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Transcript of 1 The Impact of Buy-Down on Sell Up, Unconstraining, and Spiral-Down Edward Kambour, Senior...
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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
2
The Research ProblemThe Research Problem
3
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
4
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
5
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
22
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
23
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
25
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.