Lecture 17 Revenue Management I - Overbooking

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Lecture 17 Revenue Management I - Overbooking
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RM Conceptual Framework Manage the Demand on
Multiple Dimensions

• Demand is multidimensional
• Product
• Customer
• Time
• Value depends on all the three dimensions

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Features shared by airlines, hotels and rental
cars

• _____ 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

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The Origins of RM American Airlines and
PeopleExpress

• American Airlines and People Express
• 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

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American Airlines and PeopleExpress

• 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
• 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

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American Airlines and PeopleExpress

• Issues
• 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
• Solution American Super Saver pricing scheme
  (1978) and Ultimate Super Saver (January 1985)
• 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
• 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

• Advance booking
• - Airlines allow the potential customers to
  advance-book for their future flights.
• Overbooking
• - Airlines usually sells more tickets than
  seats!

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Advance booking

• 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.
• 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

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Overbooking

• 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.

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Review of Random Variables

• 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 XL if demand less than 150, H
  if demand higher than 150
• Pr(XL) Pr(100) Pr(101) Pr(150)

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Basic Definitions
Discrete Continuous
Probability Pr(Xa) Pr(a X b) òa,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) òx lta f(x)dx
Mean EX Sx x Pr(X x) EX òx xf(x)dx
Variance VarX Sx (x EX)2Pr(X x) VarX òx(x EX)2f(x)dx
VarX EX EX2 EX2 (EX)2
Standard deviation SDX Sqrt(VarX)Coefficie
nt of variation CVX SDX/EX
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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
EX(0.20)(100)(0.10)(125)(0.23)(150)(0.30)(17
5)(0.17)(200)153.5
VarX(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
STDXSqrt(1,162.8)34.1
CVX34.1/153.50.22
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Profit-maximizing over-booking a numeric model

• 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

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What is the chance of having N(S) no shows?

• First of all we notice that N(S) is always
  smaller or equal to S, the number of tickets
  sold.
• Take S 3 as an example, then N(S) can be either
  0, 1, 2, or 3.

NO shows 0 1 2 3
Chance
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What is the expected revenue of selling S tickets?
NO shows 0 1 2 3
Revenue
of tickets sold 0 1 2 3
Revenue
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What is the expected profits of selling S tickets?

• If S 2

NO shows 0 1 2
Chance
Revenue
Cost
Profit
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What is the expected costs of selling S tickets?

• If S 3

NO shows 0 1 2 3
Chance
Revenue
Cost
Profit
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Summary

• How does the profit when S2 compares to the
  profit when S3?
• In this case does the airline want to overbook or
  not?
• What are the factors that you think will
  influence the decision of overbooking?

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Important lessons for over-booking

• The company should be more aggressive in
  over-booking when
• The probability of no shows _______
• The revenue from each paying traveler ________
• The cost of dispensing over-booked customers
  ________

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Next Lecture

• Revenue Management II
• Description of task 2 posted