Continuous pricing

How it works

Background

For decades an airline's price could only move in steps: a flight is sold in a handful of fare classes, each filed in advance at a fixed amount, and revenue management decides which of them are open. Continuous pricing lets the price land anywhere, $287 instead of $243 or $332, and it's the main pricing argument behind offer-based distribution (NDC). The page sells the same shoppers on the same flight twice, once through a class ladder controlled with EMSR-b and once with a price set at any amount from the same forecast, over 2,000 simulated departures.

Shoppers

The flight has 150 economy seats and a 180-day booking period. Each departure gets a number of shoppers drawn from a Poisson distribution whose mean is shoppers per seat × seats, scaled for each departure by a gamma factor with a 25% coefficient of variation so that some departures are much busier than others. Shoppers arrive at a rate proportional to exp(−t / 55), t being days before departure, so about 40% of them come in the last 30 days.

Each shopper has a willingness to pay (WTP), drawn from a lognormal distribution with a spread σ = 0.5 and a median that climbs as departure nears:

m(t) = $160 × r^{((180 − t) / 180)³},

where r is the late-booker premium. The median stays close to $160 for the first months and rises quickly in the last weeks, as business travellers book. A shopper buys if the price on offer is at or below their WTP, and walks away otherwise. There are no fences and no competitor: every shopper sees the lowest fare open, or the one continuous price.

Class ladder, controlled with EMSR-b

The ladder has 6, 10 or 26 fares between the lowest and the highest fare, with equal percentage steps (geometric) or equal dollar steps. At each of the 10 data collection points (DCPs: 180, 120, 90, 60, 45, 30, 21, 14, 7 and 3 days out), EMSR-b (Belobaba, 1992) sets nested protection levels on the seats left, from the forecast of demand still to come. Between two DCPs, a class closes when it has sold its booking limit, so the lowest open fare steps up as the flight fills.

Because shoppers buy the cheapest fare they see, class demand isn't independent, so EMSR-b runs on fare-adjusted inputs (Fiig, Isler, Hopperstad and Belobaba, 2010). If class j is the lowest one open in a period, the forecast sells Q_j = λ · S(f_j) seats, λ being the shoppers expected in that period and S(f) the share willing to pay at least f, and earns R_j = f_jQ_j. Each class's adjusted fare is the marginal revenue of opening it, (R_j − R_j−1) / (Q_j − Q_j−1), taken along the upper concave hull of the points (Q, R); classes off the hull or with a negative adjusted fare stay closed. The buy-down page shows what happens without this step: the ladder would lose much more, and not because of its price points.

Continuous price

The continuous price comes from the same forecast, the same arrival rate and WTP distribution, through a dynamic programme (Gallego and van Ryzin, 1994). With V(t, c) the expected revenue still to come with c seats left, the price is

p*(t, c) = argmax_p S_t(p) · (p − ΔV), with ΔV = V(t, c) − V(t, c − 1),

the price that maximises what a sale brings minus the value of the seat it uses up (ΔV is the seat's bid price). V is solved backwards from departure on a time grid fine enough for at most one shopper per step. The price is rounded to the dollar and recomputed every six hours and after every sale, so it moves with the seats left as the ladder's open class does between DCPs, but without steps. The forecast never changes during the booking period here, so re-optimising at each DCP gives the same prices.

The simulation and the charts

2,000 departures are generated from a fixed random seed, and both policies see exactly the same shoppers, so the gain is measured shopper by shopper rather than between two samples. Revenue, load factor and average fare are averages per departure. In the breakdown, a shopper who bought under both policies counts for the difference in price; one who bought under only one of them counts for the whole fare, split by what the other policy did at that moment (a price above their WTP, or nothing on sale). The dashed line in the last chart reruns the same dynamic programme with the price limited to the ladder's fares: the gap between it and continuous pricing is the value of the price points alone, and the gap between it and EMSR-b comes from how the ladder is controlled.

Continuous and offer-based pricing in the industry

The class ladder. A published airline fare is filed in advance, through ATPCO for most carriers, and sold in a booking class, one of up to 26 letters on each cabin. Revenue management doesn't set prices; it opens and closes classes. A GDS or an agency can price a ticket on its own because every possible price is already on file, which is also why the price can only move in steps (Commercial 101, chapter 02).

Continuous pricing. The airline's own system computes the price at the time of the request and can land between the filed levels. Lufthansa Group launched it in October 2020 on most European routes of Lufthansa, SWISS and Austrian, sold on its own websites and through NDC connections but not through GDSs using the old EDIFACT messages, and said the prices are based on market factors such as season, day of travel and time before departure, not on personal data (Business Travel News, 27 Oct 2020). The group's guideline for agencies describes a price derived from its filed fares and booking classes, never higher than the standard fare for the same itinerary and valid only on the day it's offered (Lufthansa Group, Continuous Pricing Logic). Singapore Airlines began a trial on 31 January 2023 on its website and app, "resulting in a smoother transition from one price point to another", with NDC partners to follow (Singapore Airlines). United also prices this way in its direct and NDC channels, while American's NDC prices at the time still came from its filed fares (Business Travel News, 9 Oct 2023).

Offers and orders. NDC, the XML/API standard IATA launched with Resolution 787 in 2012, lets an agency ask the airline for a complete, priced offer instead of assembling the price from filed fares (Commercial 101, chapter 04). IATA's Modern Airline Retailing programme builds on it: "Dynamic Offers" combine continuous pricing with dynamic bundling, aiming to move "away from static fare filings and booking classes", and ONE Order replaces the PNR and the e-ticket with a single order record (IATA, Dynamic Offers; IATA, Airline Retailing). ATPCO, which carries the filed fares, reported in 2024 that about a quarter of flight offers were already dynamically generated, with a goal of 80% by 2026 (Travel Weekly, 12 Apr 2024).

Words to keep apart. Wittman and Belobaba (2019) separate choosing which fare products to offer (assortment optimisation), moving filed fares up or down (dynamic price adjustment) and setting prices from a continuous range (continuous pricing). None of these requires personalisation. When prices do vary by customer segment, the gains can be larger but depend on how competitors react: in MIT's PODS simulations, one airline using segmented continuous pricing gained up to 17%, mostly at its competitors' expense, and competitors could neutralise much of it (Long and Belobaba, 2024). This page has one airline and no segments, so it measures only the value of the price points and of the control method. More on where this is heading in RM 101, chapter 07 (dynamic pricing) and chapter 08 (offer and order).

Sources

• Gallego, G. and van Ryzin, G. (1994), "Optimal dynamic pricing of inventories with stochastic demand over finite horizons", Management Science 40(8), 999–1020.
• Belobaba, P. (1992), "Optimal vs. heuristic methods for nested seat allocation", AGIFORS Reservations and Yield Management Study Group (EMSR-b).
• Fiig, T., Isler, K., Hopperstad, C. and Belobaba, P. (2010), "Optimization of mixed fare structures: Theory and applications", Journal of Revenue and Pricing Management 9(1–2), 152–170.
• Wittman, M. D. and Belobaba, P. P. (2019), "Dynamic pricing mechanisms for the airline industry: a definitional framework", Journal of Revenue and Pricing Management 18(2), 100–106.
• Long, Y. and Belobaba, P. (2024), "Airline revenue management with segmented continuous pricing: methods and competitive effects", Journal of Revenue and Pricing Management 23(1).
• Industry: Business Travel News (2020, 2023), Lufthansa Group, Singapore Airlines, IATA, Travel Weekly on ATPCO.
• Fares, for scale: the default $130–$620 range is the one on the booking limits and buy-down pages, invented around the 2025 US average domestic fare of $387 (BTS). All other parameters are in continuouspricing.json and are assumptions. Links checked September 2026.

Limitations

• Both policies are handed the true demand model. In practice the WTP curve is estimated, and a continuous price amplifies estimation errors that a coarse ladder would round away; the gain here is an upper bound for a given model.
• One flight leg, one cabin, no competitor. A price a few dollars above a competitor's can lose the booking outright, and competitors react, which this page can't show.
• Shoppers see one price and have no fences, bundles or ancillaries. Real offers mix fare families, bags and seats, which is where dynamic bundling and offer-based retailing go beyond price points.
• Shoppers are myopic: they don't wait for a lower price or shop again later. Prices that move after every sale can teach customers to watch them.
• No cancellations, no-shows, overbooking or groups, and the forecast is never updated with the bookings of the departure itself.

More on pricing beyond the fare ladder in Revenue Management 101, chapter 07. This is a personal project and isn't affiliated with any airline.