Operations management
Session 18: Revenue Management Tools
RM: A Basic Business Need
Session 18
Increasing Revenue
Reducing Cost
 What are the basic ways to improve profits?
Revenue
Management
$
Profits
Operations Management
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Elements of Revenue
Management
 Pricing and market segmentation
 Capacity control
 Overbooking
 Forecasting
 Optimization
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Pricing: How does it work?
 Objective: Maximize revenue
Example (Monopoly): An airline has the following demand
information:
Price
0
50
100
150
200
250
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Demand
?
150
120
90
60
30
d = (3/5)(300-p)
160
140
120
demand

100
80
60
40
20
0
0
50
100
150
200
250
300
price
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Pricing: How does it work?

What is the price that the airline should charge
to maximize revenue? Note that this is
equivalent to determining how many seats the
airline should sell.

The revenue depends on price, and is:
Revenue = price * (demand at that price)
r(p) = p * d(p)
= p * (3/5) * (300 – p)
= (3/5) * (300p – p2)

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We would like to choose the price that maximizes revenue.
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Finding the price that maximizes
revenue.
Revenue is maximized when the price per seat is $150,
meaning 90 seats are sold.
16000
14000
revenue
12000
10000
8000
6000
4000
2000
0
50
100
150
200
250
price
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Finding the price that maximizes
revenue.
r(p) = p*d(p) = (3/5)*(300p-p2)
r’(p)=0 implies (3/5)(300-2p)=0 or p=150
Pricing each seat at $150 maximizes revenue.
d(150)=(3/5)*(300-150)=90
This means we will sell 90 seats.
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What if the airline only holds 60
people?
Is it possible we would want to sell less than 60 seats?
To answer this question, plot revenue as a function of demand.
First note that actually, revenue = price * min(demand, capacity).
Second note that it is equivalent to think in terms of price
or demand; i.e., d(p) = (3/5)*(300-p) implies p(d) = 300-(5/3)d.
Then, r(d) = p(d)*d = 300d-(5/3)d2.
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What if the airline only holds 60
people?
16000
14000
revenue
12000
10000
r(d) = p(d)*d
= 300d-(5/3)d2.
8000
6000
4000
2000
0
0
20
40
60
80
100
120
140
160
demand
It is obvious from the graph that revenue is maximized when
90 seats are sold (demand is 90), as we found originally.
It is also clear that we want to sell as many seats as possible up
to 90, because revenue is increasing from 0 to 90.
Conclusion: sell 60 seats at price p(60)=300-(5/3)*60=200.
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Pricing to Maximize Revenue:
The General Strategy
 Write revenue as a function of price.
 Find the price that maximizes the revenue function.
 Find the demand associated with that price.
 Ensure that there is enough capacity to satisfy that
demand. Otherwise, sell less at a lower price. (This
assumes that the revenue function increases up until the
best price, and then decreases.)
 Is this strategy specific to airlines? No.
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Pricing and Market Segmentation
 Should it be a single price?
 Most airlines do not have a single price.
 Suppose the airline had 110 seats, so that the
revenue-maximizing price of $150 (equivalently
selling 90 seats) meant having 20 seats go unsold.
 Is there a way to divide the market into customers
that will pay more and those that will pay less?
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Market Segmentation
Passengers are very heterogeneous in terms of their needs and
willingness to pay (business vs leisure for example).
A single product and price does not maximize revenue
price
p3
additional revenue by segmentation
revenue = price • min {demand, capacity}
p1
p2
capacity
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demand
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Pricing and Market Segmentation
 It is the airline interest to:

Reduce the consumer surplus

Sell all seats

How can this be achieved?


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Sell to each group at their reservation price (segmentation
of the market)
In the previous example, price tickets oriented for business
customers higher than $150 and those oriented for leisure
customers lower than $150.
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Pricing and Market Segmentation
 The idea of market segmentation does not just apply to
airlines. Where else do we see this?
 Why are companies using a single price?

Easy to use and understand

Product can’t be differentiated

Market can’t be segmented

Lack of demand information

Consumers don’t like that different customers are getting the
“same products” at different prices.
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Pricing and Market Segmentation
 What are the difficulties in introducing multi-prices?

Information


May be hard to obtain demand information for different
segments.
How to avoid leakages from one segment to
another?

Fences
 Early purchasing, non refundable tickets, weekend stay over.

Competition
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Revenue Management
Dilemma for Airlines
 High-fare business passengers usually book later
than low-fare leisure passengers
 Should I give a seat to the $300 passenger which
wants to book now or should I wait for a potential
$400 passenger?
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The Basic Question is Capacity
Control
Business Travelers
Leisure Travelers
•Price Insensitive
•Book Later
•Schedule Sensitive
•Price Sensitive
•Book Early
•Schedule Insensitive
fd = Discount Fare
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ff = Full fare
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The Basic Question is Capacity
Control
 Consider one plane, with one class of seats.
 We would like to sell as many higher-priced tickets
to business customers as we can first, and then
sell any leftover seats to leisure customers at a
discount.
 The problem is that the leisure customers book
early, and the business customers book late.
 How do we decide how many seats to reserve for
the business class customers?
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Two-Class Capacity Control
Problem
 A plane has 150 seats. Current s=81 seats remaining.
 Two fare classes (full-fare and discount) with fares ff = 300
> fd = 200 > 0.
 Should we save the seat for late-booking full-fare
customers?
 We need full-fare demand information,
 Random variables, Df.
 Ff (x) = Probability that Df < x.
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Capacity Control: Tradeoff
 Cannibalization - If the company sells the ticket for $200
and the business demand is larger than 80 tickets then,
the company loses $100. Cost = ff – fd (=100) for each fullfare customer turned away.
 Spoilage - If the company does not sell the ticket for
$200 and the business demand is smaller than 81 tickets
then, the company loses $200. Cost = fd (=200) for each
“spoiled” seat.
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Marginal Analysis
 If we sell the discount ticket now, we get fd right
away.
 How much do we expect to generate by holding
the seat?
fd
Sell
P(D>s)
ff
Hold
P(D<s)
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Decision rule
 Criteria: comparing fd and ffP(D>s)
 Accept discount bookings if fd > ffP(D>s)
 If 200 > 300(1–F(80)) or 0.667 > (1–F(80)). Then
sell the ticket for $200. Otherwise wait and don’t
sell the ticket.
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Example
 Two fairs: $200, $300
 The demand for the $300 tickets is equally likely to be
anywhere between 51 and 150
 With 81 seats left, should the airline sell a ticket for $200?

P(D>=81)=1-F(80) = 0.7

200 < 0.7*300 = 210

Clearly the airline should close the $200 class.
 What if there were 101 seats left?
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Booking Limit
 What is the booking limit (the maximum number
of seats available to be sold) of the $200 class in
this case?

200 = (1–F(x))*300

1/3 = F(x)

F(83) < 1/3 < F(84)


Accept discount bookings until 84 seats remain. Then accept
only full-fare bookings.
In other words, we will sell 150-84=66 seats to the discount
class. 66 seats is the booking limit.
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Booking Limit: Intuition
 If booking limit is too low, we risk spoilage (having
unsold seats).
 If booking limit is too high, we risk cannibalization
(selling a seat at a discount price that could have
been sold at full-fare).
Revenue
Booking Limit
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Two-Class Capacity Control
Problem: Another example
 A plane has 150 seats.
 Two fare classes (full-fare and discount) with fares
ff = 250 > fd = 200 > 0.
 The demand for full-fare tickets is equally likely to
be anywhere between 1 and 100.
 What is the booking limit that maximizes revenue?
 Intuitively, should this be higher or lower than in
the previous example?
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Overbooking
 Airlines and other industries historically allowed passengers to
cancel or no-show without penalty.
 Some (about 13%) booked passengers don’t show-up.
 Overbooking to compensate for no-shows was one of the first
Revenue Management functionalities (1970’s).
bkg
} no-shows
} no-shows
cap
90 days prior
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departure
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Overbooking: Tradeoff
 Airlines book more passengers than their capacity
to hedge against this uncovered call, Airlines need
to balance two risks when overbooking:
Spoilage: Seats leave empty when a booking
request was received. Lose a potential fare.
Denied Boarding Risk: Accepting an additional
booking leads to an additional denied-boarding.
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Overbooking
 Sophisticated overbooking algorithms balance the expected costs
of spoiled seats and denial boardings
 Typical revenue gains of 1-2% from more effective overbooking
expected
costs
total costs
spoilage
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capacity
Operations Management
denied
boarding
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Example
 The airline has a flight with 150 seats. The airline
knows the number of cancellation would be
between 4 to 8, all numbers are equally likely.
 Fair price is $250; denied boarding cost is
estimated to be $700.
 How many tickets should the airline sell?
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Example
 The airline has a flight with 150 seats. The airline
knows the number of cancellation would be
between 4 to 8, all numbers are equally likely.
 Fair price is $250; denied boarding cost is
estimated to be $700.
 How many tickets should the airline sell?

Clearly the airline should sell 154 seats because the number of
cancellations is known to be at least 4.
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Marginal Analysis: Overbooking
Sell 155 seats?
Revenue increase
P(C>=5)
Seats for everyone.
Sell
P(C<5)=P(C=4)
1 person w/out seat
250
250-700
=-450
Hold
0
 Criteria: Does E[revenue increase] exceed 0?
Yes. (4/5)*250+(1/5)*(-450) = 110 >0.
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Marginal Analysis: Overbooking
Revenue increase
Sell 156 seats?
250
Sell
250-700
=-450
Hold
0
No. It is best to sell 155 seats.
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Overbooking Example 2
 The airline has a flight with 150 seats. The airline
knows the number of cancellations will be 0,1,2,
or 3. Furthermore,

P(C=0) = 0.01, P(C=1) = 0.1, P(C=2) = 0.8, P(C=3) = 0.09
 Fair price is $250; denied boarding cost is
estimated to be $700.
 How many tickets should the airline sell?
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Overbooking Dynamic
In general, we might let the number of seats
overbooked change over time …
Bookings
Number of seats sold
No-show
“Pad”
Capacity
Bookings
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A
B
Operations Management
Departure
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What have we learned?
 Basic Revenue Management

Pricing

Market Segmentation

Capacity Control

Overbooking
 Teaching notes, homework, and practice revenue
management questions posted.
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