operations management session 18: revenue management tools
TRANSCRIPT
Operations management
Session 18: Revenue Management Tools
Session 18 Operations Management 2
RM: A Basic Business Need
What are the basic ways to improve profits?
ProfitsProfits$$Red
ucin
g C
ost
Incr
easi
ng R
even
ue
Revenue Management
Session 18 Operations Management 3
Elements of Revenue Management
Pricing and market segmentation
Capacity control
Overbooking
Forecasting
Optimization
Session 18 Operations Management 4
Pricing: How does it work?
Objective: Maximize revenue Example (Monopoly): An airline has the following demand
information:
Price Demand0 ?50 150100 120150 90200 60250 30
0
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0 50 100 150 200 250 300
price
de
ma
nd
d = (3/5)(300-p)
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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)
We would like to choose the price that maximizes revenue.
Session 18 Operations Management 6
Finding the price that maximizes revenue.
0
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50 100 150 200 250
price
rev
en
ue
Revenue is maximized when the price per seat is $150,meaning 90 seats are sold.
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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=150Pricing each seat at $150 maximizes revenue.
d(150)=(3/5)*(300-150)=90This means we will sell 90 seats.
Session 18 Operations Management 8
What if the airline only holds 60 people?
Then, r(d) = p(d)*d = 300d-(5/3)d2.
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.
Is it possible we would want to sell less than 60 seats?To answer this question, plot revenue as a function of demand.
Session 18 Operations Management 9
What if the airline only holds 60 people?
r(d) = p(d)*d = 300d-(5/3)d2.
0
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10000
12000
14000
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0 20 40 60 80 100 120 140 160
demand
rev
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It is obvious from the graph that revenue is maximized when90 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.
Session 18 Operations Management 10
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.
Session 18 Operations Management 11
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?
Session 18 Operations Management 12
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
Market Segmentation
price
demand
revenue = price • min {demand, capacity}
capacity
p1
p3
p2
additional revenue by segmentation
Session 18 Operations Management 13
Pricing and Market Segmentation
It is the airline interest to: Reduce the consumer surplus Sell all seats How can this be achieved?
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.
Session 18 Operations Management 14
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.
Session 18 Operations Management 15
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
Session 18 Operations Management 16Operations Management 16
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?
Session 18 Operations Management 17Operations Management 17
The Basic Question is Capacity Control
Leisure Travelers
•Price Sensitive•Book Early•Schedule Insensitive
fd = Discount Fare
Business Travelers
•Price Insensitive•Book Later•Schedule Sensitive
ff = Full fare
Session 18 Operations Management 18
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?
Session 18 Operations Management 19Operations Management 19
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.
Session 18 Operations Management 20Operations Management 20
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 full-fare 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.
Session 18 Operations Management 21Operations Management 21
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?
ff
0
Hold
P(D<s)
P(D>s)
fdSell
Session 18 Operations Management 22Operations Management 22
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.
Session 18 Operations Management 23Operations Management 23
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?
Session 18 Operations Management 24Operations Management 24
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.
Session 18 Operations Management 25Operations Management 25
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).
Booking Limit
Revenue
Session 18 Operations Management 26Operations Management 26
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?
Session 18 Operations Management 27
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
90 days prior departure time
} no-showscap
} no-shows
Session 18 Operations Management 28
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
Number seats soldcapacity
expectedcosts
total costsspoilage
deniedboarding
Session 18 Operations Management 30
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?
Session 18 Operations Management 31
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
Criteria: Does E[revenue increase] exceed 0?
Yes. (4/5)*250+(1/5)*(-450) = 110 >0.
250
250-700=-450
P(C<5)=P(C=4)1 person w/out seat
Revenue increase
Sell
Hold
P(C>=5)Seats for everyone.
0
Sell 155 seats?
Session 18 Operations Management 33
Marginal Analysis: Overbooking
Sell 156 seats?
No. It is best to sell 155 seats.
250
250-700=-450
Sell
Hold
0
Revenue increase
Session 18 Operations Management 34
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?
Session 18 Operations Management 35
Overbooking Dynamic
Departure
Capacity
Time
Bookings
Number of seats sold
Bookings
No-show “Pad”
A B
In general, we might let the number of seatsoverbooked change over time …
Session 18 Operations Management 36
What have we learned?
Basic Revenue Management Pricing Market Segmentation Capacity Control Overbooking
Teaching notes, homework, and practice revenue management questions posted.