Copyright Robert L. Phillips. 2006. All Rights Reserved. Copyright Robert L. Phillips 2006. All...

Copyright Robert L. Phillips 2006. All Rights ReservedCopyright Robert L. Phillips. 2006. All Rights Reserved.

A Decision Analytic Approach to Revenue Management

Robert L. Phillips

Nomis SolutionsStanford University

March 13, 2006

Property of Nomis Solutions Inc. - Confidential MaterialCopyright Robert L. Phillips. 2006. All Rights Reserved.

Agenda

• Introduction to Revenue Management

• Elements of Revenue Management• Capacity Control• Overbooking• Network Management

• An RM System Example


What is Revenue Management?

The allocation of fixed capacity to different customer classes with different fares in order to maximize profitability.

A special case of Pricing and Revenue Optimization, applicable in situations with:• Fixed and perishable capacity (and therefore opportunity costs)• Advanced bookings• Fixed fare classes• Uncertain demand and customer behavior (no-show, cancellation)


Basic Revenue Management Business Assumptions

• Fixed, immediately perishable capacity -- airline seat, hotel room night, gas pipeline capacity, etc.

• Units of capacity are identical - “a seat is a seat”

• Reservations (bookings) for future capacity accepted prior to its use

• Marginal costs per unit sale are fixed and small relative to price per unit

• A finite number of fixed prices are set ahead of time.

• The seller can control the number of units that he will provide for sale at each price at each time before departure.

• The seller has opportunities to change availabilities at intervals prior to departure based on bookings received.

• The goal of the seller is to control availability by fare class in each time before departure in order to maximize revenue (= contribution)

This is the “basic revenue management” business problem. Each of the assumptions can be relaxed to create a variation.


History of Revenue (Yield) Management

• Early 60’s - Overbooking Analysis, News-vendor Problem

• Late 70’s - Airline deregulation

• 1981 - Rise of Peoples Express (Discount Airline)

• 1982 - Adoption of Controlled Super-Saver fares (American Airlines)

• 1983 - 1990 Development of first leg-based Airline Revenue Management Systems by major airlines. Development of Commercial Revenue Management Systems (Aeronomics, DFI, PROS, SABRE)

• 1985 - 1990 Development of early hotel (Marriott, Hyatt) Systems. Commercial hotel RM systems (Aeronomics, DFI, OPUS)

• 1989 First O&D Airline Revenue Management System (SAS)

• 1990 First Rental Car System (Hertz)

• 1990’s E-Commerce, distribution control, lifetime customer value issues

• 1995 - today. Pricing and Revenue Optimization Systems (Talus, Manugistics, Khimetrics, ProfitLogic, …)


Revenue Management Industries

Industry Capacity Unit

Capacity Types

Capacity Fixed?

Network

Passenger Airline Seat 1 - 3 Largely Origin and Destination

Hotel Room Night 1 - 5 Yes Length of Stay Rental Car Rental Day 3 - 10 No Length of Rental Broadcasting Time unit many Yes Commerical Block Events Seat 1 - 10 Yes None Cruise Line Berth 1 - 15 Yes None Concert/Sporting Event

Seat 1 - 10 Yes None

Air Freight Weight, Volume 1 - 3 Largely Origin and Destination


The Basic Revenue Management Question

A supplier (airline, hotel, made-to-order manufacturer) takes reservation for some stock of fixed capacity.

A customer is “on the phone” requesting a particular fare. Do we say “yes” and sell him at the requested fare or do we say “no”?

Why we would say yes: • To get his revenue

Why we might say no: • Because we don't have sufficient capacity to accommodate him• Because he might displace a future, more profitable booking


Revenue Management Elements

• Capacity Control: How to allocate limited capacity to different classes of customer?

• Overbooking: How many total bookings to accept?

• Network Management: How to manage bookings across a complex service network?

• Additional Topics: Customer value management; group management; integration with pricing, scheduling, etc

We will discuss capacity control, overbooking, and network management.


Agenda





Basic Airline Segmentation

Leisure Travelers

•Price Sensitive•Book Early•Schedule Insensitive

fd = Discount Fare

Business Travelers

•Price Insensitive•Book Later•Schedule Sensitive

ff = Full fare


Two-Class Capacity Management Problem

• Fixed capacity C

• Two fare classes (full-fare and discount) with fares ff > fd > 0. Marginal costs are 0.

• Discount fares book first. All seats not sold at discount are available for sale at full fare.

• No cancellations or no-shows.

• The demands at each fare are random variables, dd and df..

• Ff (x) = Probability that df < x.

How many seats should we save for late-booking full-fare customers?


Capacity Control Problem Tradeoffs

• Cannibalization - Seats were sold at fd, but some full-fare customers were turned away due to lack of seats. Cost = fd - ff for each full-fare customer turned away.

• Spoilage - Discount passengers were turned away but the plane left with empty seats. Cost = fd for each “spoiled” seat.

How do we set b -- the first period booking limit -- to optimally balance cannibalization and spoilage and maximize expected total revenue?


Capacity Control Problem: Marginal Analysis

RelativeImpact

Hold b Constant

0

fd - ff

fd

0

b b+1

dd < b

dd > b

df > C - b

df < C - b

1-Fd(b)

1- Ff(C-b)

Ff(C-b)

Fd(b)


Optimality Condition for Two-Class Problem

The optimal booking limit b* solves Ff(C-b*) = 1 - fd/ff . This is known as Littlewood’s Rule.

Littlewood's Rule is a simple variation on the standard critical fractile solution to the newsvendor problem.


Two ways to implement Littlewood's rule

• Set booking limit b* and hold

• Use Littlewood's rule as the basis a dynamic decision rule:

Accept discount bookings as long as fd > [1-Ff(C-xd)]ff, where xd is the number of discount bookings already accepted.


0

1

0 10

Accepted Bookings

$

Interpreting Littlewood's Rule

Acceptance Criterion: fd > [1-Ff(C-xd)]ff

This is expected opportunity cost!

fd

ExpectedOpportunity Cost


$9,000

$10,000

$11,000

$12,000

$13,000

$14,000

$15,000

100 105 110 115 120

Booking Limit (b)

Re

ve

nu

e

Total Revenue

Expected DBCost

ExpectedNet Revenue

Net revenue as a function of booking limit


TimePeriod: n n-1 3 2 1

…

Fare:

FirstBooking Departure

fn fn-1f3 f2 f1

Bookings: xn x3 x2 x1xn-1

Low Fare Bookings High Fare Bookings

Standard Structure for Multi-Class Problem

The basic assumption -- bookings occur in order of fare, that is: low to high.


Nesting -- a Three-Class Example

x1 = seats reserved for 3

x2 = seats reserved for 2 and 3

b2 = Booking Limit for 2

b1 = BookingLimit for 1

We assume three classes 1,2, and 3, booking in order,

with f1 < f 2 < f3

Aircraft Seating Capacity


Relative Impact

Hold b3 Constant

0

p3 – p1

p3

0

b3 b3+1

d3 < b3

dd > b3

Displace Class 1 Booking

1-F3(b3)

No Displacement

F3(b3)

Displace Class 2 Booking p3 – p2

q1

q2

1-q1-q2

Capacity Control with three fare classes


Solving the multi-class problem

• In general, the capacity allocation problem with more than two classes does not have a closed-form solution.

• Two solution alternatives:• Solve by dynamic programming -- generally too computationally intensive.• EMSR heuristics -- formulate as a series of two-class problems and approximate

the solution.





Agenda


Overbooking

Airlines and other industries historically allowed passengers to cancel or no-show without penalty. Airlines book more passengers than their capacity in order 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.


Denied Boarding Cost

Consists of four elements:

1. Provision Cost of meals or lodging provided

2. Reaccom Cost of putting a bumped passenger on another flight

3. Direct Cost of direct compensation to the passenger -- usually a discount certificate for future travel

4. Ill-will Cost for involuntary denied boarding.

Voluntary denied boardings have a higher cost than involuntary denied boardings.


Denied Boarding Rates

1993 1997 2000

Voluntary 15 21 20

Involuntary 1 1 1

Total 16 22 21

Denied Boarding Rates per 100,000 Boardings

Source: US DOT. Large US domestic Carriers


Marginal Analysis: Overbooking

D < b

0

f-d

f

0

s does not increase

s s+1

(s|b) > C

(s|b) < C

b b+1

RelativeImpact

D > b

F(b)p

(1-p)


Overbooking Problem Solution

We want to find the smallest b* such that:

F(b*)p[Pr{(s|b*)>C}(f-d) + Pr{(s|b*)<C}f] = 0

or:

Pr{(s|b*) > C}(f-d) +[1- Pr{(s|b*) > C}]f = 0

Pr{(s|b*) > C} = f/d


Overbooking Revenue

$8,000

$9,000

$10,000

$11,000

90 100 110 120

Booking Limit

Re

ve

nu

e

C b*

PassengerRevenue

OverbookingCost

NetRevenue


Departure

Capacity

Time

Bookings

Booking Limit

Bookings

No-show “Pad”

A B

Overbooking Dynamics





Agenda


...Monday Tuesday Wednesday Thursday FridayResources:

Monday 3-Night Stay

Tuesday 2-Night Stay

Wednesday 3-Night Stay

Products:

...

Hotel Network

Friday 1-Night


July 2002

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

9,000

Fina

l Boo

king

s

Riders Aboard Total Seats

SF

O

SA

C

RN

O

SL

C

GS

C

DE

N

OM

A

CH

I

Passenger Train Capacity and Load


Hotel Example

Su M T W Th F Sa

Capacity

Unc

onst

rain

ed

Occ

upan

cy

Day of Week


San Francisco(SFO)

Denver(DIA)

St. Louis(STL)

Flight 1 Flight 2

Why the Problem is Hard

SFO – STL Fare = $400SFO – DIA Fare = $200DIA – STL Fare = $250

Which passengers we want to accept depends upon expected demands for all products. Sometimes we prefer SFO-STL pax, sometimes we prefer SFO-DIA or DIA-STL pax.


San Francisco(SFO)

Denver(DIA)

St. Louis(STL)

Flight 1 Flight 2

When the Problem Really gets Interesting...

Market Y-Class M-Class B-Class G-Class

SFO-STL $600 $400 $300 $250

SFO-DIA $280 $200 $150 $140

DIA-STL $350 $250 $180 $110


San Francisco(SFO)

Denver(DIA)

St. Louis(STL)

Flight 1 Flight 2

Bid Pricing

Market Y-Class M-Class B-Class G-Class

SFO-STL $600 $400 $350 $250

SFO-DIA $280 $200 $150 $140

DIA-STL $350 $250 $180 $110

BP = $190 BP = $230

Set a bid price equal to the opportunity cost (λ) on each leg.


Mon Tue Wed Thur Fri Sat Sun

31

d=85

b=$84.34

1

d=93

b=$92.07

2

d=112

b=$153.12

3

d=108

b=$112.34

4

d=99

b=$92.57

5

d=65

b=$54.30

6

d=80

b=$62.33

7

d=91

b=$88.47

8

d=102

b=$122.00

9

d=135

b=$172.15

10

d=120

b=$142.34

11

d=92

b=$95.67

12

d=53

b=$42.34

13

d=44

b=32.34

14

d=67

b=$54.37

15

d=85

b=$72.48

16

d=110

b=$122.47

17

d=97

b=$99.97

18

d=93

b=$92.34

19

d=72

b=$55.18

20

d=66

b=$54.54

21

d=86

b=$89.11

22

d=104

b=$130.02

23

d=157

b=$199.93

24

d=140

b=$178.25

25

d=122

b=$122.20

26

d=95

b=100.69

27

d=85

b=$85.18

28

d=84

b=$84.33

29

d=92

b=$93.44

30

d=114

b=$155.67

31

d=100

b=$101.01

1

d=82

b=$78.77

2

d=60

b=$53.92

3

d=75

b=$62.74

Hotel Bid Price Calendar


Agenda





Sporting Event Revenue Management

A classic Revenue Management opportunity:

• Fixed, immediately perishable inventory

• Seating sections in stadiums are similar to cabins in airplanes

• Section prices are fixed prior to season starting

• Season tickets are offered first; all other seats are free-sell

• Bookings come in over time…from a year out to the day of the game

• Most baseball teams have a range of discounts that apply to a seating sections - market segments

• Jnr, Snr, 4H, buy-one-get-one-free


EventRM – Challenges

• Industry resistant to change -

• Very risk averse -- like quick sell-outs (especially concerts)

• Fear public perception of venue trying to “gouge” the fans with higher prices -- want to increase revenue without increasing price

• Bookings do not follow traditional industry approach of lowest value books first, highest value books last• value of ticket is not correlated to time of booking

• Availability denials not currently captured

• Data can be sparse


EventRM – What it Does

• Forecasts demand for each market segment • historical data enables market segmentation

• Maximizes expected revenue from forecasted remaining demand into remaining capacity

• Recommends which market segments to sell to• venue sets rate structure for market segments• event manager determines which market segments are always open• event manager has final say on which segments to keep open for

sale or to close

• DOES NOT recommend changes in price


Event Overview


Pricing Screen


Booking Pace


Demand Forecast


Optimization Parameters


Re-Optimize


Optimization


Availability Controls


Summary

• Revenue management is the science of setting availabilities for multiple fare classes in the case in which capacity is constrained and perishable.

• The decision analytic approach gives lots of insight and some useable answers to basic revenue management problems without lots of annoying multiple integrals!

• Many dynamic revenue management implementations involve calculating the opportunity cost of a unit of remaining capacity and accepting only those requests whose fare exceeds the opportunity cost.

Copyright Robert L. Phillips. 2006. All Rights Reserved. Copyright Robert L. Phillips 2006. All...

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