RM Market Simulator

Individual revenue management techniques—EMSR-b booking limits, bid-price controls, dynamic pricing—are powerful in isolation. But how do they perform when two airlines compete for the same passengers? This discrete-event simulator lets you find out.

Introduction

Closed-form solutions for revenue management assume a single firm facing exogenous demand. In practice, airlines compete: a passenger turned away by one carrier may book with a rival. The Passenger Origin-Destination Simulator (PODS) developed at MIT (Belobaba and Hopperstad (2004)) was the first large-scale tool to study this interaction. Our simulator captures the same core dynamics in a simplified, interactive form.

By configuring two airlines with different RM policies and watching hundreds of replications, you can directly observe phenomena that are difficult to derive analytically: revenue spill from under-protection, spoilage from over-protection, and the competitive advantage of sophisticated pricing in heterogeneous markets.

The Market Model

Definition — Market Structure

Two airlines compete on a single route with identical capacity $C$ seats each. Three customer segments arrive over a $T = 60$ day booking horizon before departure.

Customers arrive according to a non-homogeneous Poisson process. Each segment has a distinct arrival pattern and willingness-to-pay distribution:

Leisure (60% of arrivals): Peak at day 15. $\text{WTP} \sim N(\$200, \$50^2)$ . Price-sensitive travelers who book well in advance.
Business (30%): Peak at day 50. $\text{WTP} \sim N(\$500, \$100^2)$ . High-value travelers who book close to departure.
Discount (10%): Uniform, mostly early. $\text{WTP} \sim N(\$120, \$30^2)$ . Extremely price-sensitive opportunistic buyers.

This creates the fundamental RM tension: cheap customers arrive first, expensive customers arrive last. An airline that sells all its seats early at low fares has no room for the high-value business travelers who appear near departure.

Each arriving customer evaluates both airlines and makes a logit choice: they compare the surplus (WTP minus offered fare) from each airline plus a Gumbel random utility shock, and may also choose not to purchase at all.

U_{ij} = \frac{\text{WTP}_i - f_j}{\sigma} + \varepsilon_{ij}, \quad \varepsilon \sim \text{Gumbel}

RM Policies

Each airline independently selects one of four revenue management strategies:

First-Come First-Served (FCFS)

The baseline: accept any customer whose WTP exceeds the lowest available fare. No seat protection, no yield management. This is the strategy most small businesses implicitly follow.

EMSR-b Booking Limits

The workhorse of airline RM (Phillips (2021)). Uses the Expected Marginal Seat Revenue heuristic to compute nested booking limits that protect seats for higher-fare classes. The demand multiplier controls how aggressively the airline forecasts future demand, and risk aversion widens the protection bands.

Bid-Price Control

Instead of class-based booking limits, the airline computes a single bid price—the minimum fare it will accept at the current state. The bid price rises with the fill rate and approaches departure, controlled by aggressiveness and time sensitivity parameters.

\pi(t) = f_{\min} + (f_{\max} - f_{\min}) \cdot \left(\frac{\text{fill}}{2} \cdot \alpha + \frac{\text{urgency}}{2} \cdot \tau \right)

Dynamic Pricing

A continuously adjusting posted price inspired by Wittman and Belobaba (2019). The price rises with both the fill rate and the urgency (proximity to departure). Customers see a single price rather than choosing among fare classes.

p(t) = f_{\text{base}} \cdot (1 + \text{fill} \cdot k_1) \cdot (1 + \text{urgency} \cdot k_2 / 2)

Interactive Simulator

Configure each airline’s policy and parameters, then explore the results in two modes:

Animated: Watch a single booking realization unfold day by day. The stacked area charts show seats filling by fare class.
Summary: Run 100–500 Monte Carlo replications and compare revenue distributions, load factors, and fare-class mix across airlines.

Play: You Are the Revenue Manager

The simulator above pits algorithms against each other—but how would you perform? In this game you receive booking requests one at a time and must decide whether to accept or reject each one. Your goal is to maximize total revenue without filling the plane too early with low-fare passengers or leaving seats empty.

After you finish, your revenue is compared against four benchmark policies: FCFS, EMSR-b, bid-price control, and dynamic pricing. Toggle the EMSR-b hint to learn the optimal accept/reject logic in real time.

Capstone: Revenue Management

This capstone brings together all the revenue management concepts from this chapter. In Play mode, you act as the revenue manager for a 180-seat flight, accepting or rejecting booking requests over a 60-day horizon. In Design mode, you configure RM policies and run Monte Carlo simulations to compare their performance.

Key Insights

FCFS bleeds revenue. Without seat protection, FCFS fills up early with discount and leisure passengers, leaving no room for late-arriving business travelers. When competing against any RM policy, FCFS consistently loses.
EMSR-b protects, but can over-protect. Setting the demand multiplier too high causes the airline to hold back too many seats, leading to spoilage—empty seats at departure because the forecasted high-fare demand never materialized.
Bid-price controls adapt continuously. Unlike class-based limits, the bid price adjusts at every booking request. This provides finer-grained control but requires good parameter calibration.
Dynamic pricing captures surplus. By posting a continuously adjusting price, dynamic pricing can extract more consumer surplus than fixed fare classes. However, it may price out marginal customers during demand lulls.
Competition amplifies spill. A customer denied by one airline may book with the competitor. This recapture effect means that under-protection is especially costly in competitive markets, as the lost revenue goes directly to the rival.

References

Belobaba, P. P. & Hopperstad, C. (2004). “Algorithms for Revenue Management in Unrestricted Fare Markets.” Proceedings of AGIFORS Reservations and Yield Management Study Group.
Law, A. M. (2015). Simulation Modeling and Analysis, 5th ed.. McGraw-Hill.
Phillips, R. L. (2021). Pricing and Revenue Optimization, 2nd ed.. Stanford University Press.
Talluri, K. T. & van Ryzin, G. J. (2004). The Theory and Practice of Revenue Management. Springer.
Wittman, M. D. & Belobaba, P. P. (2019). “Dynamic Availability of Fare Products with Knowledge of Customer Context.” Journal of Revenue and Pricing Management, 18, 400–415.

Revenue Management Simulator