How many extra tickets should an airline sell?

AA SLAA HLAI SLAI HL Solid Also in: Finance, Statistics

Research question

For a 180-seat flight with a given no-show rate, how many tickets maximise the airline's expected revenue once compensation for bumped passengers is included?

Adapt it: change the place, the data or the comparison until the question is yours.

Why it makes a good exploration

Airlines deliberately sell more seats than they have. The binomial distribution and expected value give a clear optimum — and the ethics of bumping passengers gives you something real to reflect on.

The mathematics you'll need

Binomial distribution of passengers who show up
Expected revenue as a function of tickets sold
Maximising a discrete function
Normal approximation (optional)

Course labels show where a technique sits; using maths from outside your course is fine if you explain it clearly and say it is new to you.

Where the data comes from

Use a published no-show rate range and published compensation rules (e.g., EU Regulation 261/2004 amounts) with citations.

Desmos graphing calculator — Free graphing and regression (y₁ ~ ax₁ + b) — fit models to your data and show residuals.

Cite every source in a footnote where you use it and in your bibliography. Check the licence of any dataset you download.

A possible outline

Set up the revenue and compensation model.
Compute expected profit for each number of tickets sold.
Find the optimum and test sensitivity to the no-show rate.
Compare risk (probability of bumping anyone).
Reflect on independence (families and groups travel together).

Pitfalls that cost marks

Treating passengers as independent without comment.
Using a no-show rate with no source.
Ignoring the reputational cost.

Showing personal engagement

Use a route you have flown.
Include groups travelling together and see how the answer changes.
Discuss fairness from the passenger's point of view.

See Criterion C: personal engagement for what examiners look for.

Taking it further

Model group bookings with a compound distribution via simulation.

Turn this idea into your IA

Plan this IAOpens the planner with this question, the maths and data sources filled in. Desmos workspacePlot your data, fit models and keep your graphs with your plan. AI feedback on a draftCriterion-by-criterion feedback with evidence from your own text. Coaching, not rewriting. Examiner reviewPete, a practising IA examiner, reads your draft and talks it through with you (€100).