01 Introduction
Goal¶
- Sell a minimum number of seats without selling every seat at discount prices, such that it is enough to cover fixed operating costs
- Sell remaining seats at higher rates to maximize revenue
Profit¶
\[ \begin{aligned} \text{Profit} &= \text{Income} - \text{Expenses} \\ &= \text{Sale Price} \times \min(\text{Demand}, \text{Quantity}) - \text{Cost} \times \text{Quantity} \end{aligned} \]
Passengers¶
Passengers have different valuations
| Business people | Others | |
|---|---|---|
| Keen on Flexibility | ✅ | ❌ |
| Booking Time | Late | Early |
| Keen on refunds | ✅ | ❌ |
| Price Elasticity | Low | High |
| Purchasing Power | High | Low |
Selling Cases¶
| Sell too many discounted seats | Not enough seats for high-paying passengers |
| Sell too many discounted seats | Empty seats at takeoff |
Lost revenue in both scenarios
Optimization¶
We can formulate using Optimization
- Objective Function: Maximize Total Revenue
- Constraints
- Seats sold \(>=\) 0
- Seats sold \(<=\) Capacity
- Seats sold \(<=\) Demand
Shadow Price¶
Marginal revenue for unit increase in demand of regular seats
2024-05-12