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

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

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!

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

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: 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 Continuous

Probability Pr(X=a) Pr(a X b) = [a,b] f(x)dx

(f(a):Probability Density Function)

Cumulative Distribution Function

F(a)=Pr(X a) = x a Pr(X = x) F(a) = Pr(X a) x <=a f(x)dx

Mean E[X] x x Pr(X = x) E[X] x xf(x)dx

Variance Var[X] = x (x – E[X])2Pr(X = x) Var[X] = x(x – E[X])2f(x)dx

Standard deviation: SD[X] = Sqrt(Var[X])Coefficient of variation: CV[X] = SD[X]/E[X]

Var[X] = E[X – E[X]]2 = E[X2] – (E[X])2

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ExampleDiscrete 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

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

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

What is the expected revenue of selling S tickets?

NO shows

0 1 2 3

Revenue

# of tickets sold

0 1 2 3

Revenue

What is the expected profits of selling S tickets?

If S = 2

NO shows 0 1 2

Chance

Revenue

Cost

Profit

What is the expected costs of selling S tickets?

If S = 3

NO shows

0 1 2 3

Chance

Revenue

Cost

Profit

Summary

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

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 ________

Next Lecture

Revenue Management II

Description of task #2 posted