Airline Revenue Management: EMSRb Algorithms, Nested Booking Limits, and Dynamic Fare Buckets

## Stochastic Optimization in Perishable Asset Revenue Management

An unsold scheduled airline seat at cabin door closure has a terminal salvage value of zero. Airline yield managers maximize total flight revenue by dynamically allocating seat inventory across multiple nested fare buckets using Belobaba's Expected Marginal Seat Revenue (EMSRb) heuristic.

### 1. The EMSRb Protection Level Equation

$$\text{Protection Level } S_{j-1} = \mu_{\text{agg}} + z_\alpha \cdot \sigma_{\text{agg}}$$

Where $\alpha = 1 - \frac{f_j}{\bar{f}_{j-1}}$ determines the critical ratio of lower fare class $j$ relative to the weighted average revenue of all superior fare classes.

| Fare Class | Typical Advanced Purchase | Flexibility / Change Rules | Target Passenger Segment | Allocated Cabin Share |
|:-----------|:-------------------------:|:--------------------------:|:------------------------:|:---------------------:|
| Y Class (Full Economy) | 0 - 3 Days Prior | Fully Refundable / Standby | Business Emergency | 12% |
| M Class (Standard Economy) | 7 - 14 Days Prior | Free Changes, Non-Refundable | Corporate Planned | 28% |
| Q Class (Discount Leisure) | 21 - 30 Days Prior | Change Fee Applies | Leisure Traveler | 45% |
| Basic Economy (Restricted) | 30+ Days Prior | Zero Changes / No Carry-on | Price-Sensitive VFR | 15% |