The Impact of Buy-Down on Sell Up, Unconstraining, and Spiral-Down

1. The Impact of Buy-Down on Sell Up, Unconstraining, and Spiral-Down Edward Kambour, Senior ScientistE. Andrew Boyd, SVP and Senior ScientistJoseph Tama, Scientist

2. The Research Problem

3. The Big Question • What is the proper model of demand, and how can it best be forecast? • Remains one of the most significant long term research issues facing revenue management

4. Goals of Present Research • Present a common model of demand and analyze an alternative model • Reasons for choosing the model we analyze: • Potential for high revenue impact • Analytically tractable • Provides firm foundation for steering the direction of the research • A near term research issue • Implementable within context of today’s predominant forecasting archetype

5. Model Background • For purposes of discussion, we consider the case of an airline with multiple fare classes on a single flight leg

6. A Common Model of Demand:Single Product Demand • A fare class represents a product with its own unique demand • A customer arrives with a desire to purchase that product, and if it is not available he does not make a purchase • Hopperstad’s passengers with fare classes stamped on their heads • For it’s obvious deficiencies, this model embodies an underlying assumption of different fare classes representing truly different products

7. An Alternative Model of Demand:Buy Down Demand • A fare class represents a different price for an identical product • Customer is fundamentally indifferent between what an M and B class ticket represent (a coach seat), but M costs $400 and B costs $200 • A customer buys the lowest priced ticket available if it is below his price point

8. Comparison of Demand Models • The two different models of demand illuminate the dichotomous nature of revenue management as it is now practiced • Are fare classes products, different prices for the same product, or some combination of the two?

9. The Research Problem • If demand is actually behaving according to one model, but is forecast using another model, what is the impact on revenue? Actual Demand Behavior Buy Down Buy Down Single Product Single Product Forecast Demand Behavior Single Product Buy Down Single Product Buy Down

10. The Research Problem in Context

11. An Industry Concern • If actual consumer behavior is best described as buy down, but forecast demand behavior is single product, does this lead to a spiraling down of revenues? Actual Demand Behavior Buy Down Forecast Demand Behavior Single Product

12. Logic Behind Spiral Down • Customers buy down, and as a result do not reveal their true willingness to pay through their ticket purchase • Forecaster assumes single product demand, thus assuming that demand in each fare class represents actual demand in that fare class (once unconstrained) • Result: Forecaster underestimates actual willingness to pay of customers, diluting revenue • As this may recur from cycle to cycle, revenue may actually spiral downward

13. Sell Up and High Yield Seat Protection • Many carriers use some form of sell up or special protection for high yield seats • Implicitly or explicitly, such efforts assume the true willingness to pay of demand is underestimated • If true willingness to pay of demand is known, sell up or special high yield seat protection is unnecessary, and is actually detrimental to revenue

14. Sell Up and High Yield Seat Protection • Models for addressing sell up or estimating sell up probabilities are frequently based on “good sense,” but lack a solid theoretical foundation • Recommendation: Focus on the demand model, and let mathematics drive proper estimates of demand, or estimates of sell up probabilities

15. Mathematical Models

16. Single Product Demand Model • The demand for each fare class is a Poisson process over the booking period • The demand processes are independent • Each fare class has a different arrival rate

17. Single Product Stat Model

18. Buy Down Model • The demand for seats is a Poisson process over the booking period • Each passenger is willing to pay up to a certain amount for his ticket • If the current lowest available fare is less than or equal to the passenger’s willingness to pay, he will purchase the lowest available fare

19. Buy Down Model (cont.) • Examine intervals during which each fare class is the lowest available • During this interval there are no arrivals in any other fare class • Lower fares are not available • Passengers will not pay higher fares

20. Buy Down Stat Model (notation)

21. Buy Down Stat Model

22. Buy Down Stat Model (cont.)

23. Buy Down Model (cont.) • Estimate the Poisson arrival rate () • Estimate the probability that a given passenger will be willing to pay an amount greater than or equal to each fare ( () ) • Model the probability as the Survivor function from a probability distribution • Estimate the parameters of the distribution

24. Buy Down Model (example) • Suppose we use the survivor function of a uniform random variable on 0 to 1/b for the willingness to pay

25. Buy Down Model • Relationship to a demand curve • If there was only one fare class, then the demand for seats under the Buy Down model would be a Poisson process with arrival rate, t(p). Thus, the expected quantity demanded is t(p) • Uniform Survivor Function is analogous to a straight line demand curve • Exponential Survivor Function is analogous to an exponentially decaying demand curve

26. Simulations

27. Simulation Goal • Examine the effect of Buy Down demand on a Revenue Management System Actual Demand Behavior Buy Down Buy Down Forecast Demand Behavior Single Product Buy Down Single Product Single Product Single Product Buy Down

28. The Experiment • network of 50 flight legs and 5,000 ODIFs • one compartment • complete network information • simulated RM system • 16 re-optimization points • no cancellations, no post-departure

29. Simulated RM System • Forecaster • Single Product Demand model • Buy Down Demand model • EMSRb optimization • Output was bookings data for 20 departure dates

30. Buy Down Arrivals • Arrival stream of passengers from the single product model • Each arrival will be associated with a fare class • Each passenger will buy the lowest available fare class product, if that fare is not greater than his associated fare

31. Buy Down Arrivals (Example) • Suppose there are two fare classes, Y and Q, with Y fare greater than Q fare Availability Q class: open Y class: open Y passenger  Q passenger   Q booking  Q booking

32. Buy Down Arrivals (Example) • Suppose there are two fare classes, Y and Q, with Y fare greater than Q fare Availability Q class: closed Y class: open Y passenger  Q passenger   no booking  Y booking

33. Simulation Results

34. Revenue Results Actual Demand BehaviorForecast Demand Behavior Buy Down Single Product

35. Revenue Results (Cont.) Actual Demand BehaviorForecast Demand Behavior Buy Down Buy Down

36. Load Factor Results Actual Demand BehaviorForecast Demand Behavior Buy Down Single Product

37. Load Factor Results Actual Demand BehaviorForecast Demand Behavior Buy Down Buy Down

38. Conclusions

39. Conclusions • If passengers utilize the Buy Down model • A RM system using a Single Product demand model may exhibit spiral down in revenue while maintaining load factor • A RM system using a Buy Down demand model may have increased revenue while lowering load factor.

40. The Next Step • It is likely that there are some passengers who are relatively fare specific, for whom the Single Product demand model is appropriate. • It is also likely that there are passengers that are price sensitive, for whom the Buy Down model is appropriate. • The next step in research is to develop a hybrid demand that accounts for both Single Product and Buy Down purchasers.