1. Airline Network Revenue Management with Buy-up
Houyuan Jiang
Judge Business School
University of Cambridge, UK
Giovanna Miglionico
Dipartimento di Elettronica Informatica e
Sistemistica, University of Calabria, Italy 

2. Outline Buy-up Dynamic program and approximate formulations
Booking policies and their quality
Computational results

3. A booking process without buy-up
request arrives
Accept
the request? No
Yes
Passengers who do not get the product they want book and travel on another carrier or do not travel at all
Buy up or upgrade or recapture

4. A booking process with buy-up
Yes No
Yes
Accept?
Accept?
Yes
A booking
request arrives
Buy up? No No

5. Literature Belobaba (OR, 1989) Brumelle, et al (TS, 1990)
You (EJOR, 2003)
Talluri and van Ryzin (The Theory and Practice of Revenue Management, 2004)
Talluri and van Ryzin (MS, 2004)
van Ryzin and Liu (WP, 2004)
Gallego et al (WP, 2004)
Buy up
Choice
modelling

6. Notation
t=T
t=0

7. Decision tree at time t A booking request arrives Accept? No Yes
Buy up?
No booking
request arrives

8. Dynamic program formulation
First-time accept
Second-time accept
Second-time reject
No buy-up
No arrival

9. Optimal booking policy

10. Dynamic program formulation without buy-up
The airline achieves a higher revenue with buy-up than without buy-up if buy-up behaviour is observed

11. Deterministic LP approximation
Revenue
Capacity constrs
Demand constrs
Buy-up constrs
Allocation for the first request
Allocation for the buy-up requests
Buy-up probability
Mean demand

12. Randomized LP approximation
d is a realization of the random demand
Each demand realization results in an RLP

13. Probabilistic NLP approximation

14. Booking Policies of network inventory control
Partitioned booking limits: Specify a booking limit for each type of products
Bid price control: Calculate the displacement cost of each leg for a product and compare the total displacement cost with the product price
Both approximate booking limits and bid prices can be calculated from DLP, PNLP, and RLP, etc

15. Booking policies based on partitioned booking limits
First time decision on product j
The number of existing bookings
of product j that are accepted first time
The number of seats
allocated to product j
Second time decision on product l for buy-ups from product j
The number of existing bookings
of product l for buy-ups of product j
The number of seats allocated to
product l for buy-ups of product j

16. Booking policies based on bid price
First time decision on product j
There are enough seats
available on relevant legs
Second time decision on product l for buy-ups from product j
There are enough seats
available on relevant legs

17. Asymptotic optimality
The partitioned booking limits policy for several models are asymptotically optimal when the initial capacity and the total demand are scaled up at the same speed.
The bid-price policy is also shown to be asymptotically optimal provided correct bid prices are used when the initial capacity and the total demand are scaled up at the same speed.

18. Computational results: T1B C D E F G
7 legs : AB, BA, CA, AD, GB, BF, EB,
8 itineraries: AB, BA, CAB, BAD,
CABF, EBF, GBF, GBAD
2 fares (16 products): Low, High
Demand: Truncated normal distributions

19. Computational results: T1

20. Effect of buy-up probability: T1

21. Conclusions Buy-up Dynamic program and approximate formulations
Booking policies and their quality
Computational results

22. A booking process with buy-up: Another angle
Yes
Accept?
Yes No
A booking
request arrives
Recommend
buy up? No

23. Booking policies based on marginal values
First time decision
Second time decision

24. Effect of buy-up probability: T1, T2, T3, T4

25. Comparisons with the non-buyup DLP model: T1, T2, T3, T4