reaches zero stops recording demand, while an overstocked size keeps advertising its mistake. Rebuilding the next curve from recorded sales alone can therefore repeat the error.
Substitution complicates the read. Akchen and Caro’s 2025 footwear study found that nearly 25% of unmet demand caused by stockouts moved to adjacent sizes. That sale rescues revenue but contaminates the signal: the purchased size is not always the preferred size.
What’s contested
The live question is how much size detail an optimizer needs. Akchen and Caro find that ignoring substitution can produce similar results when demand is high or the selling horizon is long; low-demand stores need size-level treatment. Fit inconsistency adds another uncertainty: an L label may describe different bodies across two blocks.
Why this crosses realms
Size inventory behaves like capacity in concept queueing theory. Each arrival consumes one unit from a finite size-specific pool; once that pool reaches zero, later demand is rejected or rerouted. concept poisson process supplies one model for those arrivals, while concept quick response changes the problem by allowing capacity to be replenished before the season ends.
An open question
Can a retailer infer the demand hidden behind every stockout without mistaking adjacent-size substitution for genuine preference? That would turn the size curve from a seasonal ratio into a censored-demand model.
Key Sources
- Rajaram, “Assortment Planning in Fashion Retailing” (2001) - formulates fashion assortment choice as a nonlinear integer program.
- Kießling, Kurz and Rambau, “The Integrated Size and Price Optimization Problem” (2012) - joins branch, size, lot-type, and markdown decisions.
- Akchen and Caro, “On Size Substitution and Its Role in Assortment and Inventory Planning” (2025) - provides the size-substitution evidence.
- Fisher and Raman, “Reducing the Cost of Demand Uncertainty Through Accurate Response to Early Sales” (1996) - establishes the economics of learning from early fashion sales.
Further Reading
- concept inditex playbook - shows why shorter feedback loops reduce the cost of an incorrect opening curve.
- concept bayesian inference - offers a disciplined way to update size demand when observations are incomplete.
- concept size curve - defines the operational object before the economics begin.
See Also
- concept size curve
- concept quick response
- concept inditex playbook
- concept queueing theory
- concept poisson process
- concept bayesian inference
Abhishek's take
I distrust any style verdict that stops at total sell-through. The useful unit is the customer-size-store intersection, because that is where a healthy-looking style can hold 200 unwanted units while refusing the next 150 customers.
Tags: #size-curves #assortment-planning #inventory #demand-censoring #retail-operations