Revenue Management
Chapter 13
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Learning Goals
Yield management (with protection levels) and
overbooking give demand flexibility where supply
flexibility is not possible.
 The Newsvendor model can be used:

– Single decision in the face of uncertainty.
– Underage and overage costs.
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Revenue (Yield) Management
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Some U.S. airline industry observations


Since deregulation in 78, 137 carriers have filed for bankruptcy until 2006.
From 95-99 (the industry’s best 5 years ever) airlines earned 3.5 cents on each
dollar of sales:
– The US average for all industries is around 6 cents.
– From 90-99 the industry earned 1 cent per $ of sales.
Carriers typically
fill 72.4% of seats while the
break-even load is 70.4%.

- Utilization is about 3% higher in 2007-08
perhaps due to flight cancellations.
Gas prices are high and
will remain so.

– Downsize airlines
– Merge. Domestic/international
– Alternate transportation means
» High speed train
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Matching supply to demand when supply is fixed

Examples of fixed supply:
–
–
–
–
–

Travel industries (fixed number of seats, rooms, cars, etc).
Advertising time (limited number of time slots).
Telecommunications bandwidth.
Size of the MBA program.
Doctor’s availability for appointments.
Revenue management is a solution:
– If adjusting supply is impossible – adjust the demand!
– Segment customers into
» High willingness to pay
» Low willingness to pay.
– Limit the number of tickets sold at a low price, i.e., control the average price
by changing the mix of customers.
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Environments suitable for revenue management






The same unit of capacity (e.g., airline seat) can be used to deliver
services to different customer segments (e.g., business and leisure
customers) at different prices.
High gross margins (so the variable cost of additional sales is low).
Perishable capacity (it cannot be stored) and limited capacity (all
possible customers cannot always be served).
Capacity is sold in advance of demand: Costly adjustment of sold
capacity.
There is an opportunity to segment customers (so that different prices
can be charged) and different segments are willing to pay different
prices.
It is not illegal or morally irresponsible to discriminate the customers.
 Is Revenue management for incoming MBA class possible?
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Revenue Management:
Booking limits and protection levels
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The Park Hyatt Philadelphia

118 King/Queen rooms.

Hyatt offers a rL= $159 (low fare) discount fare for a
mid-week stay, targeting leisure travelers.

Regular fare is rH= $225 (high fare) targeting
business travelers.

Demand for low fare rooms is abundant.

Let D be uncertain demand for high fare rooms.
– Suppose D has Poisson distribution with mean 27.3.


Assume most of the high fare (business) demand
occurs only within a few days of the actual stay.
Objective: Maximize expected revenues by
controlling the number of low fare rooms sold.
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Yield management decisions




1.
The booking limit is the number of rooms to sell in a fare class or lower.
The protection level is the number of rooms you reserve for a fare class or higher.
Let Q be the protection level for the high fare class. Q is in effect while selling
low fare tickets.
Since there are only two fare classes, the booking limit on the low fare class is
118 – Q:
–
You will sell no more than 118-Q low fare tickets because you are protecting (or
reserving) Q seats for high fare passengers.
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Sell no more than the low
fare booking limit, 118 - Q
118
Q seats protected for
high fare passengers
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The connection to the newsvendor


A single decision is made before uncertain demand is realized.
There is an overage cost:
– D: Demand for high fare class; Q: Protection level for high fare class
– If D < Q then you protected too many rooms (you over protected) ...
– … so some rooms are empty which could have been sold to a low fare
traveler.

There is an underage cost:
– If D > Q then you protected too few rooms (you under protected) …
– … so some rooms could have been sold at the high fare instead of the low
fare.

Choose Q to balance the overage and underage costs.
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Optimal protection level

Overage cost:
– If D < Q we protected too many rooms and earn nothing on Q - D rooms.
– We could have sold those empty rooms at the low fare, so Co = rL.

Underage cost:
– If D > Q we protected too few rooms.
– D – Q rooms could have been sold at the high fare but were sold instead at the
low fare, so Cu = rH – rL
Cu
rH  rL
*
F
(
Q
)


 Optimal high fare protection level:
Co  Cu
rH


Optimal low fare booking limit = 118 – Q*
Choosing the optimal high fare protection level is a Newsvendor
problem with properly chosen underage and overage costs.
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Hyatt example

Critical ratio:

Poisson distribution with mean 27.3
Cu
r  r 225  159 66
 h l 

 0.2933
Co  Cu
rh
225
225
Q
10
11
12
13
14
15
16
17
18
19
F (Q )
0.0001
0.0004
0.0009
0.0019
0.0039
0.0077
0.0140
0.0242
0.0396
0.0618
L (Q )
17.30
16.30
15.30
14.30
13.30
12.31
11.31
10.33
9.35
8.39
Q
20
21
22
23
24
25
26
27
28
29
F (Q ) L (Q )
0.0920 7.45
0.1314 6.55
0.1802 5.68
0.2381 4.86
0.3040 4.10
0.3760 3.40
0.4516 2.78
0.5280 2.23
0.6025 1.76
0.6726 1.36
Q
30
31
32
33
34
35
36
37
38
39
F (Q ) L (Q )
0.7365 1.03
0.7927 0.77
0.8406 0.56
0.8803 0.40
0.9121 0.28
0.9370 0.19
0.9558 0.13
0.9697 0.09
0.9797 0.06
0.9867 0.04
– You can also use poisson(Q,mean=27.3,1)=0.29 Excel function to solve for Q.
Answer: 24 rooms should be protected for high fare travelers.
Similarly, a booking limit of 118-24 = 94 rooms should be applied
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to low fare reservations.
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
Related performance measure calculations

How many high-fare travelers will be refused a reservation?
– Expected lost sales = 4.10, From Table 13.2

How many high-fare travelers will be accommodated?
– Expected sales = Expected demand - Lost sales = 27.3 - 4.1 = 23.2

How many seats will remain empty?
– Expected left over inventory = Q - Expected sales = 24 - 23.2 = 0.8.

What is the expected revenue assuming all low fare rooms are sold
– $225 x Exp. Sales(=23.2) + $159 x Booking limit(=118-24=94) = $20,166.
– Without yield management worst case scenario is selling all the rooms at the low
fare and making $159 x 118 = $18,762.
– With revenue management revenue increases by (20,166-18,762)/18,762=7.5%
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Example: Bulk Contracts



Most consumers of production, warehousing, and transportation
assets face the problem of constructing a portfolio of long-term
bulk contracts and short-term spot market contracts
– Long-term contracts for low cost
– Short-term contracts for flexibility
The basic decision is the size of the bulk contract
The fundamental trade-off is between wasting a portion of the lowcost bulk contract and paying more for the asset on the spot market
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Example: Bulk Contracts
For the simple case where the spot market price is known but
demand is uncertain, a formula can be used
cB = bulk rate
cS = spot market price
Q* = optimal amount of the asset to be purchased in bulk
Overage cost of buying too much in bulk: cB.
Underage cost of buying too little in bulk: cS- cB.
F (Q * ) 
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Cu
c  cB
 S
C o  Cu
cS
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Numerical Example for Bulk Contracts: Buying
transportation capacity to bring goods from China
Bulk contract cost = cB = $10,000 per million units
Spot market cost = cS = $12,500 per million units
Normal monthly Demand for transportation:
m = 10 million units, s = 4 million units
Q* = Norminv((12.5-10/12.5),10,4) million units
The manufacturer should sign a long-term bulk contract
for Q* million units per month and purchase any
transportation capacity beyond that on the spot market.
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Revenue Management:
Overbooking
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Ugly reality: cancellations and no-shows



Approximately 50% of reservations get cancelled at some point in
time.
In many cases (car rentals, hotels, full fare airline passengers) there
is no penalty for cancellations.
Problem:
– the company may fail to fill the seat (room, car) if the passenger cancels at
the very last minute or does not show up.

Solution:
– sell more seats (rooms, cars) than capacity.

Danger:
– some customers may have to be denied a seat even though they have a
confirmed reservation.
– Passengers who get bumped off overbooked domestic flights to receive
» Up-to $400 if arrive <= 2 hours after their original arrival time
» Up-to $800 if arrive >= 2 hours after their original arrival time
– According to April 16, 2008 decision of the Transportation Department
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Hyatt’s Problem
The forecast for the number of customers that do not show up
( X ) is Poisson with mean 8.5.
 The cost of denying a room to the customer with a confirmed
reservation is $350 in ill-will (loss of goodwill) and penalties.
 How many rooms (y) should be overbooked (sold in excess of
capacity)?


Newsvendor setup:
– Single decision when the number of no-shows in uncertain.
– Insufficient overbooking: Overbooking demand=X >y=Overbooked
capacity.
– Excessive overbooking: Overbooking demand=X <y=Overbooked
capacity.
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Overbooking solution

Underage cost when insufficient overbooking
– if X >y then we could have sold X-y more rooms…
– … to be conservative, we could have sold those rooms at the low fare, Cu = rL.

Overage cost when excessive overbooking
– if X <y then we bumped y-X customers …
– … and incur an overage cost Co = $350 on each bumped customer.

Optimal overbooking level: F (Y ) 

Critical ratio:
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Cu
.
Co  Cu
Cu
159

 0.3124
Cu  Co 350  159
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Optimal overbooking level

Poisson distribution with mean 8.5
Q
0
1
2
3
4
5
6
7
8
9



F (Q )
0.0002
0.0019
0.0093
0.0301
0.0744
0.1496
0.2562
0.3856
0.5231
0.6530
Q
10
11
12
13
14
15
16
17
18
19
F (Q )
0.7634
0.8487
0.9091
0.9486
0.9726
0.9862
0.9934
0.9970
0.9987
0.9995
Optimal number of overbooked rooms is y=7.
Hyatt should allow up to 118+7 reservations.
There is about F(6)=25.62% chance that Hyatt will find itself
turning down travelers with reservations.
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Revenue Management:
Complications
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Revenue management challenges …

Demand forecasting.
– Wealth of information from reservation systems but there is seasonality,
special events, changing fares and truncation of demand data.


Dynamic decisions.
Variable capacity:
– Different aircrafts, ability to move rental cars around.


Group reservations; Cargo overbooking.
How to construct good “fences” to differentiate among customers?
–
–
–
–

One-way vs round-trip tickets.
Saturday-night stay requirement.
Non-refundability.
Advanced purchase requirements.
Multi-leg passengers/multi-day reservations for cars and hotels:
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A solution to the multi-leg customer: buckets
Heathrow
O’Hare
JFK



With segment control there are only three
booking limits for the O’Hare-JFK leg, one
for each fare class.
But an O’Hare-Heathrow customer may be
more valuable, so you could have six
booking limits, one for each fare-itinerary
combination.
But that leads to many booking limits, so
group similar fare-itineraries into buckets:
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Fare class
Y
M
Q
O'Hare to
JFK
$724
$475
$275
Bucket Itinerary
0
1
2
3
O'Hare to Heathrow
O'Hare to Heathrow
O'Hare to JFK
O'Hare to Heathrow
O'Hare to JFK
O'Hare to JFK
O'Hare to
Heathrow
$1,610
$829
$525
Fare class
Y
M
Y
Q
M
Q
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Another solution to multi-legs: bid prices
Heathrow
Fare class
Y
M
Q
O’Hare
JFK
Bid price


O'Hare to
JFK
$724
$475
$275
O'Hare to JFK
$290
O'Hare to
Heathrow
$1,610
$829
$525
JFK to Heathrow
$170
Assign a bid price to each segment:
A fare is accepted if it exceeds the sum of the bid prices on
the segments it uses:
– For example, an O’Hare-JFK fare is accepted if it exceeds $290
– A O’Hare-Heathrow fare is accepted if it exceeds $290+$170 = $460

The trick is to choose good bid-prices.
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Summary


Yield management (with protection levels) and overbooking give
demand flexibility where supply flexibility is not possible.
The Newsvendor model can be used:
– Single decision in the face of uncertainty.
– Underage and overage costs.

These are powerful tools to improve revenue:
– American Airlines estimated a benefit of $1.5B over 3 years.
– National Car Rental faced liquidation in 1993 but improved via yield
management techniques.
– Delta Airlines credits yield management with $300M in additional revenue
annually (about 2% of year 2000 revenue.)
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Summary of the Course
 Modules
–
–
–
–
–
–

1. Flow analysis
2. Formulations
3. Queues
4. Quality
5. Inventory
6. Revenue management
The efficient transformation of inputs into outputs
to suitably satisfy customers.
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The End
My teaching is over
Your learning is forever
Towards better
Do not give up ever
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