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

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

Down

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

DownEdward Kambour, Senior Scientist

E. Andrew Boyd, SVP and Senior ScientistJoseph Tama, Scientist

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The Research ProblemThe Research Problem

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The Big QuestionThe 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

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Goals of Present ResearchGoals 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

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Model BackgroundModel Background

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

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A Common Model of Demand:Single Product DemandA 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

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An Alternative Model of Demand:Buy Down Demand

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

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Comparison of Demand ModelsComparison 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?

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The Research ProblemThe 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

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The Research Problem in Context

The Research Problem in Context

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An Industry ConcernAn 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

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Logic Behind Spiral DownLogic 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

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Sell Up and High Yield Seat ProtectionSell 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

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Sell Up and High Yield Seat ProtectionSell 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

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Mathematical ModelsMathematical Models

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Single Product Demand ModelSingle 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

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Single Product Stat ModelSingle Product Stat Model

fare classes

arrival rate for the th fare class

demand for the th fare class

Poisson( )

exp( ) ( ) =

!

i

i

i

i i

xi i

ii

n

i

X i

X

f xx

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Buy Down ModelBuy 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

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Buy Down Model (cont.)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

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Buy Down Stat Model (notation)Buy Down Stat Model (notation)

interval length

fare classes

class the lowest available

fare for class

demand arrival rate

( ) willingness to pay

number of arrivals

number of bookings in class

i

i

t

n

j

p i

X

Y i

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Buy Down Stat ModelBuy Down Stat Model

Poisson( )

( ) exp / !

0 if

| Binomial( , ( ))

( | ) ( ) 1 ( )jj

x

i

j j

x yyj j j

j

X t

f x t t x

Y i j

Y X x x p

xf y x p p

y

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Buy Down Stat Model (cont.)Buy Down Stat Model (cont.)

0

( , ) ( ) 1 ( )

exp / !

( ) ( , )

( ) exp( ( )) / !

jj

j

x yyj j j

j

x

j jx

y

j j j

xf x y p p

y

t t x

f y f x y

t p t p y

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Buy Down Model (cont.)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

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Buy Down Model (example)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

( ) 1

( ) 1 exp 1 / !

E 1 ( )

jy

j j

j

p pb

f y t pb t pb y

Y t pb t tb p

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Buy Down Model 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

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Simulations Simulations

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Simulation GoalSimulation 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

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The ExperimentThe 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

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Simulated RM SystemSimulated RM System

Forecaster Single Product Demand model

Buy Down Demand model

EMSRb optimization

Output was bookings data for 20 departure dates

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Buy Down ArrivalsBuy 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

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Buy Down Arrivals (Example)Buy Down Arrivals (Example)

Suppose there are two fare classes, Y and Q, with Y fare greater than Q fare

Q passenger Q booking

Availability

Q class: open

Y class: open

Y passenger Q booking

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Buy Down Arrivals (Example)Buy Down Arrivals (Example)

Suppose there are two fare classes, Y and Q, with Y fare greater than Q fare

Q passenger no booking

Availability

Q class: closed

Y class: open

Y passenger Y booking

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Simulation Results Simulation Results

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Revenue ResultsRevenue Results

2.6

2.7

2.8

2.9

3

3.1

3.2

3.3

3.4

0 5 10 15 20

Departure Dates

Millions

of U

SD

Actual Demand Behavior Forecast Demand Behavior

Buy Down Single Product

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Revenue Results (Cont.)Revenue Results (Cont.)

2.6

2.7

2.8

2.9

3

3.1

3.2

3.3

3.4

0 5 10 15 20

Departure Dates

Millions

of U

SD

Actual Demand Behavior Forecast Demand Behavior

Buy Down Buy Down

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Load Factor ResultsLoad Factor Results

0.50.550.6

0.650.7

0.750.8

0.850.9

0.951

0 5 10 15 20

Departure Dates

Load F

act

or

Actual Demand Behavior Forecast Demand Behavior

Buy Down Single Product

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Load Factor ResultsLoad Factor Results

0.50.550.6

0.650.7

0.750.8

0.850.9

0.951

0 5 10 15 20

Departure Dates

Load F

act

or

Actual Demand Behavior Forecast Demand Behavior

Buy Down Buy Down

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ConclusionsConclusions

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ConclusionsConclusions

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.

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The Next StepThe 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.