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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, Scientist

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2 The Research Problem

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

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

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5 Model 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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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 u Hopperstads passengers with fare classes stamped on their heads For its obvious deficiencies, this model embodies an underlying assumption of different fare classes representing truly different products

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7 An Alternative Model of Demand: Buy Down Demand A fare class represents a different price for an identical product u 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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8 Comparison of Demand Models The two different models of demand illuminate the dichotomous nature of revenue management as it is now practiced u Are fare classes products, different prices for the same product, or some combination of the two?

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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 Single Product Forecast Demand Behavior Single Product Buy Down Single Product Buy Down

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10 The Research Problem in Context

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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

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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

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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 u 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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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

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15 Mathematical Models

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

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17 Single Product Stat Model

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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 u If the current lowest available fare is less than or equal to the passengers willingness to pay, he will purchase the lowest available fare

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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 u Lower fares are not available u Passengers will not pay higher fares

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20 Buy Down Stat Model (notation)

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21 Buy Down Stat Model

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22 Buy Down Stat Model (cont.)

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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 ( ( ) ) u Model the probability as the Survivor function from a probability distribution s Estimate the parameters of the distribution

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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

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25 Buy Down Model Relationship to a demand curve u 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) s Uniform Survivor Function is analogous to a straight line demand curve s Exponential Survivor Function is analogous to an exponentially decaying demand curve

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26 Simulations

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

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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

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

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30 Buy Down Arrivals Arrival stream of passengers from the single product model u 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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31 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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32 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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33 Simulation Results

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34 Revenue Results Actual Demand Behavior Forecast Demand Behavior Buy Down Single Product

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

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36 Load Factor Results Actual Demand Behavior Forecast Demand Behavior Buy Down Single Product

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37 Load Factor Results Actual Demand Behavior Forecast Demand Behavior Buy Down Buy Down

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38 Conclusions

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

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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.

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