FLIGHT TRANSPORTATION LABORATORY
REPORT R87-1
RESERVATIONS FORECASTING IN
AIRLINE YIELD MANAGEMENT
JOAO SA
RESERVATIONS FORECASTING
IN AIRLINE YIELD MANAGEMENT
ABSTRACT
This report shows the application of Regression Analysis
in reservations forecasting in airline yield management.
The first three chapters highlight the need for yield
management and the automation of seat inventory control. The
seat inventory control problem is related to the determination
of an optimal allocation of seats among the various fare
classes being offered in a flight so as to maximize revenues.
In order to determine such optimal seat allocation, forecasts
of final bookings need to be made.
Forecasting alternatives are presented in this
An example of application of Time Series Analysis is
an alternative in providing such forecasts. Results
via Time Series Analysis were not encouraging enough
providing acceptable estimates.
report.
given as
obtained
in
Regression Analysis is also presented as a forecasting
tool. Although regression models were developed for each market,
a generalized model structure was thought to be preferable
in view of the reduction of modeling efforts, data handling
and model specification, that are needed for forecasting final
bookings for all markets/flights/classes. A general structure
model is presented in this thesis as the result of the search
for structural behavior across markets and flights.
Regression Analysis results are presented for a set of
five citypairs, one flight in each directional market, i.e.
ten flights in total. These results evidenced that a general
structure model via regression analysis can indeed be used in
the forecasting module of an automated seat inventory control
system, and thus provide better estimates of final bookings
when compared to Time Series Analysis or historical averages.
CONTENTS
I
Introduction ........................................
2
The Need for Yield Management .......................
2.1
The Airline Industry Before Deregulation ........
2.2
The Airline Industry After Deregulation .........
2.3 The Need for Yield Management ...................
3
The Automation of Seat Inven tory Control ............. 14
3.1 Seat Inventory Control . ..
4
.........
.....
. 14
3.2
Seat Allocation Models - An Overview ............. 17
3.3
Reservations Forecasting Module .................. 23
Exploratory Data Analysis ........................... 28
4.1 Data Sample Description .........................
28
4.2 Distribution Analysis ........................... 48
5 Reservations Forecasting .............................. 71
5.1 Alternatives in Forecasting .....................
73
5.2 Time Series Analysis ............................ 75
5.3 Regression Analysis ............................. 83
..........
6 Conclusion.................... .........
....109
6.1 Summary ........................... ...............
109
6.2 Topics for Further Research ....... ...............
114
Bibliography
..
.
.
.
.
.
.
.
.
.
-
.
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-
-
-
--
-
-
.1
6
LIST OF FIGURES
Figure
4.01
Distribution Plot
, M-class Flight F1 Market A/B
..
51
4.02
Distribution Plot
, M-class Flight F2 Market B/A
..
53
4.03
Distribution Plot , M-class Flight F4 Market C/D
4.04
Distribution Plot
M-class Flight F3 Market D/C
4.05
Distribution Plot
M-class Flight F1 Market E/F
59
4.06
Distribution Plot
M-class Flight F2 Market F/E
61
4.07
Distribution Plot
M-class Flight F1 Market G/H
..
63
4.08
Distribution Plot
M-class Flight F2 Market H/G
..
65
4.09
Distribution Plot
Y-class Flight F1 Market I/J
67
4.10
Distribution Plot
, Y-class Flight F1 Market J/I
69
55
..
57
LIST OF TABLES
Table
4.01
Data Sample
: General Characteristics
4.02
Data Sample
: Markets & Flights
4.03
Reservations Load Factor on Boarding Day ..........
35
4.04
Reservations on Boarding Day, Totals
37
4.05
Reservations on Boarding Day, By Class
39
4.06
Reservations on Boarding Day, By Class,
4.07
Authorized Booking Levels
4.08
Bookout Analysis .............
5.01
Time Series Analysis ARIMA(3,0 ,2)
.............
....
(observations)
By Month
....
30
32
..
41
.....
42
45
Reservations on Boarding Day
M-class, Flight F1, Market A/B
5.02
Time Series Analysis ARIMA(0,1
78
Seasonal
Reservations on Boarding Day
M-class, Flight F1, Market A/B
5.03
5.05
Flight
F 1 .....
Regression Analysis
Summary
Market B/A
F 2 ........................... . 95
5.08
... .. .... .. ...... .. .. .. 93
Summary
, Flight F4
..............
97
Regression Analysis Summary
Market D/C
5.07
, Flight
Regression Analysis
Market C/D
5.06
80
Regression Analysis Summary
Market A/B
5.04
....................
, Flight
F 3 ............................
Regression Analysis
Summary
Market E/F
, Flight
F1 .....
Regression Analysis
Summary
Market F/E
, Flight F2
. . ............
.......
.......................
.
98
100
0..
..
101
5.09
Regression Analysis
Summary
Market G/H , Flight F1 .....
5.10
5.11
5.12
Regression Analysis
Summary
Market H/G , Flight
F2
Regression Analysis
Summary
Market I/J , Flight
F1 .....
Regression Analysis
Summary
.....
.......................
103
.......................
104
Market J/I , Flight F1 .......
..
.. ..................
106
107
.........
6 Conclusion
...........................................
6.1 Summary ... -
109
. ....................................
109
6.2 Topics For Further Research ..................... 114
Bilbiography ........................................... 116
CHAPTER ONE
INTRODUCTION
The
Airline
Industry,
since
its
very
inception, has experienced many changes that have constantly
challenged
improve
it
and
management
contributed to intensify operations and
of
the
today's
diversified
air
transportation markets.
The introduction of jet aircraft in commercial
operation
required airlines to quickly adapt and respond to
the "new equipment". Markets that were served with over than
a day's flight could then be reached within
The
the
same
industry experienced rapid growth in passenger traffic.
The combination of new equipment and traffic growth
competition
,
which
made
some
airlines
some
other
airlines
more
standpoints,
that could not cope with these
changes experienced financial problems,
out
favored
operate
efficiently both in operational and managerial
while
day.
and eventually went
of business.
Technological
scenario
of
aircraft
guidance
innovations
advances
in
systems,
the
new
have
airline
aircraft
dominated
industry.
with
the
New
more fuel
efficient engines, and new navigational aids can be cited as
examples of technological innovations that have,
one way or
the other, changed the Airline Industry.
Today, the U.S. Airline Industry experiences a
rather different source of innovation.
Managerial
deregulation of the
industry
scenario
innovations
Airline
in
Industry
the last years.
caused
have
just
the
beginning.
the
dominated
the
The "fare war" that
immediately followed the Airline Deregulation Act
was
by
in
1978,
Price competition among airlines
became a vivid reality.
Price
price-availability
competition
competition
has
.
quickly
evolved
to
Seats allocated to lower
fares are capacity controlled,and there are
limitations
or
restrictions associated to low fare seats.
The airline product, a seat in a flight from A
to
B,
has
now two dimensions
emergence of a vast set of airline
fare and restriction.
products
has
The
generated
the
need of a sophisticated decision support system devoted
to
the
development/management
restriction policies.
of
price-availability-
Such management decisions are central
to the permanence of an airline in the marketplace, and they
have changed the airline industry.
CHAPTER TWO
THE NEED FOR YIELD MANAGEMENT
Airline Industry
The deregulation of the U.S.
launched
into
industry
the
a new era.
The change from a
regulated to a "free" market caused radical modifications in
the airline industry.
highlight
the
The objective of this chapter
different
that
environments
subject to in these two periods.
is
airlines were
A brief comparison between
these periods is presented in the next two sections of
chapter.
to
this
The third section highlights the need for an Yield
Management System.
2.1 THE AIRLINE INDUSTRY BEFORE DEREGULATION
deregulation,
Before
controlled
by
Board-CAB.
The
a
government
decision
of
body:
either
existing services in any given market,
approval of the CAB.
airlines
US
the
were
Civil Aeronautics
flying
or
expanding
was subjected to the
Fares were calculated
by
using
the
mileage-based
CAB.
Standard Industry Fare Level,
Fare levels
and
structure
were,
adopted by the
therefore,
Markets were regulated and controlled.
fixed.
Marketing decisions
of airlines were dependent of the CAB.
Fare discounting was, nevertheless,
in
the
U.S.
Airline
Industry
before
practiced
deregulation.
concept at that time was that the revenue of a flight
be
increased
by
offering
the
unsold
The
could
seats to a new and
different segment of passengers.
This new market segment consisted of some
passengers
operating
that
would only travel at a discount fare.
cost
associated
to
considered as being minimal,
ticketing,
costs
would
segment"
The
was
since the full fare passengers
would already have absorbed most
Incremental
'this "new
few
of
typically
the
operating
involve
baggage handling and on board meal
costs.
reservations,
service
for
these "additional" passengers.
Few
few passengers.
at
regular
The majority of passengers would still
full
airline's "regular"
market ,
seats were sold at discount fare to these
fares.
fly
Revenue was not diverted from the
passengers
and
with low yield passengers,
a
new
and
was created.
different
Yield is
defined as the revenue per passenger-mile of traffic carried
by an airline.
A limited set of "discount" tickets
available
criteria.
tickets
some
to
passengers
For instance,
with bulk travel,
group basis.
also
pre-determined
senior citizens could buy
a lower price.
at
meeting
was
airline
There were discounts associated
being either on a family basis
or
on
a
Thus, some discount tickets were available for
those who would meet these pre-determined criteria.
A step
practice
eye"
was
flights
then
towards
observed
(i.e.
late
a
more
complex
discounting
with the introduction of "red
night
flight
services).
These
flights/seats at a discount were available to anyone willing
and
able
to
travel
practice differed
passenger
would
at
late hours.
from
the
not
need
existing
to
qualifications (age,organizations)
This new discounting
in
meet/have
,
the
sense
that
pre-determined
nor need to travel
in
"bulk"- (family or group). Anyone could buy a ticket on these
flights .
Seat inventory management was
the
regular
flights
of
an airline.
alternatives (airline product)
not
needed
in
The available set of
available to passengers
was
relatively small :
(1) first and regular coach class seats;
(2) limited possibilities of "discount" tickets in
regular flights;
(3) few special flights at discount fares.
The
management
of flight revenue was a
relatively straightforward task. Once the potential of sales
of full fare passengers was estimated for
the
remaining
passengers.
seats
were
made
Profit maximization
+maximization
of
flight
a
available
was
loads.
No
given
for
strongly
special
low yield
related
passengers.
filling
up
planes
Revenue
with
maximization
as
many
was
revenue
to
attention or
routine was used for controlling the seats sold to
fare
market,
discount
achieved
by
passengers
as
possible. Regular full fare passengers accounted for most of
the revenue.
passengers,
revenue
The remainder or unsold seats were sold to few
at a discount
passengers
revenue optimality
as
fare.
A
flight 'with
as
much
possible was thought to be reaching
For
the
profit
maximizing
airline,
revenue and cost would have to be taken into account,
revenue
maximization
maximization.
a flight
business.
with
does
not
always
lead
to
since
profit
Nevertheless, the dominant criterion was that
high
load
factor
was
the
sign
of
good
2.2
THE AIRLINE INDUSTRY AFTER DEREGULATION
marked the beginning of a new era.
Industry
Airline
The deregulation of the U.S.
With deregulation,
U.S.
airlines were allowed to enter or leave any domestic market,
services.
increase or reduce existing
management
considered
as
was
to
up
the
of
an
airline to fully decide where and
should
be
offered.
staff
when services
It
market
as
profitable
in
decided to offer services only
market
If
B,
market
A
was
not
an airline could
B.
Any
airline
could offer services in market B. No government approval was
needed.
Fares
were
Today,
experienced a real change.
determines
how
much
so the industry
deregulated
also
should
it is
it
the
charge
airline
in
a
who
given
market/class.
As a consequence, new airlines were created and
more airlines started to
in
fly
traditionally
profitable
markets. Unprofitable markets experienced either a reduction
in
the
level
of
service
or
they
were abandoned.
competition was inevitable in busy markets.
Fare
Competition was
increased as result of the "free market" era.
The marketplace, formerly regulated and subject
to
limitations,
gave
place
to
a
"free"
and
strongly
competitive market.
With the freedom to enter or leave
market,
started
airlines
to
increase
any
competition
in
profitable markets,
by offering more seats/flights at lower
and
The
lower
prices.
advent
of
low-cost/low-yield new
entrant carriers led to a fare war.
A fare war immediately followed the free
market era.
Airlines were forced,
entry
once again, to react and
adapt to a new scenario : stiff competition and
low
fares,
full
fare,
with a high level of diversity.
Passengers
because few
who
alternatives
used
were
to
fly
available,
at
started
taking
advantage of these lower fares. They benefited from the fare
reduction
by
flying
at
more
competitive prices.
increased as a response to low fares.
created
because
consequence,
to fly
of
some
at
New markets were even
extremely
discount
Demand
low
fares
fares.
became
a
As
a
common
practice, and today, only few passengers fly at nominal full
fares.
Established
competitive.
carriers,
and
They
airlines
needed
to
neededIk
compete
to
with
to offer/match some low fares,
also needed to avoid fare diversion,
remain or be
new
entrant
and yet they
which happens
when
a
potential high yield passenger takes advantage of a low fare
or
they needed to maintain,
most importantly,
But,
seat.
even recover profitability.
The creation of a very complex
was
response of the airline management to the fare war
the
challenge.
and low-cost/low-yield carriers
more
structure
fare
fare
low
attract
passengers,
regular/traditional
maintain
to
a
with differential pricing,
services
able
were
airlines
of
set
complex
offering
By
maintain
passengers,
a
competitive image in the market and remain profitable.
attached
Restrictions and limitations were
some
the cheaper the fare
a general rule,
fares
and,
as
the
more
restrictions/limitations
gets,
discriminating
associated
differentiate
an
restrictions,
different
in
passengers
it
has.
offering different fares,
passengers,
to
airline
respect to price,
By
with
can
and pursue
profit maximization.
Evidently,
coexist
time,
levels
with
structure
could
not
the cost structure that was in effect at that
specially for
were
the new fare
old
and
established
airlines.
Cost
no longer compatible with fare/revenue levels.
Low fares must be followed by low costs.
It would have been
impossible to survive in the low fare market without drastic
changes
in the cost structure.
were forced to reduce cost.
As a consequence,
airlines
2.3
THE NEED FOR YIELD MANAGEMENT
Today,
the
in
part
important
every
concept of
"incremental"
passengers
no
single
class/passenger
is
The
apportioning of flight costs.
cost
associated
to
an
lower
fare
Management of flight revenue
longer exists.
became a complex task. The optimal combination of passengers
and fares is now the what airlines aim at. A flight need not
to be at its maximum load factor,
product
seats/fares
but
rather
the
overall
sold needs to be maximized: a "revenue
load factor" maximization problem.
Management decisions related to how many
seats
to sell at what price, became crucial for airlines. From the
complexity
derived from managing such decisions has emerged
the need of Yield Management. An Yield Management System is,
therefore,
airline
to
tool
a decision support
designed
to
help
determine how many seats should be sold,
the price levels.
Finding such answers is
central
an
given
to
the
permanence of the airline in the market place.
The
longer a proxy to
maximization
of
flight revevue.
passenger
infer
the
load
flight
flight
factor
of a flight is no
revenue % performance.
load
has
The
been replaced with
Profit
degree
of
maximization
success
is
now
related
to
the
that an airline achieves in selling the
right number of seats to the right number of passenger so as
to maximize revenue.
while at the
same
time
keeping
the
associated costs down.
The
revenue
maximization
major components: seats and fares.
increased
problem has now two
Average
yields
be
by either increasing price levels or reducing the
proportion
of
categories.
In
seats
sold
in
both cases,
the
lowest
fare
product
the potential of sales in each
and every fare level has to be estimated so as
the
can
to
optimal number of seats to each fare class,
allocate
maximizing
the revenue of a flight.
Pricing and seat inventory
control
represent,
therefore, the core of Yield Management.
"While
pricing
is
component of yield management,
it's
own
revenue
through
clearly
an
important
no one airline can influence
pricing,
without
taking
the
reactions of its competitors into account. Revenue increases
resulting from pricing actions are possible only when all of
the major competitors in a market agree implicitly to follow
a price leader."(1)
Prices are
published
in
airline
guides
and
in
everyone.
An airline can
monitor
always
available to
are
that
systems
reservation
displayed
and
follow
its
competitors price changes.
Seat inventory control, on the other hand, is a
logistical
component
of
yield management that is entirely
under control of each individual airline.
component
that
It is an in-house
only the airline itself knows and controls,
with the exception of some few one-price-only
yield airlines.
As a consequence,
seat
management
inventory
low-cost/low-
airlines do not know the
decisions
of
the
competitor
airlines.
While
pricing
decision of one airline
is
alone,
Through seat inventory control,
of
managing
departure
revenue
basis,
from
which
a
would
not
fully dependent on the
seat/class
allocation
is.
airlines have the potential
be
a
on
flight
far
departure
more
by
difficult to
replicate via pricing.
Today,
is
evident.
marketplace
efficient
the need for an Yield Management System
Airlines
without
Yield
can
it.
no
The
Management
important to an airline.
longer be profitable in the
competition
System
is,
is
strong.
therefore,
An
very
CHAPTER THREE
THE AUTOMATION OF SEAT INVENTORY CONTROL
The seat inventory control problem
to
the
determination
of
an
being
decisions,
offered
such
as
in
related
optimal (revenue maximizing)
allocation of seats on the aircraft among the
classes
is
a
flight.
capacity
various
Other
allocation,
fare
management
equipment
utilization, aircraft routing cannot be dissociated from the
seat
inventory
control
with each other,
problem.
These decisions interact
and as a consequence,
the seat
inventory
control problem has to either use them as input, or interact
with them.
3.1 SEAT INVENTORY CONTROL
A flight leg seat inventory control approach is
On a flight leg basis,
the
aircraft seating capacity is divided among classes with
the
commonly
objective
used in the industry.
of
revenue
maximization
on
that
flight
leg.
maximization over the whole flight
of an airline,
simplicity
because it
maximizes
revenue
the entire
flight
network
leg revenues,
its
makes it very attractive.
a
With
flight
destination of passengers
passengers
and/or
to
lead
Although the flight leg approach might not
flying
true origin and
leg approach,
are not taken
account.
All
the same class are treated equally.
The
deficiency of this approach is
into
that seat allotment
decisions
on a leg basis do not assure revenue maximization
over
the
whole flight.
A
more
coherent
origins and destinations - O&D,
different
classes
for
should
approach
when
a flight.
consider
allocating
seats
to
The O&D approach becomes
complex when one considers the possible
combinations
of
multiple
of
spoke
leg
operations by
flight.
the
The
difficulty.
The
airlines
number
of
increase
has
hub
added
certainly
possible
and
a
further
O&D combinations
can
become unmanageable and, as a consequence, this approach can
hardly be pursued.
In
allocated
to
order
to determine how many seats should
each class on a
future flight
departure,
airline has to have estimates of expected loads in each
every
class,
as
well
With these two parameters
be
the
and
as the associated average revenues.
for each class,
the
airline
can
then
figure
out
the
best
seat/class
allocation
that
maximizes flight revenues.
Expected
loads
have
to
be
transformed
in
expected bookings. Because of large incidence of no-shows in
some markets,
determining
class.
substantial analysis has
the
number
of
seats
to
to
be
devoted
be assigned to each
Overbooking analysis determines the level
bookings
for
a
of
total
flight that will minimize the total of the
costs associated with denied boarding of passengers and
costs
in
the
in
lost
revenues
the
associated with no-shows and
unsold seats.
The estimates of expected loads,
by
flight,
together
by class
and
with estimates of what will happen on
the boarding day, (i.e. no-shows, go-shows, upgrades, etc.
are then used to generate booking thresholds for each class,
on a given flight leg. These limits can then be input in the
reservations system of
monitored.
the
airline
and
bookings
can
be
3.2
SEAT ALLOCATION MODELS - AN OVERVIEW.
The seat inventory control system is a decision
support system
that
provides
system of an airline,
helping
inputs
to
the
the yield management analyst
to determine booking limits or thresholds.
flight
leg
based system,
reservation
In the (case of a
limits are given by class and by
flight leg.
Several alternatives have been proposed as core
routine of a seat inventory control
apart
from
determination
of
system.
overbooking
This
routine,
policies,
intended to determine whether to accept or reject a
are
request
for a seat (reservation) according to the fare paid.
Littlewood
allocation
total
routine,
expected
f2
in
probabilistic
flight
model. In his routine,
fare
[2],
revenues,
1972,
suggested
based,
using
that
a
seat
maximizes
a "marginal seat"
a low-yield passenger paying a lower
should be accepted as long as the expected revenue
from selling all S1 seats to passengers
fare fl is less than f2.
paying
the
higher
That
is
if f2 > f1
,
. P(S1)
take f2 passengers,
where:
fl = higher fare;
f2 = lower fare ;
P(Si) = probability of selling S1 seats at f1
fare.
The aircraft seating capacity
divided in two compartments.
is
case,
simple
(C)
,
in
this
One with S1
seats, calculated with the probability distribution function
(pdf) of fl passengers,
compartment
takes
the
and fares
(f1 and f2).
The
other
that is (C - Si).
remaining seats,
Note that the pdf of f2 was not needed in the seat allotment
decision process.
Mayer [3], in 1976,
suggested a two class seat
allocation model that would utilize dynamic programming (DP)
as
a
framework.
He suggested a simple model to be used to
determine initial seat allotments,
DP-based
model
should
be
used
and that a
multi-period
to modify initial limits,
taking into account bookings already made.
I
The set of assumptions he made in deriving
his
model was:
(1) no cancellations;
(2) total loss of rejected bookings
(no vertical shift );
(3) in each booking period, low fare passengers
make reservations before high fare
passengers;
(4) the demand in each period is independent of
the actual demand in all previous periods.
He
did not benefit
concluded
from
a
that
the initial seat allotment
DP-based
approach.
Littlewood's model to set initial allotment.
a model that permits corrective action
He
suggested
From there on,
(reallotment),
such
as a DP-based one, should be used.
Buhr
[4]
contributed
probabilistic approach in 1982,
model
for
the
a two leg flight ( A to B to C ).
from
allocating
an
marginal
suggesting a seat allotment
based on the expected "residual"
revenue
to
revenue,
additional
His model was
defined
as
the
seat to passenger
flying from A to B as the product of the average fare from A
to B,
times the probability of selling more than x seats in
the A/B market, or :
AB()
= P
AB
(x)
.
R
AB
where,
E (x) = expected residual revenue
AB
P (x) = probability of getting more that x
AB
passengers in the A/B market ; and
= average fare the A/B market.
R
AB
For the two leg flight, the demand for each O&D
market were assumed as independent.
For each of
the
three
markets, expected residual revenues were calculated and seat
allotment decisions were taken based on such revenues,
that
is
E
AC
(x) -
(E (y) + E (y))
BC
AB
|-->min,
where y is the seat capacity allocated to local
passengers.
AB
and
BC
An
extension
to
the
simple
marginal
seat
allotment model, proposed by Belobaba [5],
handles multiple
fare
legs.
classes
and
flight
with
multiple
expected bookings in a fare class i,
the
expected
Given the
revenue
for this class is given by :
E(Ri)
where
= fi
. bi(Si)
fi is the net fare or the yield to the airline from a
passenger
booked
in
class
i,
and
bi
is
the
expected
revenue
for
class
bookings, given a seat allotment Si.
The
expected
marginal
(EMSRi) is defined as the increase in revenue when the
allotment is increased by one seat,
i
seat
i. e. Si+1 seats. EMSRi
is, therefore, calculated with the following expression:
EMSRi = fi . P[ ri > Si ],
where ri is the total reservations made on class i.
Given a natural ranking of fares fl > f2 > f3 >
f4
etc.
,
in
order
to
maximize
flight
revenue,
the
reservation process should be able to discriminate bookings,
giving
revenue.
priority
to
Although the
passengers
assessment
that
of
contribute most with
the
probability
having Si passengers at the fare level fi is made,
of
priority
to
should always be given
leads
to
a
nested
yield
higher
version
passengers.
of authorized booking limits,
higher
where the authorized booking limit for a given
class
with
overlaps
the
This
fare
authorized booking limit for all
subsequent lower fares. For example,
in the case of a three
where fl > f2 > f3, the authorized limit (AU)
class flight,
for each class should be as:
AU1= C
AU2= C-S1
AU3= C-S1-S2
where
= seating capacity of the aircraft;
C
Si = number of seats protected for class 1;
S2 = number of seats protected for class 2;
r1 and r2 represent reservations made in class 1 and 2.
A protection level is calculated for each class
in order to achieve this priority.
a class in the
accepted
minimum
of
reservations
that
are
in that fare class and that must be protected from
lower fare classes.
always
number
The protection level for
In the
above
example,
from f2 and f3 passengers.
protected
S1
seats
Likewise,
are
S2
seats are always protected from f3 passengers. No protection
level
for
f3,
of
course.
Note
that
nothing
prevents
passengers paying higher fare from taking up low fare seats.
In
the example,
reservations,
up to C passengers paying fl fare can make
and up to to (C-Si) for passengers paying f2.
3.3 RESERVATIONS FORECASTING MODULE
Central to any model briefly presented here, is
the
ability
of
knowing
the
fare
and
the
probability
distribution function for each class i, in every market.
Airlines
can
obtain
sampling tickets on a class i,
problems
fare figures by
for a given market.
Several
arise when averaging fares within a class.
each class there is a multitude
often
average
they
are
of
fare
not well structured.
codes,
Within
and
very
It is very common to
observe price overlapping between adjacent fare classes.
The average fare , calculated by class, may not
be representative,
if too many fare codes exists.
Not only
prices vary but also restrictions change.
Another
problem associated with fare averaging
is the pro-rating of fares.
from A to C,
to B to C,
tend
When a passenger buys a
and the service he gets is a one-stop flight A
the apportioning of fares in legs AB and BC will
to drive down the AB and BC average fare calculations.
With the increase of the airline hub-and-spoke
the
ticket
pro-rating problem tends to be widespread.
allocation routine were O&D based,
exist.
this problem
operation
If the seat
would
not
Due
to
this high degree of non-homogeneity it
is really difficult to define what is the "average
and
to
function.
distribution
probability
together
several fare data analysis performed
Fortunately,
thesis show that although there is a high degree
this
with
its
estimate
service"
of non-homogeinity within each fare class, the overall class
pattern,
result tends to exhibit a stable
far
as
average
prices are concerned, especially for higher fare classes.
reason for this result is that within each
The
class there is always a "dominant fare code".
of
fly
passengers
with
majority
The
The
fare code tickets.
dominant
remaining passengers use other fare code tickets (within the
same class) but with different proportions
dominant
each
The
time.
fare code tends to be less predominant as the fare
Therefore,
disperse.
passengers are
For the lower fare class,
gets lower.
the
more
fare aggregation within the same
class should be more meaningful and yield better result than
for lower fare classes, provided there is no radical changes
in fare levels.
forecasting
in
This may result
reservations
for
a
higher
better
ability
in
fares than for lower
ones.
The seat inventory control routine will need
forecast
element
final loads,
that
provides
and (2) updates
on
(1)
such
a
initial estimates of
estimates,
reservation process for a flight is under way.
as
the
These
bookings,
two
are then
routine.
The
reservations
inputs,
used
automated
by
of
the
an
by
limit
class
automated
itself.
There
are
booking
one
booking
by
on
limit
calculates
flight.
limit
reservation
taking reservation as early as
and expected
system
and
providing such thresholds is dependent
system
fare
automated
booking
thresholds,
promptness
namely
The
routine
the
in
reservation
systems that start
year
in
advance.
The
usefulness of generating booking thresholds so early in time
are, of course, questionable. As a general rule, reservation
systems have some form of booking limit introduced
6 weeks before departure.
at least
From there on, booking thresholds
limit the number of seats made available in each
class,
in
every market.
The
Automated
intended
Seat
to
reservation
Inventory
provide
forecasting
Control
the
System
flights.
A
seat
is
should
be
an
primarily
allocation
for
individual
routine will then use
these estimates of expected bookings to calculate
seats
of
dynamic booking limit adjustment
routine with estimates of expected bookings
future
module
allocated/protected
for
how
many
each upper fare
class.
The
involves
initial
first
step
estimates
advance of flight departures.
in
of
reservations
final
forecasting
bookings,
well
in
These estimates are typically
needed
for each future flight,
up to 90 days out,
and are
used to set initial authorized booking limits. Sophisticated
forecasting models are of little use,
error
time
associated
interval.
conservative
and outweighed by the
with the forecast produced for such large
As
a
consequence,
approach
is
thought
a
simplistic
as
being
the
but
most
appropriate and effective.
These initial estimates
later
need
to
be
improved
in the bookings process as more information (data) on
the specific flight for which more
accurate
forecasts
are
needed.
A simple forecasting model is suggested for the
initial estimation of final bookings.
It consists of moving
average process that is sensitive to day of
week
variation
only. That is to say, for instance, that a 8-week average is
used
to
describe
flight (e.g.
or
estimate
flight F1),
final bookings for a given
on a specific day of
week
(e.g.
Monday).
Although
hand
for
future
no
flights
information on actual bookings on
is
ever
used,
nor
additional
adjustments are made for cyclic or seasonal variations other
that on weekly basis, the implicit assumption of this simple
approach
is
that a small sample of final demand for recent
flights will be representative of the demand
for
the
same
flights in the near future.
The
final
step
in
the
development
forecasting module is to improve the estimates
to
come,
averages.
expected
over
those
These new
strictly
estimates
of
of
a
bookings
based on recent historical
are
used
to
re-calculate
revenues ,and again the seat allocation routine is
used to update allotments.
CHAPTER FOUR
EXPLORATORY DATA ANALYSIS
An exploratory data
give
analysis
is
designed
to
the forecaster more insight into the variable (s)he is
trying
to
variations
forecast.
Trends
across markets,
in
daily
booking
levels,
and seasonalities are among the
characteristics the forecaster searches.
are extremely confidential and,
Reservations
very reluctantly,
data
airlines
make them available. The exploratory data analysis presented
in this thesis represents a moment of
which
actual.
and
recent
data
rare
was
opportunity
available.
As
in
a
consequence, extensive data analysis are presented here.
4.1 DATA SAMPLE DESCRIPTION
A sample of five city-pairs
was
selected
for
data statistical analysis and hypothesis testing. The sample
included
short,
a variety of market types and stage lengths
one short-medium,
two
medium
and
one
long
.
One
haul
markets were included in the sample.
One of the medium-haul
markets was a Canadian market.
A total of 28
sample.
sample period.
included
in
the
At least two flights were operating
in
any
for any of the five markets. The sample period
given month,
was from January,
Industry
were
did not operate throughout the whole
flights
Some
flights
1986
through
June,
1986.
The
Airline
no major abnormality during the sample
registered
period. Therefore, it is expected that the data set provides
a normal picture of what happens in the
first
half
of
an
year.
Data
was collected from the actual database of
an existing US airline.
flights
selected.
In
Table 4.01 shows
assigned
to
markets
and
order to maintain confidentiality of
the data presented in this thesis,
were
the
markets
,and
single
single
capital
digit
letters
numbers to
flights. Distances and flight times were rounded.
For instance,
the flight F1 in the A/B
market
departs at 09:00 am. The distance flown is approximately 500
miles,
and
the aircraft type is a B73S.
Additional market
characteristics are also given in Table 4.01.
29
TABLE 4.01
MARKET
DATA SAMPLE
GENERAL CHARACTER IST ICS
FLT
NLMBER
DISTANCE
(MILES)
FLIGHT
TIME
DEPART
TIME
-(HH: MM)
(HH:MM)
AIRCRAFT
TYPE
A/B
Fl
F2
F3
500
1:30
09:00a
01:50p
07: 19p
0735
8/A
F1
F2
F3
500
1:30
10:00a
02 :OOp
06: 15p/08:30p
B735
C/D
F1
F2
F3
F4
300
0:55
08:30a
12:OOn
03 :25p
06:50p
B725
B735
0725
0733
D/C
F1
F2
F3
F4
300
0:55
09: 15a
11:15a
05:10p/06:15
0 9 :30p
8735
B725
0733
0725
E/F
F1
F2
2000
5:00
07:50a
05:00a
0725
F/E
Fl
F2
2000
4:15
10:10a
05: OOp
0725
G/H
F1
F2
1200
2:30
06 :3 5 p/1 2 :2 5
09:45a/09:45
B725
H/G
Fl
F2
1200
2: 30
08: 15a
05: OOp
0725
I/J
F1
F2
F3
750
1:40
11:10a
05: 10p
09:30p
0725
J/I
F1
F2
F3
750
1:40
07:4 0a
01: 4 Op
05: 50p
6725
SOURCE :Official Airline Guide,
North Aamerican Edition,
1986.
MARKET CHARACTERISTICS
Short-medium haul hub feeder
with a minimum oF two daily flights
each way, and with high load factors.
Short-haul hub feeder, very stable
business market, with a minimum of
three daily flights, with consistently
high load factors.
Long-haul hub leg, with high
load factors, with two daily Flights
each way.
Medium-haul leg with an average load
factor arnd a good mi x of traffic.
Two daily flights , each direction.
Medium-hub feed ,with high load factor-,
different fare structure/mix. A
Canadian market, with two daily flights
each direction.
Table 4.02 shows how many days a
operated,
throughout the sample period, on a monthly basis.
Some flights started operation only June, e.g.
the
C/D market.
some
flight
flight was created,
one,
e.g.
flight
ceased
operations.
Within the sample
Sometimes,
departing at the same time as
F2 in the G/H market,
the
a new
old
or the new flight
departed between one and two hours later, e.g.
the D/C markets.
flight F2 in
Some flights operated throughout the whole
sample, e.g. flight F1 in the A/B market.
period
flight
given
flight F3 in
In both cases, the old and the new flights
were considered as the same flight.
DATA SAMPLE
MARKETS & FLIGHTS
TABLE 4.02
MARKET
OBSERVATIONS
FLT
NUMBER
JAN.
FEB.
MAR.
APR.
MAY
JUN.
A/B
F1
F2
F3
31
30
0
28
28
0
31
31
0
30
30
0
31
31
0
30
30
30
B/A
F1
F2
F3
31
0
31
28
0
28
31
0
29
30
0
30
31
0
31
30
30
30
C/D
Fl
F2
F3
F4
30
0
31
31
28
0
28
28
31
0
31
31
30
0
30
30
31
0
31
31
30
30
30
30
D/C
Fl
F2
F3
F4
0
30
31
31
0
28
28
28
0
31
31
31
0
30
30
30
0
31
31
31
30
30
30
30
E/F
F1
F2
31
31
28
28
31
31
30
30
31
31
30
30
F/E
F1
F2
31
31
28
27
31
31
30
30
31
31
30
30
G/H
Fl
F2
26
30
24
27
29
30
26
29
26
31
30
30
H/G
Fl
F2
26
30
24
27
29
30
26
29
27
31
30
30
I/J
Fl
F2
F3
29
31
31
28
28
28
31
31
31
30
0
29
31
0
30
30
30
30
J/1
Ft
F2
F3
31
28
0
28
28
0
31
29
0
30
30
0
31
31
0
30
30
30
The markets in the sample exhibited high levels
of bookings on boarding day.
load
factors
boarding
defined
,
day,
divided
Table 4.03 shows
here as total reservations on the
by
the
seating
aircraft assigned to that flight.
factor will be loosely used
factor,
which
is
passenger cabin,
already
defined.
means
that
with
but rather the
capacity
of
the
From now on the term load
meaning
calculated
not
the
actual
load
departure loads in the
reservations
load
factor
It can be observed that there were months
in which the average load
which
reservations
in
factor
was
greater
than
100%,
the average flights were overbooked.
This is the case of markets A/B, B/A, D/C, E/F, and F/E.
It is interesting to observe,
still
on
Table
4.03 the change in the performance of reservations caused by
the introduction of a new flight in the market.
For the A/B
market, the third flight introduced in June, a night flight,
exhibited a reservations load factor that ranked second.
the
opposite
direction,
market
B/A,
the
third
In
flight
exhibited the highest reservations load factor in the month.
Reservations load factors in the
were bellow average, with
A/B
market.
This
result
other
flights,
in
June,
the exception of flight F1 in the
suggests
that
some
of
demand
generated by the new flight might be the result of diversion
of "regular" passengers from other flights.
The new flights in the C/D and D/C markets,
on
the other hand, exhibited very low load factors, and one may
also
speculate
about
passenger
diversion.
There
overall reduction in load factors in the month of
the
reduction
of
load
factors
seasonality in the market demand
cannot
solely
justify
the
was
a
was an
June.
consequence
If
of a
then
passenger
diversion
observed
reduction
in demand
levels.
For
different.
the
J/I
market,
the
result
was
very
Flight F3 showed a reservations load factor that
ranked second, but the overall market behavior suggests that
reservations demand was indeed increased in the
the
I/J
case,
there
were
three
market.
In
flights from January to
March. When the third flight came back in operation in June,
reservation levels were brought back to normal levels.
TABLE 4.03
,MARKET
RESERVATIONS
LOAD FACTOR ON BOARDING DAY
ALL CLASSES
FLT
NUMBER
AVERAGE LOAD FACTOR
JAN.
FEB
MAR.
APR.
MAY
JUN.
A/B
F1
F2
F3
74
89
0
80
88
0
101
99
0
89
90
0
98
90
0
95
61
71
B/A
F1
F2
F3
73
0
80
84
0
88
97
0
100
84
0
94
85
0
107
54
82
72
C/D
F1
F2
F3
F4
97
0
89
48
96
0
86
48
91
0
85
50
84
0
76
31
84
0
78
41
81
47
57
41
D/C
F1
F2
F3
F4
0
87
84
49
0
89
92
58
0
86
100
65
0
72
81
53
0
78
86
57
37
70
70
66
E/F
F1
F2
77
86
86
97
104
102
60
79
78
89
101
101
F/E
F1
F2
93
68
99
74
111
90
96
61
105
62
114
91
G/H
F1
F2
41
56
39
51
71
80
58
77
70
93
30
87
H/G
F1
F2
49
50
47
51
77
80
65
74
83
95
64
77
I/J
F1
F2
F3
58
66
80
61
76
87
65
72
79
66
0
94
74
0
84
82
49
59
J/I
F1
F2
F3
67
60
0
82
81
0
82
80
0
92
59
0
85
64
0
57
74
63
Seating capacity
(all classes)
B735 -115
8725 -148
B733 -128
Table 4.04 shows
flight on the boarding day.
reservation
averages
for
Reservations were totaled,
a
for
all classes, and then averages were calculated by month. The
result is presented
average
on
table
.
4.04
For
instance,
in January for flight F1 in the C/D market was 144
reservations, for the month of January.
This table presents
the intensity in bookings for each market analyzed.
The
C/D
activity.
June only,
bookings
and
D/C
markets
exhibited
a
high
market.
reservation
In this example, a total of six flights, eight in
one can also observe
did
not
vary
too
that
much
the
from
high
month
exception made only in June,
when flights were
same
also
stability
markets.
the
pattern
is
observed
in
level
to
month,
added.
the
on
The
other
TFABLE 4. 04
MARKET
.
REVERVAT IONS ON BOARD ING DAY
(ALL CLASSES)
AVERAGE TOTAL BOOKI NGS
FLT
NUMBER
JAN.
FEB.
MAR.
APR.
MAY
JUN.
A/B
Fl
F2
F3
85
102
0
92
101
0
116
114
0
102
103
0
113
103
0
109
70
82
B/A
Fl
F2
F3
84
0
92
97
0
101
111
0
115
97
0
108
98
0
123
62
94
83
C/D
Fl
F2
F3
F4
144
0
132
61
142
0
127
61
134
0
126
64
124
0
113
40
124
0
116
52
120
54
85
53
D/C
F1
F2
F3
F4
0
129
108
72
0
132
118
86
0
127
128
96
0
106
104
79
0
115
110
84
43
104
90
97
E/F
Fl
F2
114
128
128
143
154
151
89
117
116
131
150
150
F/E
F1
F2
137
100
146
110
165
133
142
90
155
92
168
134
G/H
F1
F2
60
83
58
75
105
119
86
114
104
137
44
129
H/G
Fl
F2
72
74
70
76
114
119
96
109
123
140
95
114
I/J
F1
F2
F3
86
97
118
91
112
129
96
106
117
97
0
139
110
0
124
121
72
87
J/1
Fl
F2
F3
99
89
0
121
120
0
122
119
0
136
88
0
126
95
0
84
109
93
Table 4.05 shows averages in
a
for
flight
on
the boarding day.
table is to show the contribution of
the
flight
load.
First
class
calculation of percentages,
contribution
the
reservations
The objective of this
different
was
also
classes
in
included in the
and the total coach compartment
is shown on the last column.
The contribution
of the first class is, on the average, less than 5% .
For the business market, the Y contribution in
the flight load would be expected to be a little higher than
the average.
that
It was indeed observed in the E/F &
participation
of
F/E
data
Y class was slightly higher in this
business market.
In the I/J & J/I market,
the contribution of Y
class was the highest. It happens to be the canadian market.
A
large
proportion
this market.
less than 8%,
of non-restricted Y seats were sold in
In the other markets the
in the average.
Y
contribution
The results are as expected.
While the expected typical contribution of Y class
than 10%,
market.
was
is
less
when there is a strong business component in this
Canadian markets usually exhibit different behavior
when compared to US markets.
The
participation
of
Q class observed in the
sample was very high. In the average, excluding the business
and the Canadian market, Q class participation was 42.27% .
TABLE 4.05
REVERVATIONS ON BOARDING DAY
BOOKINGS BY CLASS
( % TOTAL )
MARKET
CLASS
FLT
Y
M
B
Q
TOTAL
COACH
A/B
Fl
F2
F3
7.00
7.33
7.00
22.83
19.67
22.00
24.83
26.50
19.00
42.83
43.33
51.00
97.50
96.83
99.00
B/A
Fl
F2
F3
6.83
5.00
7.83
22.00
27.00
22.67
22.33
16.00
23.33
46.17
50.00
43.50
97.33
98.00
97.33
C/D
Fl
F2
F3
F4
6.00
9.00
4.33
2.17
28.17
24.00
31.67
34.83
24.83
27.00
24.67
19.67
37.83
38.00
36.17
41.33
96.83
98.00
96.83
98.00
D/C
Fl
F2
F3
F4
6.00
5.17
3.50
5.17
24.00
30.67
32.83
23.50
21.00
24.83
23.00
26.33
46.00
36.67
37.83
42.50
97.00
97.33
97.17
97.50
E/F
Fl
F2
15.00
16.33
13.83
11.50
27.33
28.67
36.33
35.83
92.50
92.33
F/E
Fl
F2
16.67
9.50
14.83
13.50
29.17
31.67
32.00
35.17
92.67
89.83
G/H
Fl
F2
5.17
3.83
16.00
17.00
17.17
22.50
57.67
53.17
96.00
96.50
H/G
Fl
F2
4.83
4.33
16.50
18.00
17.17
20.83
58.17
52.67
96.67
95.83
I/J
Fl
F2
F3
35.33
35.25
.26.17
33.00
28.00
18.00
8.50
10.50
19.50
18.17
21.25
32.00
95.00
95.00
95.67
J/I
F1
F2
F3
29.00
39.33
6.00
28.67
25.S0
25.00
10.50
9.83
13.00
27.67
19.83
53.00
95.83
94.50
97.00
4.06
Table
but on a monthly basis.
level
which was always greater that
was the Y class limit,
capacity.
the coach class seating
markets, i. e.
lower.
As
authorized
routine
J/I
observe
could
One
business
the
In
markets.
C/D & D/C, the authorized limit was slightly
reservation
the
limits,
proposed
and
by
Belobaba,
seat
the
considering
one
airline nest
this
of
system
allocation
could calculate the
average protection level assigned to each upper fare
For instance,
the
exception made
"high" authorized level assigned to M-class,
only to the Canadian I/J &
reference
The
by class and by month.
by flight,
airline,
the participating
of
system
reservation
the
to
were
that
Table 4.07 shows the authorized booking limits
imposed
class
of
breakdown
the
the flight load,
in
participation
shows
for flight F1 in the A/B market,
protection level for
Y
class
was
7%,
January. The M protection level was 15%
the B class it was 33%
( 55%-22%).
in
the
class.
the average
month
of
( 22% - 7% ),and for
REVERVAT IONS ON BOPDING DAY
BOOK1NGS BY CLASS
( X TOTAL )
TAELE 4.06
MAE
FLT
OUMBER
Y BOOKINGS (X)
JAN.
A/8
FEB MAR. APR.
MAY JUN.
JAN.
FEB.
M BOOKINGS
(x)
MAR.
MAY JUN.
APR.
Fl
F2
F3
8
1
0
8
7
0
5
4
0
6
7
0
6
10
0
9
5
7
31
23
0
21
19
0
18
10
0
21
20
0
22
B/A
F1
F2
F3
7
0
10
8
0
9
6
0
6
8
0
6
6
0
7
6
5
9
27
0
27
21
0
19
19
0
19
C/D
FI
F2
F3
F4
30
0
36
40
26
0
30
40
D/C
F1
F2
F3
F4
0
37
40
28
- -- -- --- E/F
F/E
G/H
H/G
JJ
I
8 BOmNGS (X)
JAN.
FEB.
MAPR.
APR.
MAY JUN.
*
JAN.
Q 80O1(05 (X)
FEB.
MAR.
APR.
MAY JLU.
0
24
19
22
24
26
0
27
29
0
26
29
0
21
29
0
24
24
0
27
22
19
36
38
0
42
42
0
46
46
0
49
40
0
44
43
0
38
51
51
20
0
24
21
0
24
24
27
23
23
0
25
24
0
27
27
0
26
21%
0
24
18
0
18
21
16
20
41
0
37
45
0
42
45
0
47
48
0
42
52
0
47
46
50
46
26
0
28
33
31
0
33
41
25
0
26
16
31
22
37
39
27
0
24
13
27
0
27
22
28
0
26
23
22
0
24
22
24
0
24
17
21
20
23
21
34
0
34
43
37
0
34
34
39
0
39
41
39
0
34
32
41
0
42
62
37
52
34
36
0
34
35
25
0
30
30
22
0
36
35
25
0
24
19
16
43
23
38
25
0
23
19
26
0
26
27
31
0
26
23
29
0
19
24
25
0
24
22
22
13
31
23
25
0
35
36
39
0
32
33
38
0
36
41
43
0
34
34
42
0
44
50
51
39
39
33
42
19
23
26
32
31
32
30
24
26
24
28
29
31
50
49
44
41
34
36
38
38
28
28
24
23
26
29
32
33
30
31
29
31
29
32
29
34
41
48
39
41
33
38
30
36
27
26
22
22
29
31
20
28
20
19
11
17
6
22
28
34
49
52
67
61
61
68
66
62
75
42
19
-- -- -- -- ---- -
-- -
--- -- -- -- -- -- -- -- --
Fl
F2
13
13
6
12
11
14
16
16
20
19
22
24
7
5
9
8
17
13
12
12
19
Ft
F2
15
8
11
7
14
17
8
18
10
25
15
9
5
12
8
16
13
16
9
13
18
21
21
Fl
F2
10
6
5
4
4
3
5
3
4
3
3
4
42
39
13
9
7
5
8
6
14
14
12
29
17
Fl
F2
7
7
4
5
3
3
4
3
5
4
6
4
41
42
11
10
7
7
5
7
10
14
25
28
16
25
33
18
23
14
17
17
13
17
16
19
32
29
56
48
70
64
73
69
65
61
53
45
Fl
F2
F3
35
33
20
35
33
21
33
37
24
38
0
24
41
0
30
30
30
38
32
27
18
28
29
14
36
30
34
0
17
43
26
25
16
18
20
10
9
19
8
17
25
0
17.
8
19
7
0
22
4
0
23
6
7
14
12
16
39
23
25
42
19
19
37
23
0
31
15
0
24
17
25
19
F1
F2
F3
26
40
0
25
36
0
27
36
0
27
46
0
32
46
0
37
32
43
33
26
0
27
21
0
31
29
0
22
20
0
27
22
0
32
35
20
7
15
0
9
12
0
8
14
0
18
12
5
0
9
9
0
32
14
0
35
27
0
29
16
0
23
21
0
23
20
0
19
21
28
,
16
15
18
18
4
5
AUTHORIZED BOOKING5 LEVELS
( YAU as 100% )
TABLE 4.07
MARKET
M LEVEL5
Y
B LEVELS
Q LEVELS
FLT
JAN. FEB.
MAR.
APR.
MAY JUN.
JAN.
FEB.
MAR.
APR.
MAY JLN.
JAN.
FEB.
MAR.
APR.
MAY JLN.
A/B
F1
F2
F3
100
100
100
93
93
0
98
95
0
99
97
0
92
96
0
92
70
0
72
85
88
76
78
0
83
77
0
84
80
0
78
76
0
68
61
0
54
67
75
45
46
0
53
50
0
48
44
0
39
33
0
35
33
0
26
35
38
8/A
F1
F2
F3
100
100
100
92
0
94
94
0
94
94
0
94
92
0
86
67
0
93
88
93
86
78
0
81
80
0
80
80
0
80
76
0
65
66
0
70
66
77
66
49
0
49
47
0
59
40
0
43
36
0
31
37
0
38
35
44
32
C/O
F1
100
100
100
100
83
0
86
95
83
0
84
91
83
0
83
91
85
0
84
90
89
0
86
89
78
93
84
92
65
0
71
79
62
0
62
76
62
0
60
76
51
0
59
69
62
0
57
65
41
64
53
71
38
0
42
52
50
0
37
59
28
0
30
54
25
0
28
44
30
0
32
43
19
35
29
45
D/C
F1
F2
F3
F4
100
100
100
100
0
86
89
84
0
87
90
91
0
83
84
91
0
70
78
77
0
91
82
92
93
82
83
91
0
70
71
72
0
65
65
73
0
62
60
72
0
39
46
57
0
69
61
68
82
55
62
67
0
44
40
51
0
33
39
44
0
25
28
39
0
15
23
32
0
32
32
42
40
28
30
41
E/F
F1
F2
200
100
84
83
92
87
92
83
92
89
92
87
71
67
73
67
73
67
65
58
70
66
67
62
48
40
44
44
35
44
27
25
37
34
37
30
23
17
F/E
F1
F2
100
100
86
92
92
90
90
75
82
86
83
89
91
80
58
72
70
72
65
66
63
68
60
72
43
50
30
53
41
43
25
30
28
38
29
41
16
33
G/H
F1
F2
100
100
93
89
93
92
92
92
93
93
94
94
92
92
78
82
75
76
73
75
73
74
78
76
71
55
59
52
59
49
53
45
47
47
55
48
41
20
H/G
F1
F2
100
100
92
94
91
92
92
92
93
93
94
94
89
82
77
80
74
74
74
72
73
73
77
77
63
61
49
50
54
46
51
45
53
49
55
50
31
30
I/J
F1
F2
F3
100
100
100
78
79
87
84
84
78
84
82
78
83
0
77
89
0
80
78
84
82
40
51
62
59
51
62
61
43
56
58
0
62
58
0
66
49
59
53
23
29
32
19
13
25
23
20
17
26
0
19
27
0
31
21
32
24
J/1
Ft
100
92
85
83
90
88
88
66
65
55
72
66
66
37
31
19
47
48
48
F2
F3
100
100
75
0
82
0
81
0
84
0
84
0
88
89
51
0
57
0
47
0
53
0
56
0
67
71
26
0
23
0
13
0
20
0
23
0
39
42
F2
F3
F4
Table 4.08 shows bookout analysis performed for
Columns with heading " # DAYS
the flights in the sample.
indicate
the
actual
closed.
Columns
number of days in which the class was
"
with
percentage of days,
"
(%)
"
heading
indicates
the
during the whole sample period in which
the class was closed. As a function of the nested authorized
booking limit reservation system,
the
following
describe a bookout in a given class:
Y is closed if:
YRES + MRES + BRES + QRES > YAU.
M is closed if:
YRES + MRES + BRES + QRES > YAU
,
OR
MRES + BRES + QRES > MAU.
B is closed if:
YRES + MRES + BRES + QRES > YAU
;OR
MRES + BRES + QRES > MAU
;OR
BRES + QRES > BAU.
Q is closed if:
YRES + MRES + BRES + QRES > YAU
;OR
MRES
;OR
+
BRES
BRES + Q+ QR
QRES > QAU.
+
QRES
BAUES>
>
MAU
;OR
equations
A
consequence
of the bookout equations in the
previous page, is the following relation :
QCLOSED > BCLOSED > MCLOSED > YCLOSED.
One can
observed
in
observe
that
this
relation
the flight F1 in the B/A market.
level
of
bookout
high
classes.
in 18.33% of the flight.
was
closed
percentage in Y bookout is likely to be the
bookout
in
other
opposite market,
class,
B/A,
rather
than in Y alone.
lowest bookout levels, for all classes.
for
all
The high
consequence
flight F2 consistently
not
Flight F2 in
the A/B market exhibit a
M
is
of
In the
exhibit
the
BOOKOUT ANALYS IS
TABLE 4.08
CLASS
MARKET
Y
8
M
FLT
* DAYS
(X)
* DAYS
(Y.)
# DAYS
(%)
* DAYS
-----------------------------------------------------
(Y.)
--------
*
FLTS
--------
A/B
F1
F2
F3
14
32
0
7.73
17.68
0.00
24
33
0
13.26
18.23
0.00
34
44
0
18.78
24.31
0.00
48
71
2
26.52
39.23
1.10
181
180
30
8/A
F1
F2
F3
12
1
12
6.63
0.55
6.63
22
3
13
12.15
1.66
7.18
15
0
25
8.29
0.00
13.81
39
4
49
21.55
2.21
27.07
181
30
179
C/D
Fl
F2
F3
F4
5
0
2
0
2.76
0.00
1.10
0.00
39
0
14
2
21.55
0.00
7.73
1.10
76
1
47
4
41.99
0.55
25.97
2.21
80
2
43
4
44.20
1.10
23.76
2.21
180
30
181
181
D/C
F1
F2
F3
F4
0
7
9
0
0.00
3.87
4.97
0.00
0
20
31
3
0.00
11.05
17.13
1.66
0
38
49
10
0.00
20.99
27.07
5.52
0
57
50
17
0.00
31.49
27.62
9.39
30
180
181
181
E/F
F1
F2
12
8
6.63
4.42
13
22
7.18
12.15
46
98
25.41
54.14
36
59
19.89
32.60
181
181
F/E
..
F1
F2
11
4
6.08
2.21
12
17
6.63
9.39
82
47
45.30
25.97
86
35
47.51
19.34
181
180
G/H
F1
F2
0
0
0.00
0.00
0
4
0.00
2.21
6
16
3.31
8.84
11
62
6.08
34.25
161
177
H/G
F1
F2
5
0
2.76
0.00
10
5
5.52
2.76
26
18
14.36
9.94
22
39
12.15
21.55
162
177
1/J
Fl
F2
F3
9
3
5
4.97
1.66
2.76
9
6
16
4.97
3.31
8.84
15
17
46
8.29
9.39
25.41
39
31
87
21.55
17.13
48.07
179
120
179
J/I
Fl
F2
F3
6
1
0
3.31
0.55
0.00
8
9
0
4.42
4.97
0.00
10
34
0
5.52
18.78
0.00
23
44
1
12.71
24.31
0.55
181
176
30
For
the
remaining markets,
the same behavior
is observed. At least one flight for each directional market
exhibited a high level of bookouts.
The
renaining
flights
showed moderate to low bookout statistics.
The
flights
that
bookouts were:
MARKET
FLIGHT
A/B
F2
B/A
F1 & F3
C/D
F1
D/C
F2 & F3
E/F
F2
F/E
F1
G/H
F2
H/G
F1
I/J
F3
J/I
F2
exhibited
high
level
of
The
did not
list
following
the
in
flights
exhibit high level of bookouts. They were
MARKET
FLIGHT
A/B
F1
B/A
F2
C/D
F4
D/C
F3
E/F
F1
F/E
F2
G/H
F1
H/G
F2
I/J
F1
J/I
F1
Statistical analysis
should
produce
that
results
on
are
above
flights
these
to
likely
be
representative of the market behavior than the original
of
28
flights
bookout.
There
correction,
i.e.
is
not
how
demand
reservations
they
because
imposed to a flight.
a
analysis,
simple
set
exhibited low level of
routine
for
bookout
to estimate what would have been the
given
that
no
seat
limitation
was
As a consequence, major attention will
be given to the flights that
statistical
have
more
did
not
bookout.
Therefore,
distribution plotting and the demand
analysis presented in this thesis will only show results for
these flights.
4.2 DISTRIBUTION ANALYSIS
The objective in this analysis was
to
produce
and examine distribution plots of reservations by fare class
for
the markets and flights in the sample,
which exhibit low levels of bookout.
data
retrieved
for
corresponds to 28 days
snapshots
were
any
flight
before
specially those
The first
refers
to
departure.
reservation
a period that
From
taken for every seven days.
there
on,
That is to say
that each flight will be analyzed in 5 seven-days'
periods,
from day 28 to boarding day, that is, periods are: T28, T21,
T14, T7 and TBD.
Analyses
made for the
M-class,
bookings-on-hand,
and
were
up
the
made
to
a
in
period
particular
expected
,
or
number of reservation
This is to say,
still to come,or bookings-to-come.
day
terms of reservations
that on
we should have data analysis for both bookings-on-
21,
hand and bookings-to-come. The objective is to observe these
two related but
means,
and
distinct
variables
standard deviation.
in
terms
of
shapes,
Exception will be made for
the Canadian markets, where the analyzed class will be Y.
Correlation analysis performed in
hand
and
final
bookings
indicated
that
bookings-on-
the correlation
between these two variables ,
This
low.
very
good
exhibit
means
in the majority of cases, was
bookings-on-hand
that
explanatory
when
power
bookings via bookings-to-come.
not
should
final
forecasting
This result corroborates the
conclusion arrived by Littlewood [1):
"The subsequent arriving passengers
can be regarded as independent
of
the booked load".
Figures
4.01
4.10
through
show distribution
plots for the flights/markets selected for data analysis.
Figure 4.01 shows distribution plots for flight
F1 in the A/B market. The shape of the distribution observed
for final
bookings,
resembles
the
bell
i.e.
shape
increase in skewness is
it
reservations
of
a
of
a
normal distribution.
increase in standard deviation,
normal distribution.
An
hand
as
On the other hand,
gets further from boarding day.
that
in
any
4.01
.
The
small
resemble
period,
going from 6.00 to
A side by side plot comparison in
.
the
Bookings-on-hand exhibits
whereas bookings-to-come is the reverse,
6.42
day,
boarding
for bookings on
observed
shape of bookings-to-come plots,
on
7.87,
going from 8.80 to
given
in
figure
table on the top right corner of figure
4.01 shows statistical analysis for this flight.
49
The notation used in these figures is
FiMBD
:
= reservations on boarding day
for flight i, M class;
FiMt
= total reservation made up to day t,
for flight i, M class,
( t = 7, 14,
21 and 28 );
FiMtBD = bookings-to-come for flight i, from
day t to boarding day, M class,
( t = 7,
50
14,
21 and 28 ).
JAN. -
teas
juN.
Sample set to -> ALL
180 observaticns used.
Descrip:ive Statistics
Maximum
Minimum
Kurtosis
Std. Dev. Skewness
Mean
- -- ------------------- - ----------- - ---- -- ----- - - -----
Variable
------- -
F1M21
F1M29
3.1444
8.1556
F1M1 :0 12.711
F1'21-3 15.150
F1M2-30 16.261
F17 S0
1
(Skewness = x3/s*' ; Kurtosis =
m aRE3E.AnAm
AaM.
£.1779
6.1703
35.232
57.4965
69.900
3.3533
6.2530
6.3647
6.7125
.79593
1.1836
4.4066
6.2310
7.1251
.13393
-. 54175
-.23213
-. 276153
8.8908
7.3746
6.8719
6.2919
5.9936
6.4 252
8.1826
8.7379
8.7971
19.406
11.250
6.5944
4.2556
F1M7
F1M7
3.000
.0000
.0000
.0020
.0000
-13.00
-31.00
-31.00
-0.00
57.10
49.00
67.00
67.:0
66.00
27.00
37.00
41.30
42.00
m4/s**4)
sOARIM4G DAY
."".
l.ess
6-
-
"".
IS&&
30
28 -
28 24 -
22 -
nL
1
3.1
10 -
12 .
20
-1
10
i,1-
0
2
4
6
A
10 12 14
22 24 26
M8 18 20
U RESEvArioms
JAM. -
28 30 32 34 36 38 40
-4
40.
0
12
4
16
OOKIWG
DAY7
-
aa.-
AU&. ias&
20
24
TM COM -
.suu.
28
32
36
40
40-
28
32
36
40
40.
DAY7
teas
F;17A
X
0,41
20
10
0
0
2
4
A
8
10 12
14
16 18
20 22
hi RE[EVATIONa
-
24 26
28 30 32
34 36
36 40 40+
-4
0
4
DAY 14
12
1s
20
NOKIMG3 To COME
Figure 4.01 : Distribution Plots
M-class
S
Flight F1
Market A/B
24
-
OAT 14
ALM. -JUN.
0
2
4
4
A
10
16
11 14
18 20
MUtEURVATIONS -
JUN.
.-
0
2
4
6
A
10
12
M
14
16
16
4&M. A.
199
22 24
26
28 .30 £2
£4 £6
£8
ta
21
TD COME - OAY
BOOKiNGS
A66L -
Is&&
24
IGAL&
40 40*
DAY 21
20 22
JUId.
JN
26
28
30
32 34
36 38
0
40
12
16
iat
20
9OO~i"G3 TO COME -
DAY28
MESERVATIONS
Figure 4.01 (cont.)
M-class
£4
JUN.
: Distribution Plots
Flight F1
Market A/B
24
AY 2A
3
6
£8
40
40-
ts
JUN.
.M .
30
28
Sample set to -) ALL
26
Descriptive Statistics -
24
Variable
22-
Mean
181observations used.
Std. Dev.
Skewness
Minimum
Kurtosis
Maximum
36
F2M40 23.337
13.011
F2M7
F2M14 6.8398
F2!21
4.6961
F2M28 3.1934
F2M7SD 10.326
F2M11
80 16.497
F2M21~8D 18.641
F2M28~SD
20.144
to-
14-
12
10
ol
24
0
(Skewness =
12
18
24
30
36
42
r[SERVAnoNs
48
O
54
#oAmai"
50
56
72
78
54
*0
10.383
8.2050
5.4896
4.5694
3.7150
7.9302
S.7049
10.121
10.361
.34722
1.1963
1.7808
2.065
'2.2790
.44086
.45437
.27984
.33458
a3/s68 3;Kurtosis
.0000
.0000
.0000
.0c00
.0000
-9.000
-6.000
-2.000
..0000
2.7745
4.9249
7.4439
8.9319
9.3770
3.2102
3.068
2.8918
2.8315
52.00
49.00
35.00
30.00
21.00
34.00
46.00
45.00
49.00
= s4/s**4)
90-
oAy
Jaas. -
JUN.
5859
40-
30.-/
20
10
-4
-3
0
3
4
9
12
15
15
21 24
27 30 33 36 39
ON
RsRYAnoHs
42 45
48 54
60 63
44+
-12-
0
6
12 18:
4
3G
.SO
-4
-3
0
3
6
9
12 15 18 21
24
RMSWVAnDms
27
30
36
42
WOOKIMCS
TD COME -
DAY 7
33 34 39
42 45 48 54 60
63
-12
-4
0
12
18
30
1a
36
42
000KIMCS
TO COME -
a" OAY 14
Figure 4.02
M-class
24
aae.
: Distribution Plots
Flight F2
Market B/A
48
4
W0 66
7.
78
60
72
78 84
44
90
DAY7
48
OAY
54
14
66
90
.au&M.ea*
.
JAm. -
ASKM, IeS
/1,
10 -
F?
-3
0
3
6
2
12
15
18 21
24 27 30 33 36 39
zwvAnoD
-6
-3
0
3
6
9
12
15
18 21
424 486
4 60 63
-12
-6
0
A
12
24
27 30 33 36 39
ON DAT
24
30
36
42
BOOKIMCS
TO COME -
Om DAr 21
RSDVA1OHS
18
42
43 48
54 60
63
-12
28
0
6
12
18
24
30
36
ODWINGS TD COME
Figure 4.02 (cont.)
M-class
-6
Distribution Plots
Flight F2
Market B/A
42
-
0F
,-
I'
I
-0
48
54
80
68
r
-F
72
78
84
50
OAY 21
48
54
DAY 28
60
66
72
78
4
90
-i.
-
gas
JWL
Sample set te -) ALL
Descriptive Statistics Variable
.33665
1.5856
1.8727
2.2730
1.8897
.365!5
.15795
.16705
.31096
10.010
5.4717
3.6615
2.9997
1.9292
6.8784
8.5907
1.970
9.5729
FIMSD
1n.267
FAX7
8.0667
F4M14 4.3667
F4M21 2.6556
1.5557
FAM2
F447 80 10.200
FAM11
80 13.900
FIM2?180 15.611
FAM28~0D 16.700
-__
180 observations used.
Std. Dev. Skewness
Mean
Kurtosis
Minimum
2.6126
6.9378
7.9251
10.058
7.1777
2.6981
2.1534
2.2709
2.4013
1.000
1.000
.0000
.0000
.0000
-3.000
-7.000
-1.000
.0300
Maxima:!
48.00
21.00
19.00
11.00
32.00
3f.00
38.00
43.00
(Skewness = t3/s"3; Kurtesis = m4/s*44)
-
6
0
12
18
vI-r
24
30
W
34
42
I
4
REEVA11GM
84
OArNG
60
66
t
72
IIII
78
I
90
84
i
904+
DAY
.IM
- .8k.
1668
*01
-20
r1~'1A
-
-12
-4
0
6
12
OAY 7
W RESERVArICUS
.
...-sa
-4
0
4
4
16
20
24 29 32 36 40
M RESWVATIOIS
30
36
42
M0COME -
48
84
,0
6
72
75 84
86
72
78
80
DAY 7
toes
uu.
d
10
12
24
80DxrC5
IL
-4
18
-
44 48952
5
00 84
86
72
76
-12 -
14
OAY
12
8is 24
30
C6
FOO&MM T1OCOM-
Figure 4.03
M-class
6a
Distribution Plots
Flight F4
Market C/D
42
44
DAY 14
60
84
;0
J&AL
JU6L
Ift"
7
0
~FIL
-6
4
4
a
2
,t
20 24
23
32
MREERVAOS
36 40
-
~4
8 52
6
11
.14
..
n1
-12
;11
-4
0
6
12
18
24
30
36
BOOKINGS TO COME
DAY21V
.AA&.-
.IuM.
42
-
48
54
60
SO
72
78
84
*0
&4
60
66
72
78
a
9o
OAT 21
....
201
A
A
t, .1~~
104
-8
-4
0
4
8
12 16 20
24
28 32 36 40
M RESERVAnOmS-
44 48 52 56
60 84 8
72
-12
76
Figure 4.03 (cont.)
M-class
-9
0
6
12
18
24
30
36
42
BOOKINGSTO COME -
DAY 28
Distribution Plots
Flight F4
56
Market C/D
48
DAY 28
3028 -
Sample set to -) ALL
Descriptive Statistics -
26
24-
Variable
Mean
181observations used.
Std. Dev.
Skewness
Kurtosis
.11119
.68521
.72749
.94272
1.2185
.40856
.30349
.19537
.12118
2.4434
2.8519
3.0515
3.6303
4.5487
2.7033
2.62E
2.5519
2.4817
Mini2um
Maximu
22-
a.-
F3M60 35.564
F3.7
19.564
F3M14 10.370
F3'21
6.1050
F3M23 3.7459
F3.7 80 17.000
F2MIl 80 26.193
F3M2I -ED 30.459
F3M28~80 32.818
12141-
77.241
11.384
6.4945
4.0959
3.1940
10.423
14.137
15.682
16.119
(Skewness x m3/s**3; Kurtosis
4.000
.0000
.0000
.0000
.0000
-4.000
-1.000
1.000
.0000
85.00
5E.00
32.00
20.00
16.00
52.00
69.00
79.00
81.00
a e4/s 3 34)
2
0
A
12
18
30
24
3
42
acuAng
J
4s 54
60
60AnIGM
6
72
64&
so
0
0
DAY
AL- aUIim **a
a.
.4
20 -
12-$
10 -
KA
PA
P771
-6
-3
0
3
6
6
12 1
18 21 24
27 30 33 36 3*
.""M. -
Jul&
42 45 45
460
63 66
-12
-4
0
6
12
OAY
7
U RE5MEvA7I0MS -
16
24
900Kin
30
36
42
710 COME -
48
&4
6"
a6
72
76
64 6
72
78
&4
DAY 7
Is"
PH
'H
1/00
01,
-4
-3
0
3
6
9
12 18 1s 21 24 27 30 33 36 3
MRaStRVA10PI
-
42
4s
4 8460
6a
DAY14
i
I
-12
-40
I
.
6
12
16
24
30
36
42
0OKINS T0 COMI -
Figure 4.04 : Distribution Plots
M-class
Flight F3
57
I
.
Market D/C
4'
CAT 14
54
So
66
go
-.wM.
tea -
I*&&
J&hL - JUW
.1M.
Is&&
.77
-1
M RESERVADolW
.IhM. -
-
IM.
-so0
12
DAY 21
19
24
3
64
8
300KIWGS 7V COME -
&
0
0
:7
49
DAY 21
I*&&
10 -
-12
M RESERYAT1oMS-
DAY 28
0
6
12
15
24
30
36
BOOKINGSTD COME
Figure 4.04 (cont.)
M-class
-6
Distribution Plots
Flight F3
58
Market D/C
42
-
48
54
DAY 28
60
66
72
78
84
90
30Ua -
Sample set to -) ALL
Descriptive Statistics -
-
36
24
12 10-
Variable
Mean
F19E
F17
F1M14
F1421
F1.M28
F1M7 ED
F1il 80
F1M2180
F1M28"B0
18.492
12.752
11.657
10.249
9.5912
5.7293
6.8343
8.2431
181observations used.
Std. 0ev. Skewness
14.380
12.965
12.295
11.475
11.792
5.5446
7.0691
8.8980
10.246
8.9006
1.2502
1.5975
1.9275
2.0563
2.2476
.56191
.73860
.3895
.18590
*3/s**3; Kur:osis
m
(Skewness
Kurtosis
4.4513
6.2956
7.2190
7.5916
Minimum
.0000
.0000
.0000
.0000
.0000
-9.000
-10.00
-17.00
-35.00
8.6765
3.0394
3.6576
3.6611
6.0279
Maximur
73.00
72.00
69.00
59.00
64.00
22.00
34.00
12.00
53.00
*4/s**4)
33
40
e 24:
1-4o2 1
-
3s
2
as
E3EAnUMOp
NS
Uo
440
s6
4 an
2 e so
a
so+*1.eo
1
4a
a
DAY
03M3T
e4
Xt-
e
sads
Y7
n
y
ds
.
20
10
10
0
0.
-a
-4
0
4
a
1
20
24
2A532
R3VAnoNs
36 40
44
48
3
526 0
4
7Z 73 730
-12
-4
0
1
112
7
ON' DAY
401sg1e
4
30
30
43
BOOKINGS10 COME -
44
54
40
64
72
79
40
DAY 7
4si
Figure
20
-a
-4
0
4
a
13
IS 30
24
25 322 36 40
&4 45
52 55
0
64
6731
76
-12
-*
4
12
15
Figure 4.05 :Distribution Plots
M-class
24
30
30
Flight F1
Market E/F
0
42
*0OK3NC 1O COME -
6f3vrvflms am oAT 14
2AT
14
47
7
46
so5
.""
-
JUPL
19&6
JAM-
UM. 08
-
.Mh
.JUOL
40-
ci-12
I7I
IT
G
I
12
ow oAy z1
wm~vAloN
-
-8
I
0
~h~-
18
24
30
CZ=
36
f
42
48
SOOKINGS 1M COME -
,
54
SO 66
,
,
,
72 78
i
84 60
DAY 21
~A*
so-A~
5
40
30
-
20
2Q
10
10 J
'6V20'4
S
O
A 272
0
1
6
0Z4
RSMRATIONtS ON DAY( 28
BOKIMGS TO CCME -
Figure 4.05 (cont.)
M-class
30 46 4
Distribution Plots
Flight F1
60
Market E/F
4a
DAY =8
54
an
66
72
7a
s4
0
I*&
ia.-
.me..
054
Sample set to -) ALL
Descriptive Statistics Variable
MVAnONS
ON
.6".- "6.
.OARDING
Mean
180observations used.
Std. Dev.
F2M0
F214
F2P14
F2M21
F2M28
F247 80
F2411 80
F2521-80
FM28-80
15.811
8.2333
5.9056
5.2778
4.3389
7.5778
9.9056
10.533
11.472
(Skewness
:
12.703
9.4951
7.7592
7.4437
6.8071
6.9955
8.8701
9.6094
10.194
Skeoness
xuriosis
1.295!5
1.979
1
1.9215
2.3957
2.6277
.98957
.81249
.745 8
.64110
4.1136
6.357 1
6.3720
10.002
11.693
4.1794
4.0811
4.0989
4.5303
Mini~um
Maxi..
.0000
.0000
.0000
.0000
.0000
-6.000
-15.00
-19.00
-25.00
57.00
43.00
35. 0:
47.00
41.00
33.03
40.0i
42.
8
a3/s*.3; Kurtosis - m4/s'
9)
DAY
.k&- j~h.
16414
to"
30.1
26
-j
24 -
11
2-
104
a4
V 01
4
-4
-3
0
3
6
.
12
1.
t.
21 24 27 30 33 3.
3
42 454
54 .0
.3 6
-.
+
4
.
-4
-EEV.n
.
-
1t
12
.
24
2.
OCnMGSTO
CrESVADOMB ON *AY 7
2.
UC
-
32
3.
40
44
A.
CAY 7
Y 14a
30
(A
J7
IIn
40j
-8
MOVAfl0IG
am OAY 146
-4
0
4
x
12
Figure 4.06 : Distribution Plots
M-class
i
DOC IOW
Flight F2
Market F/E
20
24
28
"0 COME -
32
3
DAY 14
40
8a
s: $.
40
A..
-
JUMa 1ea
AsAs.-
ISma
.nna.
101
rsurvAnOmS
cm DAY 21
UOOKINc To COME
-
DAY 21
501
.Ma". -
.A&Le
t*na
.M
.-
JUN.
20
24
$sag
O0-I
40 -
20
A
20
10
-6
-3
0
3
6
9
-2
1
18
21
24 27 30
33 36
39
42
AS 48 54 60
63
-8
-4
0
4
8
RESERVAONS OM DAY 28
16
28
POOKIWCS TO COME -
Figure 4.06 (cont.)
M-class
12
Flight F2
istribution Plots
Market F/E
32
36
DAY 28
40
44
48
52
56
60
.1*M.
10
- .MIU. teas
-,
Sample set tc -> ALL
Descriptive Statistics -
25 .4
Mean
Variable
F1.43D
F17
F1414
F121
F1M28
F'A7 80
F1M180
FY.21'SD
FIM2880
177observations used.
Std. Dev. Skewness
9.5876
5.0329
4.0113
3.3955
2.5028
4.5537
5.5763
6.1921
7.0847
(Skewness = 63/s*23; Kurtosis
3.5150
3.9874
4.086
5.0292
7.3824
4.6258
3.9173
3.5200
3.6601
39.00
22.00
20.00
20.00
19.00
25.00
29.00
30.00
32.00
.0000
.0000
.0000
.0000
.0000
-5.000
-5.000
-7.000
-6.000
= @A/s'84)
aw.0*
-
0
1.0552
1.157
1.2575
1.5439
1.9954
1.3625
1.1649
1.0470
1.0703
8.7441
4.8464
4.2707
4.0748
3.5099
6.0367
6.9819
7.3002
7.7788
Maximur
Minimum
Kurtesis
12
4
20
1
24
22
32
39
40
~4
48
32
SO
44
6
RMstNAnONS ON 90AJolNG DAY
- .51*.
1660
401
A
20
10
a0
VA VAV-
.
-
-3
0
3 6
9
12
21 24 27 30 33
is I8
36
39 42-45
48 54 60
-8
43 6+.
-0
4
0
£
aXfvAno0s Do DAY7
A.-
JUN.
12
'6
20
NOUI0GS
19&6
0
"M6. -
24
i
8
Cut -
36
40
44
44
52
5
90
34
40
44
48
5:
54
40
MAY7
0*6
.0UN.
50
P5
40
cnV, /, -'A'A,4r-V1 ,
20
V
lV)
V
10
-4
-3
0
3
4
9
12
15
18
21
24
RESERVAnMSON
27 30
33 36 3
42 45 44
54
0
63
.,
-
0
4
a
DAY 14
16
20
24
.8
OOxiNGS
TO COME -
Figure 4.07 : Distribution Plots
M-class
12
Flight F1
Market G/H
32
DAY14
.j~M.
-
.AJ&.
18&
20
-s
-3
0
3
4
9
12 15
18 21
24
E5ERVAT0MS
27 30 33
36 39
42 45 48
4
60
83
-8
-4
0
4
8
12
OM DAY 21
16
20
24
28
I0KW'ZS TO COME -
32
36
40
44
48
52
Si
,
,
5:
54
60
DAY 21
JU6m. 19&6
.W.-
50
z
20
201
-
AV
a
5
A
V0 Li-1$
VVA
'A.
10
V/,
10
0
-4
-3
0
3
6
,r1~ _
9
12
15
18
21
24
27 30
33
3
i i i i ea
39
42
43
48
54 60
-a
43
-4
0
8
,
12
Figure 4.07 (cont.)
M-class
16
20
24
28
BOOI:CS TO COME-
E5ERVAT.ONS ON DAY 28
Distribution Plots
Flight F1
Market G/H
32
DAY
,
,
3S
40
28
44
48
80
.A..
- JU..
1e6
Sample set to -> ALL
Descriptive Statistics
WWVAnOZ ON
Mean
F2M80
F2.47
F21414
F2M21
F2M28
F2N7 ED
F2MI 8D
F2M21-8D
F2M98~8D
18.458
10.350
6.9209
5.1582
3.8023
8.1073
11.537
13.299
14.655
(Skewness
*
4.6206
15.177
32.974
42.539
69.124
2.8912
2.7405
3.1032
2.9438
1.1536
2.7474
4.4785
5.2529
7.1373
.75510
.782!3
.65665
.79869
15.469
11.427
9.7559
8.8175
7.8935
8.0032
10.723
12.200
12.555
Minimum
Kurtosis
Maximut
98.00
88.00
90.00
96.00
86.00
35.00
43.00
52.00
56.00
.0000
.0000
.0000
.0000
.0000
-8.000
-3.000
-23.00
-2.000
3/s"3; Kurtosis T m/s"4)
DAY
BOAING
s.
.66.L
177observaticns used.
Std. Dev. Skewness
Variable
0Is*
.Ua.
-
JA.
to&&
.j
rA-
:o4
204
~ 5 -1 'rx
M-i
-4
-4
0
44
48 52
56 60
64 88
72 7
68.
-12
r
,
I
rrrrrrA.,.rrAA..
A r-7
'
4
12 16 20 24 2S 32 36 40
r
P
20-
-4
0
6
1:
1&
mE3ERVATNS
ON OAY 7
Ah&
-
IM.
24
30
36
.4&06. -
leas
aL
48
42
BOKINGS T COME -
54
40
54
60
66
72
73
A4 So
OAY7
leas
401
A
104
-8
-4
0
4
8
12 16
20 24
2
RE5tVAfnOM
32
36
40
44 4852
"4 10
44
"
.12
72 78
-4
0
6
12
Figure 4.08
M-class
18
24
30
34
42
0ORIMCSI0 COME-
ON DAT 14
Distribution Plots
Flight F2
Market H/G
48
OAT14
64
72
78
849
0
JAN. -
-8
-4
0
4
8
12
.1MM. less.-
16 20 24 28
32 36 40
44
48 52
56
60
64
8
72
76
-12
-6
0
6
12 18
tESERVATIOMS ON DAY 21
JA". - Jum.
less
5
A"& -JUN.
U.
24
30
SOOKINC
Is&&
36
42
48
TD COME -
54
66
6
72
78
84
90
DAY 21
Jm.- .1MM. to"
40
20.4
1r
"'AK-
20 J
A
10
-6
-4
0
4
8
12
16 20
24 28 32 36 40 44452
RESEYAT1OoS
om
.6
60 646
72 76
-12
DAY:8
Ki
-
0
6
12
'8
24
30
36
42
800"iNG;S TU COME -
Figure 4.08 (cont.)
M-class
f,'A VA
-Th1 V4 /r
0-
D istribution Plots
Flight F2
66
Market H/G
48
DAY 28
54
60
6
72
78
84
90
-
~m.
t~a6
Sample set to -) ALL
181 observations used.
Descriptive Statistics Variable
Mean
Kurtosis
Std. Dev. Skewness
Minime
P.3
A.a
4
--
F1MID
33.414
F1v7
36.414
F114
35.315
F1M21
32.713
FI121
30.276
FiM7 80 -3.0000
F1M1I 80 -1.9006
F1P.21-0 .70166
F1N28~80 3.1381
V71
00
1.3495
1.1379
1.13.11
1.2593
1.4118
-2.4831
-. 32923
-. 20316
-.22423
18.656
20.924
22.328
23.651
24.502
6.9873
9.4717
11.646
12.390
(Skewness a a3/s"3; Kurtosis .
"0
0
10
20
4
5
MtVAT1IN
2.000
6.000
5.000
3.0C0
1.000
-49.00
-32.00
-32.00
-33.00
4.7802
13.880
3.9236
4.0552
3.6612
i1"
1::
11!
11~
119.0
35.
39..
a4/s"4)
M
[IrA
ON
I0
5.3380
4.1375
4.0560
4.3340
GOE
o
70
t0
100
I0
120
10
OW BOARMWO OAY
~M.
30
.JUW. laaa
-
401
11
20
®r"-1A.,
'0
AKr~
k.~
~V~VA
V,
0
10
20
30
40
50
60
ESRVAnONS
4 F,-
70
80
90
100
110
1-:0
130-
-'6-I2
-
0
4
On DAY 7
a
1
00tWCS
-.
30
:0
'0 COME -
-.
UU
12
to
242"'A
32
34
a
40
s2
DAY7
. A
40
1
/AA
0
to
20
30
40
S0
60
70
8
120
1300,
-to
-12
-6
-4
6
NESERVAnOMS COOCAY 14
a
o0NOS
Figure 4.09 : Distribution Plots
Y-class
4
Flight F1
Market I/J
1-0
10 COME -
24
2
DAY 14
32
86
4
'O
4
32
AMIL1 -
.1MM.
JSAG.- JUIL
I*5*-
1M.
IS&O
"-4I
0
10
2
30
40
50
o
EEVATIONS Of
-. &L
-
0
70
ao
6o
100
110
120
-16
130.
-12
-8
-4
0
4
a
12
6s 20
00(KINGS
TO COME -
OAY 21
....
.U&1..
-M..
24
25
32
3
40 44
4e
52
DAY 21
.e
7
20
1
&
1
'7
Ii
104~
..i
r23 i ,i7
20
4AV
(--AVAV
0
10
20
30
40
50
60
70
0
90
100
110
120
-16
130..
-'
-8
-4
o0
RESERYAOMN
CHDAY 2
a
I2
I6
20
SOOKINGS 'O COME -
Figure 4.09 (cont.)
Y-class
4
D istribution Plots
Flight F1
68
Market I/J
24
:a
2AY 25
32
36
40
44
45
1:
.1an. -.
AI.
0ea4
2S.
Sample set to -) AL.
as-
Descriptive Statistics -
179cbservations used.
2423-
Variable
Mean
F1?80
F1.7
F1M1i
F121
FIM28
FIM? 80
FIM11 10
F1,21-8D
F1N28~8D
35.073
36.514
35.225
34.453
34.520
-1.4413
-.16201
.61453
.55307
Std. Dev. Skewness
Std. Dev.Skewness
23.250
1.0442
24.254
.96106
25.853
1.0526
1.1066
27.355
30.476
1.0933
-1.0050
4.4026
-. 75446
6.67;0
-. 65930
9.9621
14.710
-1.3151
a. -
14 12IQ
Mini mum
Minimus
Kurtosis
Kurtosis
Maxim
Maxie~~t
3.000
4.000
1.000
1.000
.0000
-18.00
-27.00
-40.00
-59.00
3.4700,
3.2470
3.5918
3.7430
3.5124
5.5798
5.3871
5.9584
5.8158
111.0
115.0
123..
123.0
133.0
10.00
17.C
39.0:
44.00
(Skewness x a3/s53; Kurt-sis a mi/s**4)
0 so 6
121824
-AM.
30 3942
ea $41505672
48
75450504
RE3ERVATIC0M5
ONIGARIMIG DAY
.AM.
-
JUN.
,s"
ao I
7
an
-
u.
.a
20-
20
IQ J
.0
_
Ab
r7
-i
t.
0-,2 -6
0
6 12
1
24 JO 36
42 45
44 50
46
72 75
34
*0
45
54
s 53
64
-'2
-4
0
UERVANOMS ON OAY 7
6
'2
15
24
30
as
42
4
000.MGS IDCOME
--
54
OA
7
45
&4
40
44
7
73
S4
V4
40 -
1
20
20
r,-j
y
1
10
0,
-12-4 0
12
IS
:2
0o34
4:
.4
E3ERVArIONS
se
6o
72 7
&4 ;0
so
ii a
-12
ON CAT 14
-4
5
6
12
Figure 4.10 : Distribution Plots
Y-class
Flight F1
69
Market J/I
15
24
NOCG
30
36
42
"a COME -
OAY 14
40
44
72
71
84
90
164a
4"L - A"L
-.
- A~a.sa
.M.-
JUN.L I*"
40
-12-6
0
6
12
18
24 30 36 42
4
54 60 86
DAY21
72 78
84
90
4a
54 60 63
-12
-9
0
6
12
A"- .JM*I
16
24
30
3
42
OOKaIGS TO COME -
KEcEVAn0S ON
48
54
80
6
72
78
84
90
80
66
72
78
8
90
RAY 21
SO&&
50*-
50
40-
40]
r/r.-
ad;4
20
20
-r/
A VA
FAV
rA/
10
10
r
r
-12 -4
0
6
12
.18 24 30 36 42 48
54 60
ON 33
RESERfATiOMS
6
72
78
84 90 48 54
60
63
-12
-4
0
6
12
25
24
30
36
42
OOMINCS TO COME -
Figure 4.10 (cont.)
Y-class
18
Distribution Plots
Flight F1
70
Market J/I
48
O
DAY
54
8
CHAPTER FIVE
RESERVATIONS FORECASTING
Forecasts are
made
because
from
the
decision
making
activity,
or plan to the timing and
process
they
analysis
assist
of
the
policy,
implementation
of
an
action, program, or strategy [7). The need to forecast final
reservation requests,
particular to this thesis, represents
a key ingredient of the decision making process in
a
Yield
Management System. Regardless of the core algorithm that the
Seat
Inventory
Control
routine
uses,
forecasts of final
reservation requests are needed.
In general, the various forecasting methods can
be divided into
scientific,
three
broad
qualitative
or
categories:
judgmental,
quantitative
and
or
decision
analysis, which is a combination of the first two methods.
Quantitative methods have been used more often,
and have gained a wide acceptance for several reasons.
rely
heavily
on
They
the existence and use of historical data,
and to a large extent, on the perpetuation of past behavior.
Forecasting methods are based on cause-effect relationships,
statistical analysis or simulation methods,
provide
a
description
of
the
which
underlying
in
turn
process one is
trying to understand, explain and make forecasts.
Qualitative methods, on the other hand, rely on
the "intuition and/or experience"
are,
as a consequence,
in describing
the
forecaster,
and
dependent on the forecaster ability
the process. Subjective by nature, this class
of forecast "models"
information
of
is
tend
to
available,
or
be
used
when
when
there
very
little
is an inherent
inability of modelling in an objective fashion.
Decision analysis, the remaining category, is a
combination of both quantitative and qualitative methods. In
this category,
assumptions on some unknown
parameters
ar-.
made, and using quantitative methods, forecasts are made.
Given
the ability of any airline to provide a
vast set of historical data ,
quantitative methods
can
be
applied to fulfill the forecast need of the Yield Management
System. Therefore, quantitative methods in forecasting final
bookings for a flight are explored in this thesis.
5.1
ALTERNATIVES IN FORECASTING
Time
Series
Analysis
are
heavily
based
on
statistical behavior. The model/parameters estimated in Time
Series Analysis do not have specific meaning. Models in this
class can be used as a forecast tool, but they do not try to
explain the underlying nature of
the
process.
Models
are
developed based on a statistical basis only.
In
nothing about
affect
the
this
the
class
real
variable
of models,
world
to
be
behavior of a time series is
causal
moving
BoxJenkins'
ARIMA
relationships
forecasted.
examined
something about its future behavior.
projection,
we presume to know
averages,
modelling
in
Instead,
order
past
to
infer
Ratio analysis,
trend
spectral
can
that
analysis,
and
be cited as examples of
Time Series Analysis methods.
The
namely
Causal
expressed
in
second
class
Methods,
of
Quantitative
methods,
concentrates on models that can be
equation
form,
relating
variables
quantitatively. Data are then used to estimate parameters of
the
equations,
and
theoretical
relationships
are tested
statistically.
In
single
equation
regression
models,
the
variable
under
study
is
explained
by
a single function
(linear or nonlinear) of explanatory variables. The equation
will often be time-dependent (i.e.
explicitly
in
the
model),
so
a time index will appear
that
one
can predict the
response over time of the variable under study.
5.2 TIME SERIES ANALYSIS
Time Series Analysis presumes that
to
the
series
be forecasted has been generated by a stochastic process
with a structure that can be characterized or described.
other words,
In
a times series model provides a description of
the random nature of the stochastic process
that
generated
the sample under study. The description is given in terms of
how
the
randomness is embodied in the process,
and not in
terms of cause-effect relationships.
Because time series analysis
deal
of statistical analysis,
and it is more
for the
fact
that
a
large
it provides better estimates
sophisticated
Simple extrapolation,
require
than
simple
extrapolations.
such as trend analysis do not account
a
time
series
is
the
result
of
a
stochastic process.
With
Box-Jenkins'
Auto
Moving Average models , known as
describe
time
series process,
moving average components.
in
the
model.
Model
original series,
times.
Parameters
Regressive Integrated
ARIMA models (8],
by using autoregressive and
A constant may also be
parameters
or for the time
one can
included
can be estimated for the
series
differentiated
i
are chosen for the terms included in the
model in such a way that it
minimizes
75
the
sum
of
square
differences
between
actual
time
series
and
fitted time
series. Model parameters, again, convey no special mean.
ARIMA models were developed and
flight
F1
in the A/B market,
and to observe model fitting
modelling
was
final
estimated
as an example of application
results.
The
data
used
Table 5.01 shows fitting
results
for an ARIMA(3,0,2) model. The equation fitted was:
.
MBD(t) = C + MA2
.
r(t)
where
AR3 = ( I + AR(1).B + AR(2).B
B
=
2
3
+ AR(3).B
backward shift operator, defined as
n
B [X(t)]= X(t-n);
MBD = final reservations, M-class;
2
MA2 = ( 1 + MA(1).B + MA(2).B
r(t)= residual at time t
and
( to be determined by model fitting )
C
for
bookings for M class for this flight,
for the six month sample.
AR3
for
= constant ;
AR(i) = coefficient i calculated for
the Moving Average components
MA(i) = coefficient i calculated for
the Auto-Regressive components.
76
The model estimated is statistically
because
the
calculated chi-square test statistic on
20 residual autocorrelations is 17.91,
at least at a confidence level of .90
=
22.3
.
Three
from
acceptable t statistics.
is
77.56,
regression
accepted,
which
five
,
meaningful
chi-square(15, .90)
parameters
do
not
exhibit
The estimated white noise variance
corresponds
of 8.81 .
which is
first
to
a
standard
error
of
From figure 4.01 one can observe that
the standard deviation of the time series variable is 8.89
No much explanatory power was gained with this ARIMA model.
ITERATION
ITERATION
ITERATION
RESIDUAL SUM OF SQUARES .....
RESIDUAL SUM OF SQUARES .....
RESIDUAL SUM OF SQUARES .....
13739
13434.9
13346.9
SUMMARY OF FITTED MODEL
parameter
estimate
stnd.error
t-value
AR ( 1)
AR ( 2)
AR ( 3)
MA ( 1)
MA ( 2)
MEAN
CONSTANT
1.00765
-.11036
.02083
1.07407
-. 22857
22.04925
1.87547
.14360
.17264
.08176
.14845
.15545
1.33373
7.01705
-.63922
.25474
7.23533
-1.47036
16.53206
prob(>ItI)
.00000
.52353
.79923
.00000
.14329
.00000
ESTIMATED WHITE NOISE VARIANCE = 77.5587 WITH 172 DEGREES OF FREEDOM.
CHI-SQUARE TEST STATISTIC ON FIRST 20 RESIDUAL'AUTOCORRELATIONS = 17.9051
Table 5.01 Time Series Analysis
ARIMA ( 3,0,2 )
Reservations on Boarding Day
M-class
Fight F1
Market A/B
Another time series model was estimated for the
=
D(t)
series
MBD(t)
intorduced in the model
for
seasonal
a
.
the
which corresponds to
original series differenced once,
MBD(t-1).
A week seasonality was
Table 5.02 shows fitting
results
The
with length of 7 days.
ARIMA(0,1,4),
equation that represents the model is
D(t) = C + MA4
.
D(t)= MBD(t) -
MBD(t-1)
r(t)
where
MBD = final reservations, M-class;
MA4 = 1 + MA(7).B
7
+ MA(14).B
14-
21
+ MA(21).B
+
28
+ MA(28).B
r(t)= residual at time t
( to be determined by model fitting
and
= constant
C
;
MA(i) = coefficient i calculated for
the Auto-Regressive components.
The calculated chi-square statistic is 17.72
< 22.3 ),
which means
that
the
Estimated white noise variance,
before:
108.23
of 10.40.
,
model
can
this time,
be
(
accepted.
was higher than
which means a standard error of regression
ITERATION 1:
ITERATION 2:
ITERATION 3:
RESIDUAL SUM OF SQUARES .....
RESIDUAL SUM OF SQUARES .....
RESIDUAL SUM OF SQUARES .....
16433.8
15282
15260.9
SUMM.ARY OF FITTED MODEL
parameter
estimate
stnd.error
t-value
SAR( 7)
SAR( 14)
SAR( 21)
SAR( 28)
MEAN
CONSTANT
-.70067
-.43076
-.24550
-.32319
-. 10325
-.36782
.08339
.10223
.10321
.09446
.30574
-8.40285
-4.21363
-2.37860
-3.42135
-.;33770
prcb(>jtj)
.00000
.00004
.01872
.00082
.73609
MODEL FITTED TO SEASONAL DIFFERENCES OF ORDER 1 WITH SEASONAL LENGTH = 7
ESTIMATED WHITE NOISE VARIANCE = 108.233 WITH 141 DEGREES OF FREEDOM.
CHI-SQUARE TEST STATISTIC ON FIRST 20 RESIDUAL AUTOCORRELATIONS
17.7191
Table 5.02 Time Series Analysis
ARIMA ( 0,1,4 )
Reservations on Boarding Day
M-class
Fight F1
80
Market A/B
to
not related
reflect
the
of error in each model presented is
level
The
poor
model
related
time
for
day
such
as
day
used
alone
to
describe
random process associated with bookings.
the need to make forecast for a
ahead,
the
flight/class
a
patterns,
they cannot be
seasonality,
days
they
variability of the parameter we are modelling.
Although reservations on boarding
exhibit
Instead,
specification.
error
week
the
Furthermore, given
departure,
flight
associated
of
say
28
with the forecast will
sharply increase as the time interval increases.
These two
examples
are
illustrative
of
the
randomness that is present in reservations data. Rather than
showing
how to use ARIMA models,
they serve to illustrate
the difficulty posed to the forecaster in modelling and
seemingly
disadvantage
of
time
series models.
Moreover,
because no structural behavior is associated with
series
model,
the
any
time
model
specification
becomes extremely time
clear
cut
can
consuming.
No
modelling,
not in an reasonable fashion, when one uses time
series models.
needed.
approach
be
developed
in
Just too many forecaster's interventions are
series analysis were applied in the remaining
Time
markets, and the results obtained were similar.For the above
reasons,
the use of time
forecasting
model
becomes
examples
a
forecasting method.
series
unattractive,
forecaster
analysis
in
although
should
never
reservation
with only two
discard
a
One
should
note
that
in the above presented
models, only reservations data on boarding day were used. No
other available data,
such
as
reservation
made
28
days
before departure for the same flight, or reservation for the
same
class
in
reservations data,
the
same
day,
were ever used.
or
even
other
That leads to the
flight
next
step which is the use of Regression Analysis in reservations
forecasting.
5.3 REGRESSION ANALYSIS
The
use of Regression Analysis in reservations
the
forecasting implicilty leads to
that
presumption
one
knows something about causal relationships that are relevant
and influences booking patterns for a given flight.
assume that there is a relationship between
in
a
directional
levels
Cause-effect
instance.
for
market,
booking
One may
relationships can also be tested among different classes
in
the same flight/market. One could argue that some passengers
that
made reservation on a full Y class did so because they
did not find a seat
among
classev;
in
among
the
"M
flights
examples that one could
compartment".
Correlation
and between markets are few
test
in
developing
need
to provide estimates of final
a
regression
model.
Given
seat requests,
forecaster
can
the
for a given flight,
launch
for a given class,
himself in model building,
that he has at his disposal a large database.
is usually available
includes :
83
the
knowing
The data that
(1) historical data from past operations of the
same flight, for
all classes, which can be
retrieved
the
from
airline
reservation
system;
(2) reservation data for the flight itself;
(3) current and past applicable fares;
(4)
changes
in
schedules/airlines
in
the
market;
(5) level of service variables, such as a new
flight was introduced in the market;
(6)
time related information,
will
depart
on
a
e.g.
as flight
Friday
morning,
Thanksgiving week;
(7) socio-economic variables
Historical
data from past flight operation can
be retrieved for all classes,
and flight build up
can be derived from the database.
patterns
Data can be retrieved and
analyzed in a seven days intervals, for instance. That is to
say
that
for
reservations
(MBD),
the
data
7 (M7),
14
M
can
class
be
(M14)
departure and so forth.
of
flight
retrieved
,21
(M21)
F1,
market
A/B,
for the boarding day
days 'before
flight
analysis
regression
about
infer
consequences
in
that,
unfortunate
one could
By including such variables,
models.
regression
fare
of
this
data was not so
fare
thesis,
very
is
It
changes.
of
power
explanatory
the
increase
should
variables
fare
Some problems were detected in the
readily available.
A
micro/macro-economic
with
model
available.
also
Current and past fares are
database that made them of little use. A "pollution" problem
was
particularly
detected in the highest fare class,
with
makes
them
exception only of the I/J & J/I markets,
are
statistical analysis and demand modelling
far
as
unusable
which
concerned.
Because reservations
not
basis,
does
explanatory
power.
on
modeled
leg
a
the absence of a fare variable
on a O&D basis,
represent
implicitly
not
were
a
then fare
If O&D forecasts are needed,
variables should inevitably be incorporated,
model
the
in
loss
other
as well
socio-economic variables, e.g income level, population ,etc.
Variables type (4) and (5) cannot be explicitly
in
introduced
the
model.
An example of a methodology for
determining
the
relationship
and
the
level
demand
Eriksen,
of
between
service
Scalea and Taneja [8].
is
created
service
index
models.
The level of service
In
has
air
transportation
been
essence,
proposed by
level
a
of
and used in regression analysis
index
generated
is
a
non-
dimensional
generalized
trip time scaled from zero to one,
which takes into account not only the number of flight,
also the number of intermediate stops,
but
direct or connecting
service, speed of aircraft, and most important, the matching
of departure schedules to time variability of demand. By the
same token that fares cannot be
(only
in
O&D models),
introduced
in
the
model,
this index cannot be applied to the
regression models developed in this thesis.
Although some variables above mentioned are not
explicitly considered in the regression models presented
in
this thesis, some structural behavior are implicitly assumed
here.
For
instance,
fare
elasticities
are
increase as one moves from a potential full
to
the
lowest
fare potential passenger.
expected
fare
to
passenger
Correlations are
expected to be higher in adjacent classes in comparison with
extreme
classes,
for
instance
,
or,
in
other
words,
reservations on the lowest fare class are not expected to be
an important explanatory variable in the regression model of
the highest fare class.
A coherent fare structure,
as well
associated set of restriction, are assumed in each and every
market analyzed. As the models presented here are the result
of a search of a structural behavior among classes and
even
markets, those implicit assumptions are of very importance.
Under these circumstances,
the models that are
presented here can be called as booking performance
models,
in the sense that they search for structural behavior and or
performance of booking for a given class, on a given flight.
The
search of a structural behavior across markets leads to
find a minimal set of explantory variables that
to
and day-of-week seasonal
week-of-year
as
such
variables,
related
time
and
classes,
and
flights
among
classes,
among adjacent fare
and bookings-to-come,
bookings-on-hand
between
examined
are
relationships
causal-effect
model,
general structure
called
so
the
building
In
these
of
function
a
as
is able to describe reservations
variables.
one
that
is
The rational in developing this kind of model
expects
a
is expected to hold across flights and markets.
that
model
is
which
model,
the formulation of a general structure
variables.
that
One may argue
loss
is
there
general
a
model
It is true that
precision when a general structure is used.
there are losses involved in adopting
in
structure
A model that is market and flight specific is by all
model.
means better than a generalized one. Because it is specified
and fitted with the data of one flight
show
fitting
better
specific
market/flight
especially
when
one
results.
Building
a
time
considers
the
may
be
flights/markets served by an airline.
variable
that
is
only,
relevant
for
the
it
models
tends
large
One may
are
that
consuming
to
task,
number
of
introduce
a
flight F1 in the A/B
market, whereas the same variable may not be of relevance in
the flight F1 in the E/F market.
Therefore,
building
models
that
are
flight/market specific has some practical disadvantages when
one
considers
that a vast set of forecasting models has to
to be generated
introduced
in
for
the
an
A/B
airline.
When
market,
for
a
new
flight
instance,
is
a general
structure model,that was fitted for the A/B market is likely
to yield better forecast than the one particularly specified
and fitted to any flight in the market. One also has to have
in mind that schedule
airline
industry,
changes
and
the
happen
ability
specific models is sharply reduced.
higher
stability
in
schedules
very
of
often
in
building
the
flight
It would require a much
that
is
observed
in the
airline industry.
Therefore,
developed
and
relevant,
those
the
if a general structure model can be
incurred
models
are
precision
preferred.
losses
With
are
a
not
general
structure model approach, forecasts of final bookings can be
made
more
efficiently
without
spending
too much time in
modeling.
Another
positive
consequence
of
a
general
structure model is the associated reduction in data handling
routines that are required for model fitting. Moreover, with
a
market specific approach,
one could run into the problem
88
of having to re-specify the model as time goes
the
also
could
model
specific
be
for
because
by,
a
determined
a model dependent
period/season of the year, or even worse,
on the data set used for fitting.
regression models presented in this thesis
The
are the result of a search of
Several
each
model
market,
regression
a
structure
general
model.
specifications and variables were tested for
and
pooled
analysis
together
in
a
Variables
effort.
time
consuming
that
showed
statistical adherence in most of all markets were kept.
The general
includes
structure
model
developed
here,
a long term cyclic (seasonal variation) component,
recent historical data,
minimum cycle is a week,
of-week variation.
as well
as
actual
bookings.
The
and the model is sensitive to day-
The variables used
model
to
forecast
bookings
class, for a given market,
MtBD ),
in
to
the
come,
general
structure
for flight F1 in M
from t days before departure,
(
are as follows:
ONE
- a constant or base booking level;
DAYS
- day of week dummy variables,
(MO,TU,WE,TH,FR, and SA relative to
SU);
Mt
- bookings-on-hand, on day t, M-class;
INDEX
- week of year non-dimensionalized index
for traffic levels and growth through
the major hub of the airline;
S5MAiB - historical average of bookings made in
M-class , between day t and departure,
for the most five recent departures of
the same flight Fi ;
MTt
- total bookings on hand ,for all future
flights in the same directional market
t days before departure.
Long-term cycles and market growth are expected
to be captured by the INDEX variable, while S5MAiB should be
sensible to shorter term trends.
Regression
analysis
Tables 5.03 through 5.12 .
results
are
shown
from
Table 5.03 shows fitting results of the general
applied
structure model
The subset used was from
the original data set.
of
a
in
fitted
is
The model
also includes a constant term.
subset
The model
variables are included in the model.
explanatory
Ten
Fl.
flight
A/B,
market
to
observation #35 to observation #181,
which means a total of
147 observations. The sample size was reduced to 147 because
of
variable.
S5MA
the
for
consequently the first non-trivial S5MA is
#35
.
( 35 = 7
5
The
and
S5MA is a 5-week lag average,
observation
).
degree
of
freedom for the F-statistic is
therefore equals to 10 (the number of explanatory variables)
in the numerator, and equals to 136 ( number of observations
minus the number of parameters to be estimated,
10-1),in the denominator.
Therefore,
the F-Statistic (10,136),
at 95%
1.91.
All
or 136=147-
the critical value of
level
of
confidence
is
which means that
runs exhibit a higher F level,
the models are accepted.
The adjusted R-squared , or R-bar squared,
all
is
runs
characterized
by
a
low
value.
remember that the dependent variable is the
difference
of
final
for
One has to
result
the
of
bookings and bookings-on-hand.
Model
fitting for differenced variables will always exhibit low
squared
statistics.
This
explain,
to some extent,
square is relatively low for each model run.
R
why R
In this example there was a
for Mondays,
Fridays,
Thursdays,
statistically
different
Sundays.
Bookings-on-hand
The
from
distinct
and Saturdays. They were
the
base
and
day,
INDEX
significant in all runs : in any run,
the
coefficients
the
were
greater
behavior
than
which
were
variables
were
t
statistic
critical
of
value
t(136)=1.98.
This
fitting
model.
capture
results
market/flight
is
an
example
of
model
that is expected for the general structure
The INDEX variable is expected to be significant and
week-of-year seasonality.
A "local" seasonality is
also expected to be captured by day-of-week dummy variables.
It was indeed possible for this flight/market to detect some
different behavior for some dummy variables.
TABLE 5.03
REGRESSION ANALYSIS
SUMMARY
FL I GHT
MARKET A/B
-
-- --- -- ---
-
- --- -- ---- --
-- --- --
-- -- -- --
MODEL RUN
(DAY)
t=28
t=21
DEPENDENT
VARIABLE
M28 BD
15.56
8.32
6.38
0.45
0.41
11.17
M21
MEAN
STD. DEV.
STD. ERROR OF REGRESSION
R SQUARED
R-8AR SQUARED
F-STATISTIC (10,136)
VAR I ABLES
value
CONSTANT
MO
TU
WE
TH
FR
SA
Mt
INDEX
55MAt
MTt
-
-- --- --
- -- - --- --- -
t=7
6D
M14 BD
M7 BD
14.44
8.24
12.01
7.72
6.09
0.42
7.56
6.34
0.45
0.41
6.09
5.35
0.28
0.23
5.29
0.38
9.79
11.01
t
-
t= 14
stat
value
+ stat
value
34.56
-3.94
0.41
1.6
3.12
5.91
-5.11
-0.51
6.57
-1.98
0.19
0.81
1.34
2.93
-2.52
-4.23
33.87
-3.86
0.45
1.35
3.31
5.32
-5.14
-0.49
6.46
-1.96
0.21
.0.68
1.42
2.65
-2.55
-4.13
-0.11
-0.32
-0.15
-2.23
-2.15
-1.97
-0.09
-0.32
-0.15
-2.11
-2.16
-1.94
t
t stat
stat
value
31.61
-2.85
1.34
1.94
3.39
4.54
-3.81
-0.42
6.21
-1.51
0.66
1.01
1.52
2.32
-1.94
-3.95
24.04
-1.36
2.14
1.37
2.28
1.36
-20.9
-0.29
5.19
-0.87
1.21
0.82
1.18
0.75
-1.21
-3.18
-0.11
-0.23
-0.16
-2.31
-1.62
-2.25
-0.08
-0.13
-0.09
-2.18
-1.04
-1.57
Table 5.04 shows fitting results for flight F2,
in the B/A market.
This is an example of a
flight
in
the
reverse direction of the one shown in the previous example.
In
this example,
for all model runs.
was
also
low
F-statistics were acceptable
R-bar squared although almost
across
runs.
The
exhibited an interesting behavior.
Saturdays
variables
were
day-of-week
While only
variables
Fridays
and
statistically significant in the
day_28 run,
all days but Mondays were
day_7
The
run.
constant
bookings-on-hand
consistently for all runs.
significant
variable
It showed an
in
the
did not behave
almost/ acceptable
t_statistics in day_28 and day_7 runs while in between the t
values
were not acceptable.
very stable behavior,
The INDEX variable exhibited a
although not
all
t-statistics
were
acceptable.
This
statistical
Although
market/flight
behavior
some
for
coefficients
statistically determined,
acceptable.
the
When
compared
of
is
an
general
example of a mixed
structure
model.
the variables could not be
the overall model performance was
to Table 5.03,
one can observe
that relatively similar results were obtained for flights in
both direction of the markets defined by the citypair A&B.
TABLE 5.04
MARkET B/A
REGRESSION ANALYSIS
SUMMARY
FLIGHT
MODEL RUN (DAY)
t=28
t=21
t=14
t=7
DEPENDENT VARIABLE
MEAN
SD.
DEV.
STD. ERROR OF REGRESSION
R SQUAiRED
R-BAR SQUARED
F-STATISTIC (10,136)
M28 BD
20.46
10.45
9.03
0.31
0.25
5.86
M21 _D
18.77
10.22
8.59
0.34
0.29
6.99
M14 8D
16.61
9.78
8.21
0.34
0.29
7.02
M7 BD
1021
8.01
6.81
0.32
0.27
6.55
VARIABLES
value
t stat
value
t
stat
24.31
2.69
26.83
3.11
1.71
0.58
0.49
1.37
-2.15
-0.75
-2.49
-0.91
-1.24
-0.43
-2.09
-0.76
-7.53
-2.35
-9.59
-3. 11
-2.01
0.66
-3.43
-1.19
-1.85
-5.69
-S.02
-1.71
-0.42
-1.41
-0.12
-0.56
-0.07
-0.91
INDEX
-0.11
-1.37
0.38
3.01
SSMAt
0.37
3.07
-0.08
-0.68
MTt
-0.11
-1.21
------------- - --------------------------- ------ - ---------CONSTANT
MO
TU
WE
TH
value
2659
1.16
-2.97
-4.32
-9.37
-4.37
-4.26
0.006
-0.11
0.35
-0.16
t
stat
value
t
stat
3.24
22.31
3.29
0.05
0.44
0.02
-1.14
-3.66
-1.71
-1.61
-7.01
-3.15
-3.21
-8.93
-3.73
-1.59
-7.31
-3.17
1.51
-4.78
-2.04
0.03
-0.16
-1.49
-1.52
-0.08
-1.38
3.06
0.19
40~'94
-1.88
-0.02
-0.33
-------------------
Table 5.05
flight
F4
in
were
this
In
results
for
day-of-week
all
example
the
from
different
fitting
R-bar statistics are little
the C/D market.
higher for this flight.
variables
model
shows
Sundays.
day,
base
in any
Thursday was constantly the busiest day in any week,
model run. The bookings-on-hand variable was not significant
in
any
model
run.
The
and
INDEX
S5MA
variables
were
constantly significant across model runs.
The general structure model behave as expected.
Fitting improvement was observed,
when compared to previous
flights/markets.
5.06
Table
shows
fitting
model
results for
R-bar squared statistics
flight F3 in the D/C market.
were
improved. All day-of-week variables were significant, in any
model run.
Bookings-on-hand were not significant again. The
INDEX and S5MA variables were siginificant in
most
of
the
runs.
The
C/D market
overall
example.
That
model behavior was similar to the
is,
all
dummy
significant in the C&D citypair markets.
variables
were
The INDEX and S5MA
variables did contribute to the general structure model. The
remaining
statistics.
variables
did
not
explicitly
improve
model
TABLE 5.05
REGRESSION ANALYSIS
SurMARY
MAR<ET C/D
MODEL RUN
FLIGHT
(DAY)
DEPENDENT
VAR I ABLE
MEAN
STD. DEV.
STD. ERROR OF REGRESSION
R SQUARED
R-BAR SQUARED
F-STATISTIC (10,136)
:
VARIABLES
--
-- -- --
CONSTANT
MO
TU
WE
TH
FR
SA
Mt
INDEX
S5MAt
MT+-
t=28
t=21
t=14
t=7
N28_8D
15.93
9.25
6.82
0.49
0.45
13.12
M21 8D
15. 11
8.84
6.63
0.47
0.43
12.28
M14_8D
13. 57
8.42
6.21
0.49
0.45
13.2
M7 BD
9.81
6.79
5.38
0.41
0.37
9.6
value
-
t
stat
- --- -- ----- -- --- ---- -- -- --- --
*
,
*
i
*
-18.83
5.49
6.63
9.38
11.68
7.92
6.81
-0.04
0.21
0.34'
0.25
value
-- -- -- --- --
-2.95
2.33
2.67
3.44
3.94
2.81
2.62
-0.09
3.05
3.12
1.91
-18.99
6.34
6.48
9.39
11.04
8.11
6.78
0.11
0.21
0.31
0.08
t stat
--
- -- --
-3.09
2.74
2.69
. 3.56
3.82
2.93
2.61
0.38
3.35
2.91
1.01
value
t stat
value
t stat
-3.04
2.24
2.23
2.74
3.45
2.33
1.83
0.45
2.93
3.01
1.91
-18.18
3.78
4.98
5.42
7.21
4.87
3.35
0.03
0.18
0.19
0.04
-3.64
1.98
2.53
2.45
2.97
2.08
1.49
0.22
3.69
-- --
-17.68
4.81
5.08
6.91
9.42
6.03
4.51
0.09
0.17
0.31
0.12
2.23
0.87
REGRESS ION AFNALYS IS
SUMMARY
TABLE 5.06
F3
FL I GHT
MAPJET D/C
MODEL RUN
(DAY)
t=28
-
-- -- ----- -- --- -
DEPENDENT VAR I ABLE
MEAN
STD. DEU.
SID. ERROR OF REGRESSION
R SQUARED
R-BAR SQUiRED
F-STATISTIC (10,136)
-
---
M21_8D
29.44
15.24
10.08
0.59
0.56
19.76
--
--------------
-----------
value
*
*
-5.21
2.08
8.15
14.19
11.84
10.31
-7.64
0.23
0.19
0
0.41
-0.29
t
t=14
t=7
M14_BD
25.33
13.71
9.67
0.53
0.51
15.73
M7 BD
16.63
10.33
7.88
0.45
0.42
-- --- - -
M28_80
31 .78
15. 66
10.04
0.61
0.58
21.91
VARIABLES
CONSTFNT
MO
TU
WE
TH
FR
SA
Mt
I1DEX
S5MAt
MTi:
----------------------
-------------
-------------------------------
stat
-0.56
0.52
2.24
3.46
3.02
2.84
-2.17
0.53
2.09
3.53
-1.27
value
-4.47
2.88
9.13
13.91
11.91
10.41
-7.66
-0.18
0.17
0.38
-0.12
---------------- ------------------------
-----
--------
t
stat
-0.46
0.87
2.47
3.34
3.02
2.89
-2.14
-0.62
1.89
3.31
-0.66
value
-3.51
4.38
9.95
14.11
10.94
6.49
-7.13
-0.27
0.14
0.28
0.07
-----------
11. 48
------
---------
t
stat
-0.38
1.35
2.72
3.41
2.84
1.82
-2.06
-1.16
1.64
2.44
0.53
value
t stat
-3.53
5.84
9.67
11.51
6.21
0.39
-5.73
-0.11
0.11
0.11
0.51
-0.47
2.24
3.27
3.46
1.94
0.13
-1.97
-0.83
1.63
1.25
0.73
Table
5.07
shows
flight F1 in the E/F market.
very low.
model
fitting
R-bar squared
They range from 0.19 to 0.16
F statistics
were
F(10,136)=1.91,
acceptable.
at
a
The
.
results for
statistics
are
Nevertheless, all
critical
value
95% confidence interval.
is
As it gets
closer to the departure day the more significant the day-ofweek dummy variables are. While the INDEX and S5MA variables
were not significant to the
variables
exhibited
model
acceptable
runs,
the
Mt
t-statistics.
and
It
MTt
is
an
example of the opposite behavior so far observed.
Table 5.08
shows
flight F2 in the F/E market.
model
fitting
results
for
R-bar squared statistics are a
little higher than in the previous example. All Fstatistics
were
also
marginally
acceptable.
observed
for
Statistical
day-of-week
significance
variables.
was
The
Mt
variable,
bookings-on-hand was not significant in any model
run.
INDEX
The
and S5MA were significant in this example.
Total bookings-on-hand (MTt) was not so
significant
as
in
the previous example.
These
two
examples
illustrate
the
behavior expected for the (INDEX & S5MA) variables
&
MTt) variables.
others are not,
are
included
distinct
vs.
When the first two are significant,
and vice-versa.
in the model,
It explains why both
(Mt
the
sets
together with the fact that no
one can a priori predict which two will be significant.
99
REGRESSION ANALYSIS
SUNMf)RY
TAdBLE 5.07
MARKET E/F
MODEL RUN (DAY)
DEPENDENT VARIABLE
MEAN
STD. DEV.
STD. ERROR OF REGRESSION
R SQUARED
R-BAR SQUARED
F-STATISTIC (10,136)
|
t=28
t=21
t=14
t=7
1128_BD
10.61
10.46
9.4
0.24
0.19
4.45
M21 BD
9.71
9.07
8.45
0.19
0.13
3.21
M14_BD
8.08
7.12
6.81
0.15
0.09
2.41
M7_8D
6.63
5.67
5.21
0.21
0.16
3.73
value
t stat
Value
t stat
value
t stat
-------------- ------ - -- ------------ - - --------- - ------ - ----- 0.42
-5.58
-1.01
-2.11
1.71
-0.42
CONSTANT
3.26
1.48
1.41
2.73
1.01
0.46
MO
1.67
3.45
1.61
0.62
-0.85
-0.29
TU
2.42
1.35
0.46
1.65
1.15
- 0.62
WE
1.55
6.27
5.98
4.54
2.26
2.95
TH
0.72
2.79
0.91
1.99
3.01
1.36
FR
0.87
4.05
2.51
0.92
1.89
1.34
.1 0
-0.51
-3.79
-0.21
-0.67
-4.35
Mt
0.07
1.59
0.01
0.22
2.74
0.13
I NDEX
1.67
0.97
0.15
0.16
1.27
0.13
ssMAt
0.16
3.32
0.35
2.22
2.92
0.39
MTt
VAR IABLES
o
F1
FLIGHT
value
4.93
3.76
4.66
3.88
7.06
2.61
1.68
-0.14
-0.04
0.07
0.14
- stat
1.57
2.23
2.81
2.39
4.31
1.52
1.01
-2.06
-1.36
0.99
2.77
TABLE 5.08
MARKET F/E
REGRESSION ANALYSIS
SUMHARY
FLIGHT
MODEL RUN (DAY)
t=28
t=21
t=14
t=7
DEPENDENT VARIABLE
MEIN
STD. DEV.
STD. ERROR OF REGRESSION
R SQUARED
R-BAR SQUARED
F-STATISTIC (10,135)
M28 BD
13.81
9.45
7.83
0.35
0.31
7.57
M21 _D
12.68
9.02
7.94
M14 8D
11.81
8.44
7.64
0.23
0.17
4.16
M7 BD
8.96
6.81
6.48
0.15
0.19
2.48
VAR IABLES
value
CONSTANT
-13.58
2.51
4.61
3.18
3.55
1.71
3.57
0.04
0.16
0.61
0.08
INDEX
SSAt
MTt
0.28
0.22
5.17
t stat
-2.55
1.01
1.83
1.29
1.42
0.68
1.31
0.26
3.08
5.43
1.11
value
-11.93
3.28
4.06
3.36
3.13
0.48
3.06
0.02
0.15
0.53
0.04
sitat
value
-2.184
1.31
1.56
- 1.33
1.21
0.18
1.08
-0.13
2.81
4.74
0.54
-8.24
3.91
4.31
4.07
3.51
2.11
3.82
-0.04
0.11
0.46
0.06
t
£ stat
-1.54
1.66
1.68
1.65
1.38
0.82
1.39
-0.29
2.01
4.17
0.89
value
-3.52
3.01
4.24
3.56
1.79
2.41
4.87
-0.14
0.05
0.29
0.07
t
stat
-0.77
1.44
1.89
1.64
0.81
1.11
2.13
-1.54
1.25
3.11
1.42
Table 5.09
F1
flight
shows
model
for
Fstatistics are acceptable,
and in
the
day_7
it reaches the minimum so far observed, 1.92 . In this
run,
example,
only
observed
for
extremely
the
One
significant.
INDEX
variable
reason
possible
the
low,
dependent
ranging
respectively.
As
a
from
always
smaller
6.65
statistically
the
high variation
While
to
means
3.97,
ranging from
consequence,
reduced. Nevertheless,
is
is
variable.
deviations are relatively high,
was
results
R-bar squared statistics are
in the G/H market.
again low.
fitting
model
are
standard
6.7
to
5.3,
performance
is
the standard error of the regression
than
the
standard
deviation
of the
dependent variable.
Table 5.10
flight
F2,
in
extremely low,
shows
model
the H/G market.
fitting
results
for
Although R-bar squared are
one can observe the distinct model behavior.
In this example, all day-of-week variables were significant.
The
INDEX
MTt
and
and S5MA variables were also significant,
Mt
showed
bad
tstatistics.
Again,
while
only
two
variables were significant.
The flight F1,
that even for a flight with
market H/G, example illustrates
very
structure model can be used.
102
small
load
the
general
TAB3LE 5.09
REGRESSION ANALYSIS
SUMMiRY
MARKET G/H
FLIGHT
- -- - -
-----------
-----------------------
---
---
---
---
MODEL RUN (DAY)
t=28
t=21
t=14
tz7
DEPENDENT
N28 8D
6.04
6.65
5.56
0.35
0.31
6.37
M21 BD
5.46
6.41
5.47
0.32
0.27
5.68
M14 8D
4.88
6.12
5.57
0.23
0.17
3.58
M7 BD
3.97
5.25
5.07
0.14
0.06
1.92
VARRIABLES
va I'ue
CONSTANT
MO
TU
WE
TH
FR
SA
Mt
INDEX
-5.35
-1.61
-0.54
-2.05
-0.81
4.31
-1.31
-0.18
0.12
0.13
-0.51
VAR I ABLE
MEAN
5TD. DEV.
STD. ERROR OF REGRESSION
R SQUARED
R-BAR SQUARED
F-STATISTIC (10, 136)
ssm)t
MTt
t
stat
value
-1.45
-0.91
-0.31
-1.16
-0.45
2.45
-0.53
-0.83
4.35
1.48
-3.44
-4.22
-1.39
-1.26
-2.61
-2.05
3.54
-0.43
0.02
0.11
0.13
-0.61
t
stat
value
-1.16
-0.81
-0.71
-1.49
-1.17
2.03
-0.17
0.11
4.13
1.61
-3.54
-4.88
-1.41
-1.06
-2.65
-1.53
3.31
-1.31
-0.24
0.11
0.09
-0.23
t
stat
value
-1.32
-0.79
-0.59
-1.49
-0.86
1.83
-0.52
-1.17
3.88
1.01
-1.67
-3.02
-1.68
-1.38
-2.27
-1.78
0.96
-2.03
-0.11
0.08
0.02
-0.07
---
t
staL
-0.89
-1.14
-0.85
-1.41
-1. 11
0.57
-0.91
-0.79
3.13
0.21
-0.74
REGRESS I ON ANALYS I5
SUMItARY
TABLE 5. 10
MARKET H/G
FL IGHT
F2
MODEL RUN (DAY)
t=28
t=21
t=14
DEPENDENT VAR IABLE
MEAN
STD. DEV.
STD. ERROR OF REGRESSION
R SQUARED
R-BAR SQUARED
F-STATISTIC (10,132)
128_ED
12. 51
11.58
10.38
M21 8D
11.26
11.21
10.44
0.19
0.13
3.18
M14 BD
9.88
0.25
0.19
4.46
VARIABLES
I.-
o
value
---------------------------------------------------------------
CONSTANT
MO
TU
WE
TH
FR
SA
Mt
:
-14.72
-12.92
:
INDEX
ssMAt
MTt
5. 69
-12.27
-13.01
*
-13.64
-11.01
-0.14
0.09
0.59
0.15
t
--
stat
---
value
------
1.42
-3.21
-3.38
-3.85
-3.33
-3.56
-2.88
-0.71
2.81
4.56
0.89
-----
---
6.14
-11.61
-12.85
-15. 14
-12.01
-12.46
-10.77
-0.26
0.09
0.45
0.22
M7_80
7.13
7.45
7.02
0.17
0.11
9.77
9.14
0.18
0. 12
3.01
stat
t
----
value
--------
1.52
-3.01
-3.31
-3.95
-3.08
-3.21
-2.81
-1.33
2.64
3.37
1.32
----
-------
4.22
-9.23
-10.81
-
12. 01
-9.55
-10.97
-10.61
-0.21
0.08
0.35
0.23
2.81
t
stat
----
1.18
-2.71
-3.16
-3.56
-2.78
-3.23
-3.15
-1.14
2.51
2.95
1.51
value
---------
t
sta
----
3.45
-7.03
-7.59
-7293
-6.52
-8.58
-8.87
-0.07
0.06
0.19
0.14
2.61
2.1
.41
Table
shows
5.11
fitting
restults for
The
Y-class.
for the
in the I/J market,
flight F1,
model
same
general
structure is applied to the Y-class in the Canadian
market.
R-bar squared statistics are low as it were in
the
case of the M-class, for domestic U.S. markets. In the day_7
run,
all
model
statistics dropped significantly,
and the
model exhibited a distinct behavior: only two variables were
significant. Nevertheless,
all
runs.
The
day-of-week
expected behavior,
different
Fstatistics were acceptable for
dummy
variables exhibited the
that is for some days (e.g.
behavior
from
TU
or
SA)
the
base day was observed,
i.e.
t_statistics were significant.
Bookings-on-hand/ (Yt)
were
significant
for
all model runs,
but day_7 run.
variable was marginally accepted in
some
The INDEX
runs,
while
the
remaining variables were not.
Table
5.12
shows
model
fitting
results for
flight F1 in the J/I market, for the Y-class.
R-bar squared
statistics
the
were
a
little
higher
that
in
previous
example.
In the day_28 model run it was 0.41 and it dropped
to
on
0.16
the
day 7.
exhibit good tstatistics.
picked
up by the model.
the first two model runs,
variable
was
significant
The day-of-week variables did not
No "local" seasonality could
be
The Yt variable was significant in
while
YTt
was
not.
in all model runs.
significant.
105
The
INDEX
S5MA was not
REGRESS 10N ANALYS IS
SUMARY
TABLE 5.11
MAIRKET
I/J
FLIGHT
Fl
MODEL RLN (DtAY)
+t=28
t=21
t14
t=7
DEPENDENT VARIABLE
MEAN
STD. DEU.
STD. ERROR OF REGRESSION
R SQUIRED
R-BAR SQUARED
F-STATISTIC (10,136)
:
Y28 BD
22.98
13.36
11.3
0.33
0.28
6.81
Y21 8D
21.36
12.21
10.77
0.27
0.22
5.13
Y14 BD
18.48
10.48
9.76
0.18
0.12
3.18
Y7BD
13.11
8.19
7.98
0.11
0.04
2.81
UAR IABLES
:
value
CONSTANT
MO
TU
WE
TH
FR
SA
Yt
INDEX
S5MAt
MTt
48.22
-5.24
-10.99
-3.93
-4.64
5.91
-6.29
-0.72
-0. 11
-0. 15
0.03
t
sfat
value
t stat
value
t stat
value
5.29
-1.28
-2.98
-1.01
-1.29
1.65
-1.79
-5.69
-1.64
-1.25
0.46
45.5
-3.34
-8.91
-1.97
-3.87
6.01
-6.36
-0.51
-0. 11
-0. 15
0.01
5.15
-0.86
-2.52
*--0.53
-1. 12
1.75
-1.91
-3.96
-1.49
-1.29
0.21
35.56
-0.41
-5.22
1.19
-1.89
6.49
-5.49
-0.27
-0. 11
-0.09
0.02
4.29
-0.11
-1.59
0.34
-0.61
2.09
-1.81
-2.21
-1.86
-0.84
0.37
25.51
1.22
-0.56
2.01
0.37
3.79
-3.42
-0.01
-0.08
-0.05
-0.05
t stat
3.62
0.41
-0.21
0.71
0.14
1.45
-1.35
-0.02
-1.89
-0.64
-1.01
TABLE 5.12
MARKET J/I
REGRES51ON ANALYSIS
SUMMARY
FI
FLIGHT
MODEL RUN (DAY)
DEPENDENT UARIA8LE
MEAN
STD. DEV.
STD. ERROR OF REGRESSION
R SQUARED
R-BAR SQUARED
F-STATISTIC (10,134)
:
:
t=28
t=21
t=14
t=7
Y28_8D
20.98
13.87
10.74
0.44
0.41
10.61
Y21_8D
19.42
10.34
9.53
0.21
0.15
3.54
YI4_BD
17.01
8.29
7.81
0.17
0.11
2.81
Y7_BD
11.36
6.62
6.04
0.22
0.16
3.88
VARIABLES
v'alue
CONSTANT
MO
TU
WE
TH
FR
SA
40.03
-3.59
-4.79
-0.84
-1.99
1.43
-0.41
-0.89
-0.15
0.24
0.07
Vlt
INDEX
55Mit
YTt
*
t
stat
6.84
-1.07
-1.39
-0.25
-0.58
0.42
-0.12
-6.22
-3.27
1.82
0.92
value
31.89
-3.37
-0.81
2.82
0.99
3.42
0.01
-0.47
-0.14
0.18
0.11
t
stat
value
5.92
-1.13
-0.25
0.91
0.32
1.13
0.01
-3.52
-3.51
1.55
1.58
23.67
-2.13
2.34
5.96
3.21
6.15
2.37
-0.11
-0.11
0.05
0.03
t
stat
value
t stat
5.16
-0.87
0.91
2.32
1.26
2.44
0.94
-0.94
-2.91
0.48
0.59
18.41
0.29
2.47
6.92
3.17
5.27
0.71
0.06
-0.06
-0.06
-0.08
5.04
0.15
1.24
3.45
1.61
2.73
0.35
0.81
-2.11
-0.81
-1.81
The
market.
adherence
For instance,
the
of
the
variables
vary from market to
model
generalized
the
in
considered
statistical
bookings-on-hand
variable
was
statistically significant in the directional A/B market, but
in
the
other
markets,
model.
direction
it
was
not.
the INDEX and S5MA variables
MTt
and
Mt
variables
In the majority of
contributed
to
the
seem to pick up explanatory
power when INDEX and S5MA variables can not. Therefore, they
work together in an almost
exclusive
basis.
Nevertheless,
all four are kept in the general structure model because one
can
never
general,
predict
the
what variables will be significant.
model
was
able
to
pick
up
In
/day-of-week
seasonality: day-of-week dummy variables were significant in
most of the cases.
variables
general
A reduction in the number of explanatory
included in the set of variables selected for the
structure
Durbin-Watson
model
causes
noticeable
reduction
of
statistics to values that are not acceptable,
which in turn means the presence of serial correlation. This
result leads to the conclusion
that
either
variables
can
only be added to this minimal set, or carefully replaced.
In
all
markets,
the
general structure model
outperformed simple estimates of bookings-to-come
based
on
local historical averages. The application 04f the model in a
Y-class,
as
in
the
case of the Canadian market,
yielded
equivalent fitting results, which may suggest that the model
can be adapted and applied to the Y-class.
108
CHAPTER SIX
CONCLUSION
6.1
SUMMARY
The forecasting module
Inventory
of
an
Automated
Control System is intended to provide the dynamic
booking limit adjustment routine with estimates of
bookings
for
individual future flights.
routine will then use these estimates of
to
Seat
calculate
how
many
expected
A seat allocation
expected
bookings
seats should be protected for each
upper fare class, in addition to bookings already on hand.
The initial work in forecasting involved models
that derived direct estimates of final bookings. Bookings by
fare class,
wanted
to
on the day of departure. was
the
forecast - the dependent variable.
variable
we
Cause-effect
relationships between this variable and a set of explanatory
(independent variable) as well qualitative and
time series behavior.
109
quantitative
these
cause-effect
of
analysis
statistical
with
together
relationships,
of
examination
Further
historical reservations data, have indicated that a focus on
The key factor
bookings-to-come would be a better approach.
to this
bookings
obtained across the
focus
the
With
testing.
data set selected for hypothesis
between
correlation
observed
and final bookings,
hand
on
an
was
conclusion
final bookings were indirectly
shifted to bookings-to-come,
bookings
estimated as the sum of actual
the
and
hand
on
estimated bookings to come.
A simple forecasting model is suggested for the
initial estimation of final bookings.
It consists of moving
average process that is sensitive to day of
variation
week
only. That is to say, for instance, that a 8-week average is
used
to
Monday).
on a specific day of
flight F1),
flight (e.g.
final bookings for a given
estimate
or
describe
week
(e.g.
Although no information on actual bookings on hand
for future flights are ever used, nor additional adjustments
variations
are made for cyclic or seasonal
weekly
the
basis,
assumption
implicit
other
of
approach is that a small sample of final demand
flights
will
be
that
on
this
simple
for
recent
representative of the demand for the same
flights in the near future.
The
first
step
in
reservations
forecasting
involves initial estimates of final bookings well in advance
110
of flight departures.
These estimates can be improved later
in the bookings process as more information
specific
flight
for
which
more
(data)
accurate
on
the
forecasts
are
needed.
The 'final
forecasting
to come,
module
step
in
the
development
of
a
is to improve the estimates of bookings
over those strictly
based
on
recent
historical
averages. The closer it gets to departure day, the better is
to
improve forecasts of final bookings.
better forecasts of final
bookings,
As a general rule,
via
bookings-to-come,
are obtained using regression analysis as the 28/days before
departure day threshold is surpassed.
The
models
analytical models (
Analysis)
to
in this thesis ranged from
Series
Analysis
and
Regression
non conventional models ( Bookings Curves and
ad-hoc methods).
(Box
Time
tested
Results obtained via Time Series
Analysis
and Jenkins' ARIMA models) were not encouraging enough
in providing better
obtained
via
estimates,
when
compared
to
results
Regression Analysis or even simple historical
averages. Any improvements were far outweighed by elaborated
data handling routines that would have to be used to fit the
models.
Non-conventional methods required too many "tuning"
interventions by the forecaster,
automated routine
is
results
improve
did
not
to
be
which is not helpful if an
developed,
over
111
and
again
Regression Analysis.
their
As a
result, effort was concentrated on Regression Analysis.
The first step was to develop
market
specific
models. Models were formulated and generated for the markets
The search was for a specific
in the data sample.
selected
structure ( model specification)
that
yielded
better
and
better model fitting results. At this level, model structure
was considered as independent of direction.
for instance,
market,
that the same model
should
also
estimated coefficients
hold
for
were
That is to say,
structure
the
for
B/A market,
allowed
to
be
the
A/B
although
directionally
sensitive.
Although it was possible to develop models that
were
specific
to
markets,
a
general structure model was
thought to be preferable in view of the associated reduction
in specific data handling routines that
for
model fitting.
would
be
required
As model generalization involves losses
in forecast precision caused by aggregation of markets, this
approach was preferred because these losses were
enough
produced
to
distort
with
consistently
the
better
forecasting
general
results.
structure
All
not
large
forecasts
approach
were
(less variable) than simple historical
average from a sample of recent flights.
*
A proposal of a general structure model is then
presented and tested in this thesis.
112
The general
structure
model
proposed
component
calculated
here includes a long term cyclic (seasonal)
short
,
over
recent
sensitive to day of
"good"
model
term
demonstrates how
and
trend
historical data,
week
fitting
cyclic
variations.
statistics,
Regression
Analysis
and the model is
Apart
this
can
components
from
model
be
showing
structure
used
in
a
forecasting module of an Automated Booking Limit System, and
thus provide improved estimates of bookings to come.
113
6.2 TOPICS FOR FURTHER RESEARCH
The
general
structure
model was developed in
this thesis for the M-class only.
As the typical
different
classes,
airline
models
need
tested for the remaining classes.
in
this
case
Y-class,
a
has,
also
at
least,
four
to be developed and
For the upper fare class,
similar
model structure can be
applied.
The expected set of build-up curves for
the
Y
class is rather similar to the set of M-class, and generally
speaking,
flights start to heavily build up during the last
week, before flight departure. Therefore, a bookings-to-come
approach, with the reference on the boarding day can also be
used.
Almost no "supply limitation"
is
also
expected
to
occur, since Y authorized booking levels are usually greater
than the total coach seating capacity.
As one moves to lower fare classes, both
up
(
behavior
change.
curves)
build-up
for instance,
For the B-class,
reaches
departure,
its
peak
at
and
least
say on day 14,
a
week
114
limitations
supply
the build-up curve
the
before
and from there on
cancellation is expected to be observed.
build
a
flight
period
of
The same phenomena
as far
is also observed in the lowest fare class, although,
as
seat
inventory
forecasting models will
phenomena
can
be
routines
control
not
taken
reference day to day 14,
be
into
are
developed.
account
concerned,
build-up
This
by
changing
as in the case of above
the
mentioned
example for the B-class.
On
the
other
hand,
the
supply
limitation
problem, caused by bookout phenomena, ( the class was closed
due to either a low authorized booking limit,
or by a large
number of reservations made in other classes.),
needs to be
carefully addressed.
A
longer
be
single
applied.
model needs to
equation
Instead,
developed,
system approach.
Now,
regression
a
using
For instance,
a
flight
build
up
no
simultaneous
equation
supply variables, such as authorized
explicitly
taken
into
cause-effect relationships such as,
for a given fight, for a given class,
the
can
multi-equation regression
levels for a given class need to be
account.
model
there was a cutoff in
because the authorized level for the
class itself was reached ( low authorized booking limit --low demand observed ---
>
> change in flight statistics) should
be investigated.
115
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Airline
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Littlewood,
Kenneth
Forecasting
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Seat
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Michael
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Buhr,
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