operations management

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?

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Revenue Management


Elements of Revenue Management

Pricing and market segmentation Capacity control Overbooking Forecasting Optimization


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

020

406080

100120

140160

0 50 100 150 200 250 300

price

dem

and

d = (3/5)(300-p)


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.


Finding the price that maximizes revenue.

02000

400060008000

1000012000

1400016000

50 100 150 200 250

price

reve

nue

Revenue is maximized when the price per seat is $150,meaning 90 seats are sold.


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.


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.


What if the airline only holds 60 people?

r(d) = p(d)*d = 300d-(5/3)d2.

02000

400060008000

1000012000

1400016000

0 20 40 60 80 100 120 140 160

demand

reve

nue

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.


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.


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?


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



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.



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.



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?


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


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?


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.


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.


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


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.


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?


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.


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


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?


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


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.


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


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?


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.


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.


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?


Marginal Analysis: Overbooking

Sell 156 seats?

No. It is best to sell 155 seats.

250

250-700=-450

Sell

Hold0

Revenue increase


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


How many tickets should the airline sell?


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 …


What have we learned?

Basic Revenue Management Pricing Market Segmentation Capacity Control Overbooking

Teaching notes, homework, and practice revenue management questions posted.

operations management

Documents

plot revenue

terms of price

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operations managementsession

operations managementfinding

function of demand

following demand information