Lecture 17
Revenue Management I - Overbooking
RM Conceptual Framework: Manage the
Demand on Multiple Dimensions
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Demand is
multidimensional
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Product
Customer
Time
Value depends on all
the three dimensions
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Features shared by airlines, hotels and
rental cars
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_____ fixed costs and ____ variable costs (up to
a point).
Capacity can be viewed as “constrained” in this
sense.
Product or service is perishable so that the
“residual capacity” is usually worthless.
Customers have different willingness-to-pay
Demand has uncertainty, which dissolves over
time
Booking happens a long time before the
“expiration date”
The Origins of RM: American Airlines and
PeopleExpress
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American Airlines and People Express
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Airline industry deregulated in 1978
Carriers free to change prices, schedules, and service
without Civil Aviation Board (CAB) approval
Large carriers, as American Airlines, accelerate development
of Centralized Reservation and Global Distribution systems
(CRS & GDS) and introduce hub & spoke networks
Low-cost airlines enter the market, e.g., PeopleExpress
American Airlines and PeopleExpress
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Head-to-head price wars with upstarts would have
been suicidal for the majors
Robert Crandall, at the time American Airlines VP of
Marketing, nailed it
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Marginal cost of unsold seats is essentially zero because
most of the costs of a flight (capital costs, wages, fuel) are
fixed.
Match prices on unsold seats rather than all seats
American Airlines and PeopleExpress
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Issues
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Solution: “American Super Saver” pricing scheme (1978) and
“Ultimate Super Saver” (January 1985)
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American Airlines needed to prevent a low-price sale from
displacing a high-price sale
American Airlines needed to ensure high-price business customers
did not switch and buy the low-price products offered to leisure
customers
Capacity-controlled fares
Purchase restrictions
Compete on price without affecting business traveler revenues
PeopleExpress went bankrupt in September 1986
No airline currently operates without a revenue management
system
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Even the low cost carriers as JetBlue Airways and Southwest
Airlines
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Airfare Classes
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Pricing strategies of airline industry
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Advance booking
- Airlines allow the potential customers to
advance-book for their future flights.
Overbooking
- Airlines usually sells more tickets than seats!
Advance booking
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This system can be used to identify and sort
consumers according to their willingness to pay
without having to ask them to reveal their
preferences.
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Students: plan well ahead and pay discount prices
Business-travelers: make last-minute decisions and pay full prices
The airline would like to maximize the profit under
the demand uncertainty it faces.
We will elaborate on this topic in the next class
Overbooking
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There will be no-shows due to a variety of reasons.
The downside of selling the same number of tickets
as number of seats is that customer no-shows result
in potential loss of revenue.
There is also a risk of selling too many tickets.
Profit-maximizing over-booking entails finding the
optimal tradeoff between selling one more / one less
ticket, given the capacity constraint.
Review of Random Variables
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A sample space is the set of all possible outcomes of an
uncertain event.
The probability of an outcome, intuitively, is the proportion
of time that the outcome occurs if the random event is
repeated over and over again.
A random variable is a real-valued function that is defined
on a sample space.
Random variables can be discrete or continuous.
Example:
 Uncertain events: demand for Medpro next week can
be 100, 101, …, 200
 Random variable X: X=L if demand less than 150, H if
demand higher than 150
 Pr(X=L) = Pr(100) + Pr(101) + … + Pr(150)
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Basic Definitions
Discrete
Probability
Pr(X=a)
Continuous
Pr(a  X  b) = [a,b] f(x)dx
(f(a):Probability Density
Function)
Cumulative
Distribution
Function
F(a)=Pr(X a) = Sx  a Pr(X = x)
F(a) = Pr(X a) = x <=a f(x)dx
Mean
E[X] = Sx x Pr(X = x)
E[X] = x xf(x)dx
Variance
Var[X] = Sx (x – E[X])2Pr(X = x)
Var[X] = x(x – E[X])2f(x)dx
Var[X] = E[X – E[X]]2 = E[X2] – (E[X])2
Standard deviation: SD[X] = Sqrt(Var[X])
Coefficient of variation: CV[X] = SD[X]/E[X]
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Example
Discrete demand for Medpro (X):
Demand (x)
Pr(Demand = x)
F(x)
100
0.20
0.20
125
0.10
0.30
150
0.23
0.53
175
0.30
0.83
200
0.17
1.00
E[X]=(0.20)(100)+(0.10)(125)+(0.23)(150)+(0.30)(175)+(0.17)(200)=153.5
Var[X]=(0.2)(100-153.5)2+ (0.1)(125-153.5)2 +(0.23)(150-153.5)2+
(0.3)(175-153.5)2+ (0.17)(200-153.5)2 =1,162.8
STD[X]=Sqrt(1,162.8)=34.1
CV[X]=34.1/153.5=0.22
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Profit-maximizing over-booking – a
numeric model
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Suppose there are 5 travelers, labeled #1, #2… #5, and
the capacity is 2 seats.
Each traveler has a probability of “no-show” that is
between 0 and 1.
Chance of “no-shows” across different travelers are
independent and identical.
The ticket price is $500 and the “penalty” for each
oversold ticket is $400.
The airline has to decide how many tickets to sell (S) in
order to maximize its profit.
The marginal cost of serving a customer on board is $0
What is the chance of having N(S) no
shows?
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First of all we notice that N(S) is always smaller or
equal to S, the number of tickets sold.
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Take S = 3 as an example, then N(S) can be either 0, 1, 2, or 3.
NO shows
Chance
0
1
2
3
What is the expected revenue of selling S
tickets?
NO shows
0
1
2
3
0
1
2
3
Revenue
# of
tickets
sold
Revenue
What is the expected profits of selling S
tickets?
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If S = 2
NO shows
Chance
Revenue
Cost
Profit
0
1
2
What is the expected costs of selling S
tickets?
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If S = 3
NO shows
Chance
Revenue
Cost
Profit
0
1
2
3
Summary
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How does the profit when S=2 compares to the
profit when S=3?
In this case does the airline want to overbook or
not?
What are the factors that you think will influence
the decision of overbooking?
Important lessons for over-booking
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The company should be more aggressive in overbooking when
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The probability of no shows _______
The revenue from each paying traveler
________
The cost of dispensing over-booked customers
________
Next Lecture
Revenue Management II
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Description of task #2 posted