Airline fare and seat management strategies with demand dependency

Abstract

This paper conceptualizes various discount strategies used by airlines. Using a constrained revenue maximization model that assumes interdependent demand, it develops rules to guide decision-making, and shows that the large fare discount-many discount seats and small fare discount-few discount seats strategies are optimal. Empirical support is provided for the large fare discount-many discount seats, the no fare discount-moderate discount seats and small fare premium-few discount seats strategies. In addition it identifies the large fare premium-very few discount seats strategies. We argue that these strategies are used in various demand situations and allow airlines to price discriminate.

Full text

Airline fare and seat management strategies with demand dependency
K. Obeng
a
,
*
, R. Sakano
b
a
Department of Marketing, Transportation and Supply Chain, School of Business and Economics, North Carolina A&T State University, Greensboro, NC 27411, USA
b
Department of Economics and Finance, School of Business and Economics, North Carolina A&T State University, Greensboro, NC 27411, USA
abstract
This paper conceptualizes various discount strategies used by airlines. Using a constrained revenue
maximization model that assumes interdependent demand, it develops rules to guide decision-making,
and shows that the large fare discount-many discount seats and small fare discount-few discount seats
strategies are optimal. Empirical support is provided for the large fare discount-many discount seats, the
no fare discount-moderate discount seats and small fare premium-few discount seats strategies. In
addition it identifies the large fare premium-very few discount seats strategies. We argue that these
strategies are used in various demand situations and allow airlines to price discriminate.
Ó2012 Elsevier Ltd. All rights reserved.
1. Introduction
The 1978 US Airline Deregulation Act removed many of the
economic regulations over airlines. Events since then, especially the
development of computer-assisted reservation systems and the
internet, have led airlines to introduce yield management systems
to provide a variety of pricing schemes and itineraries to induce
passengers to self-select services according to their willingness to
pay. The result is second degree price discrimination with travelers
paying different fares for the same flight. Airlines also practice third
degree price discrimination by grouping their customers according
to elasticity of demand and charging each group a different fare.
Since airlines face capacity constraints in terms of limited aircraft
seats, they must make decisions in terms of how many discount
seats to offer and the discount fares to charge to maximize
revenues.
We consider demand dependency and conceptualize the
following fare-discount and discount-seats strategies: small fare
discount-many discount seats, small fare discount-few discount
seats, large fare discount-many discount seats, large fare discount-
few discount seats as well as a fare premium-no discount seat
strategy and ask if there are others not revealed by this
conceptualization.
2. A typology of strategies
A number of strategies are used by airlines practicing price
discrimination. Among them is the large fare discount-few discount
seats strategy that is used when demand is very less elastic and
a large fare discount is required to attract few additional travelers to
fill capacity (Pels and Rietveld, 2004). The second, is large fare
discount-many discount seats and it is applicable when demand is
less price elastic but when many seats must be sold as in off-peak
(Mantrala and Rao, 2001). A third strategy is a small fare
discount-few discount seats and applies were demand is elastic,
and a fourth is offering small fare discount-many discount seats
such as in tourist or other markets where demand is very elastic.
While they are important, these strategies do not represent
a complete list of what airlines do.
Despite this void, theoretical support for some of the more
common strategies can be seen by considering the seat allocation
problem of a constant average cost airline that offers a two-class
coach service (high- and discount-fare seats) in a given origin-
destination market.
1
The discount-fare seats are restricted and
those unable to meet them buy high-fare seats. The demand of each
fare class is down-sloping and, following Botimer and Belobaba
(1999), are interdependent. There are a limited number of high-
fare paying passengers all of whom buy seats every time and the
airline faces the constraint that it cannot overbook flights, and
everyone who buys a ticket shows up for the trip. The airline
operates an aircraft of capacity V
c
seats, and assuming inverse
demand functions, the fare for each class depends upon the number
of seats demanded by each of the classes. These quantities are Q
1
seats for the high-fare F
1
and Q
2
seats for the discount-fareF
2
. Thus,
F
2
¼F
2
(Q
1
,Q
2
) and F
1
¼F
1
(Q
1
,Q
2
) are the inverse demand functions
*Corresponding author. Tel.: þ1 3363347231; fax: þ1 3363347093.
E-mail address: obengk@ncat.edu (K. Obeng).
1
This assumption of constant cost means average cost and marginal cost are the
same for each passenger regardless the class of ticket purchased. This assumption
also avoids a marginal cost function that depends on the outputs of both classes.
Contents lists available at SciVerse ScienceDirect
Journal of Air Transport Management
journal homepage: www.elsevier.com/locate/jairtraman
0969-6997/$ esee front matter Ó2012 Elsevier Ltd. All rights reserved.
http://dx.doi.org/10.1016/j.jairtraman.2012.06.001
Journal of Air Transport Management 24 (2012) 42e48

where discount fare is less than the high-fare and the derivatives of
the fares with respect to the quantities Q
1
and Q
2
are negative.
In maximizing its revenue TR ¼Q
1
F
1
(Q
1,
Q
2
)þQ
2
F
2
(Q
1
,Q
2
), the
airline faces the constraint that the number of passengers cannot
exceed plane capacity. Thus, Q
1
þQ
2
V
c
and the Lagrangian of this
optimization problem is,
Max L¼Q
1
F
1
ðQ
1
;Q
2
ÞþQ
2
F
2
ðQ
1
;Q
2
Þþ
l
ðQ
1
þQ
2
V
c
Þ(1)
where,
l
is a Lagrangian multiplier. From this, if the demands for
high- and discount-fare seats are completely independent as when
there is no switching then revenues are Q
2
F
2
(Q
2
) and Q
1
F
1
(Q
1
) for
discount- and high-fare paying passengers. Substituting them into
Eq. (1) and taking the partial derivatives with respect to Q
1
and Q
2
,
setting the results equal to zero and solving gives MR
1
¼MR
2
.
Where MR
1
¼F
1
(11/ε
11
) is the marginal revenue from each
additional high-fare paying passenger, MR
2
¼F
2
(11/ε
22
) is the
marginal revenue from each additional passenger paying
a discount fare, ε
11
and ε
22
are high- and discount-fare elasticities
of demand. It implies that absent demand dependency, fewer
discount seats should be offered if the marginal revenue MR
2
of an
additional discount-fare passenger is less than the marginal
revenue MR
1
of an additional high-fare paying passenger.
However, if there is demand dependency, which implies that
switching is allowed, the airline chooses Q
1
and Q
2
to maximize
revenue and from Eq. (1), the first order conditions for revenue
maximization are,
vL=vQ
1
¼F
1
ðQ
1
;Q
2
ÞQ
1
vF
1
ðQ
1
;Q
2
Þ
vQ
1
Q
2
vF
2
ðQ
1
;Q
2
Þ
vQ
1
þ
l
¼~
MR
1
Q
2
F
2
ðQ
1
;Q
2
Þ
ε
12
Q
1
þ
l
(2)
vL=vQ
2
¼~
MR
2
Q
1
F
1
ðQ
1
;Q
2
Þ
ε
21
Q
2
þ
l
(3)
Where, ε
21
is the cross-elasticity of discount seat demand from
changes in high fares and ε
12
is the cross elasticity of high-fare seat
demand from changes in discount fares. Also, ~
MR
1
¼F
1
ðQ
1
;Q
2
Þ
½11=ε
11
and ~
MR
2
¼F
2
ðQ
1
;Q
2
Þ½11=ε
22
are own price contri-
butions to the marginal revenues of an additional high- and
discount-fare paying passenger. The second terms in Eqs. (2) and
(3) are the contributions of switching to marginal revenue. Alter-
natively, they are the additional revenues lost when an additional
passenger switches from one fare class to another.
Solving these equations for
l
and equating the results gives.
~
MR
1
Q
2
F
2
ðQ
1
;Q
2
Þ
ε
12
Q
1
¼~
MR
2
Q
1
F
1
ðQ
1
;Q
2
Þ
ε
21
Q
2
(4)
Let b
MR
1
¼~
MR
1
Q
2
F
2
=Q
1
ε
12
and b
MR
2
¼~
MR
2
Q
1
F
1
=Q
2
ε
21
be the marginal revenues of high- and discount-fare paying
passengers with switching. Then, with demand dependency
revenues are maximized where both marginal revenues are equal.
Furthermore, since ~
MR
1
>~
MR
2
the sufficient condition for
marginal revenue equalization with switching is Q
2
F
2
/ε
12
Q
1
>Q
1
F
1
/ε
21
Q
2
. This implies that with switching the decrease in
the marginal revenue of an additional high-fare passenger is
larger than the decrease in the marginal revenue of a discount
fare passenger; a condition met with more passengers switching
from high- to discount-fare seats than from discount- to high-fare
seats.
Fig. 1 shows marginal revenue equalization for high- and
discount-fare paying passengers. For clarity, we have included
high-fare seats demand D
h
, its corresponding marginal revenue
MR
1
, the demand and marginal revenue b
D
h
,b
MR
1
when the high
fare changes, discount-fare seats demand D
d
and its corresponding
marginal revenue MR
2
,aswellas b
D
d
and b
MR
2
depicting where both
demand and the marginal revenue of a discount-fare passenger
have changed. MR
1
and MR
2
show where switching is not consid-
ered and the two demands are independent. Here, marginal reve-
nues equalization is at “a”where MR
1
¼MR
2
. To the right of “a”the
marginal revenue from an additional discount fare passenger is
greater than the marginal revenue from an additional high-fare
passenger and the airline benefits by offering many discount
seats. To the left, the reverse is true and each additional high-fare
paying passenger adds more to revenue than does an additional
discount-fare paying passenger.
With switching, the marginal revenue of high-fare seats MR
1
shifts down to Mb
R
1
and MR
2
shifts to Mb
R
2
. If the downward shift of
MR
1
is less than a similar shift of MR
2
the number of discount seats
would increase and vice versa. For the case where the downward
shift of discount fare seat demand is larger than the downward shift
in high-fare seat demand marginal revenues are equalized at “b”
and there are more discount-seats than high-fare seats. Regardless
of where marginal revenues are equalized Fig. 1 shows that capacity
is fully reallocated between high- and discount-fare paying
passengers with demand diversions occurring. Additionally, both
the seat allocation and optimal fares are simultaneously deter-
mined. For example, drawing vertical lines through the marginal
revenue equalization point “b”to the demand lines of high- and
discount-fare paying passengers gives their respective optimal
fares b
Fand b
F
2
, the fare discount as the difference between them
and the optimal seat allocation as b
Q
1
and b
Q
2
.
Also, solving Eq. (4) for the discount fare gives F
2
¼F
1
[1(1/
ε
11
)þ(Q
1
/ε
21
Q
2
)/1(1/ε
22
)þ(Q
2
/ε
12
Q
1
)]. Since the discount fare is
less than the high fare the term in brackets in this equation takes
values between zero and one. Further, since discount seat demand
is more elastic than high-fare seat demand, for the discount fare to
be less than the high fare Q
1
/ε
21
Q
2
<Q
2
/ε
12
Q
1
from which
Q
1
<Q
2
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ε
21
=ε
12
p. This shows that there must be more high-fare
seats than discount-fare seats because the cross-elasticity of
High Fare ($)
Seats
Discount Fare
F1
Dd
OO
Dh
Dh
MR2
Q1
MR2
MR1Dd
b
F1F2
F2
MR1
a
Q1
Q2 = VC – Q1
Q2 = VC – Q1
Fig. 1. Marginal Revenue Equalization.
K. Obeng, R. Sakano / Journal of Air Transport Management 24 (2012) 42e48 43

discount-fare seat demand from changes in the high fare (ε
21
)is
greater than the cross-elasticity of high-fare seat demand from
changes in the discount fare (ε
12
). Given that, the term in brackets
in the equation is positive and less than one, it approximates the
probability of having more high-fare seats than discount-fare seats
if the airline optimizes its seat allocation to maximize revenue or
Pr(Q
1
>Q
2
). Substituting this into the discount fare equation gives
F
2
¼F
1
*Pr(Q
1
>Q
2
), that is the expected revenue from a discount
fare.
2
An advantage of our equation is that it provides a relatively
simple way of approximating the probability of more high- than
discount-fare seats and avoids having to make distributional
assumptions about this probability.
Using the expected revenue equation, the fare-discount (
D
F) is
the product of the high-fare and the probability of having more
discount seats than high-fare seats:
D
F¼F
1
F
2
¼F
1
*f1PrðQ
1
>Q
2
Þg ¼ F
1
*PrðQ
2
>Q
1
Þ(5)
If the probability of finding a discount seat is high, then discount
seat demand is less elastic and Eq. (5) shows the amount of the fare-
discount is large and vice versa. These results show that as the
probability of finding a discount seat increases a large fare
discount-many discount seats strategy is required for revenue
maximization. Alternatively, as the probability of finding a discount
seat reduces a small fare discount-few discount seats strategy is
required for revenue maximization.
Thus, revenue maximization supports only two of the concep-
tualized strategies. Perishable asset pricing studies have also found
that the large fare discount-many discount seats strategy applies to
products whose demands are less elastic, or which are hard to sell
and whose elasticities of demand increase as the end of a shopping
period approaches. Early in a shopping period the discounted
quantity is large and for a product whose elasticity increases
toward the end of a shopping period the strategy of a large fare
reduction early and a small fare reduction later could bring about
large changes in quantity demanded. For airlines this strategy
implies offering a large fare discount well ahead of a flight date
when there are many seats and a small fare discount as the flight
date approaches and there are few discount seats.
3
It could also
apply when airlines are returning their planes from low to high
demand markets where premium fares can be charged.
4
To fill seats
airlines can minimize their losses by charging low fares possibly
reflecting variable costs. Similarly, it could apply to off-peak situ-
ations when airlines attempt to fill many seats by offering large fare
discounts, e.g., weekend flights. Comparatively, the small fare
discount-few discount seats strategy applies when airlines face
elastic demand.
Although the revenue maximization model captures only two
strategies, the peak pricing studies have supported the fare
premium-no discount seats strategy, while perishable asset
pricing studies have supported the other two. The latter suggests
a large price markdown close to the end of a shopping period for
products whose price elasticities decrease with time, for example
large fare discounts on stand-by tickets to fill few available
airplane seats. This is the case of the large fare discount-few
discount seats strategy. Also, Coulter (1999) shows that some
companies have price markdowns that increase from the
beginning to the ending of shopping periods. That is, small
markdowns at the beginning of a shopping period when the
available quantity is large (i.e., a small price discount-large dis-
counted quantity), and large markdowns close to the end of
a shopping period when available quantity is low to dispose of
hard-to-sell inventory (i.e., a large price discount-few discounted
quantities).
3. Methodology
The revenue maximization, peak pricing and the perishable
asset analysis support five fare-seat management strategies. Still
the question is what empirical evidence is there to support them?
Are there other fare-seat management strategies which airlines use
besides those noted? Answers to these questions are obtained
using a two-step approach. First, we assume flights with similar
fare discount-discount seats characteristics form distinct groups
and then use cluster analysis to identify these groups. The charac-
teristics of the groups provide some indications of fencing, and
a comparison of their mean discount fares and mean discount seats
to the overall mean values of the observations provides a basis for
identifying the strategies airlines use. That is, the difference
between the mean discount fare for available airplane seats of
a cluster and the mean discount fare for similar seats for all
observations is the amount of the extra discount over the average
discount fare if negative, or a premium above the average discount
fare (less discount than the average) if positive. This approach
recognizes that airline consolidators buy tickets in bulk at discounts
from airlines and pass some of the discounts to passengers in the
fares they advertise. Further, it uses observed discount fares, which
are those offered on consolidators’websites, as an instrument for
actual fares since both are highly correlated. Once the strategies are
identified, the second step orders them by offered discount fare and
identifies their statistically significant characteristics using an
ordered logit model whose independent variables include those
used in the cluster analysis. The signs and sizes of the marginal
effects of the variables in this model are used to describe the
strategies.
We assume that y
*
i
is a continuous latent variable representing
the strategies, where iis a strategy, x
j
a set of jvariables that affect
the choice of each strategy and
b
a set of coefficients. Then the
latent regression for the strategies is:
y
*
i
¼X
j
b
j
x
ij
þε
i
(6)
Where, ε
i
is a random error and the ordered true values of the
strategies are y
i
¼0,1,2,3,.,iand are assumed to be generated by
the process,
y
i
¼
8
>
>
>
>
<
>
>
>
>
:
0if y
i
<
m
0
1if
m
0
<y
i
<
m
1
2if
m
1
<y
i
<
m
2
:::::::::::::::::
iify
i

m
i1
(7)
In Eq. (7),
m
is a set of threshold parameters that defines the
boundaries of the strategies. If the cumulative density function of
the error term ε
i
is logistic, then the probability of observing each
strategy is,
2
Replacing a discount fare with a bid price makes this result identical to
Littlewood’s(1972)formula.
3
Obeng’s (2008) work on temporal variation in airfares confirm this strategy by
showing that the amount of the fare discount airlines offer reduces as the flight day
approaches.
4
Airlines park their planes overnight in low demand markets where there is
space and return them to high demand markets early morning.
K. Obeng, R. Sakano / Journal of Air Transport Management 24 (2012) 42e4844

The ordered logit model is non-linear and, as a result, inferences
cannot be made from the signs and sizes of its coefficients but from
the marginal effects of the variables. Following Greene (2007) the
effect of an increase in a variable on the probability that a flight is
based on a particular strategy is,
vP
i
=vx
j
¼f
m
i1

b
0
xf
m
i

b
0
x
b
j
(9)
The left-hand-side is the partial derivative of the probability of
strategy iwith respect to variable jand f(,) is the logistic density
function. In the case of a continuous exogenous variable, its
marginal effect shows how a unit increase in that variable affects
the probability that a flight is based upon a particular strategy. On
the other hand for a discrete exogenous variable its marginal effect
is the change in the probability that a flight is based upon
a particular strategy when that variable takes a value of one versus
a value of a zero.
Among these variables is the cost of providing service. This
cost affects the choice of a strategy in two ways. One, a higher
average cost may make an airline choose a small fare discount-
few discount seats strategy because its profitmarginissmall
prior to any discount. Two, lower average cost may make an
airline choose a large fare discount-many discount seats strategy
especially when a large capacity aircraft is used. If an aircraft must
be returned to a high demand market, the airline chooses a large
capacity aircraft even if the demand for the first leg of the flight is
relatively low because profits from the second leg will outweigh
the cost of the first. However, pilot and fuel costs can be consid-
ered fixed because they must be borne whether or not there are
passengers. Hence, variable costs are those associated with flight
attendants and on-board services. If in charging full fares the
aircraft would return empty, the airline minimizes its losses by
pricing based on variable cost and this results in very low fares
with many discount seats.
One cost factor is network complexity; airlines with complex
networks with many nodes and circuitous routes have high costs
and higher fares unless there are network economies of scale. Berry
(1990) found that serving a large number of routes reduces cost
which in turn reduces fares. In comparison longer routes increase
cost and fares. Hayes and Ross (1998) and Borenstein and Rose
(1994) found route length is associated with high fare dispersion.
To account for trip length we use trip time which is the sum of in-
flight time, layover time, and departure delay. Because in medium-
and small-size markets, direct flights may use smaller planes, their
costs per seat mile may be high leading to attempts to recoup them
in higher fares and few discount seats. For example, while the cost
per seat mile to operate a 235 seat Boeing 757-300 is $0.0244, the
corresponding costs for 50 seats Embraer Regional Jet (ERJ-145)
and 49 seats Canada Regional Jet (CRJ-145) both used in short haul
services are $0.0863 and $0.0945 (Coyle et al., 2011). Therefore,
direct flights are a characteristic that affects cost and is included. In
addition, direct flights are interacted with the number of days
before a flight to capture the scarcity of seats on them as the
departure date approaches. Of course, competition from airlines
emerging from bankruptcies affects fare levels as well. American
Airlines echoes this point in its pricing policy by noting that in
markets where its competitors have reorganized the competitors’
costs are low and result in low fares that American must match
(AMR, 2010). Though reorganization affects fare dispersion it is not
included as a variable but is captured, along with other omitted
variables, through airline fixed effects.
Besides cost, demand factors affect strategy choice. Pels and
Rietveld (2004), for example, show that airfares are cheaper if
bought well in advance of trip dates when there are many discount
seats. Therefore, the days left for a flight when a seat is available is
included. Other demand variables are discount seats on originating
and connecting flights. Further, airline passengers have a disutility
for layover time just as they have for waiting time. This disutility is
likely higher than that associated with in-flight time because
layover is a greater inconvenience especially if it involves changes
in concourses, gates and long waiting times. We include squared
layover time to emphasize this greater inconvenience and to
capture the possibility that it could lead to a strategy choice
emphasizing fare discounts and discount seats. Finally, to capture
passenger demand the geometric mean of the passengers on both
flights is included.
5
Differences in strategy choice may also be
temporal such as daily to reflect peak and off-peak conditions. As
such the days left before a flight when an itinerary is available is
again a variable in the equation.
4. Data
The data were collected for a weekday airline round-trip from
a non-hub airport, Greensboro, North Carolina to Boston, Massa-
chusetts, a distance of 645 airline miles. The trip began from
5:30ame11:30am on a Monday and returned any time on Friday of
the same week. American, Delta, US Airways, Continental, United,
and Northwest provided services in this corridor with Canada
Regional Jets, Embraer and Boeing 737 aircrafts.
6
Data were
collected using the online search engine, ORBITZ, because it
provided information on aircraft type and aircraft diagrams from
which to determine airplane seat capacity and available discount
seats. The on-line search was a 100% enumeration of listed flights
during a specified 2 h in the afternoon of each weekday of the three
weeks prior to the trip.
7
The enumeration collected information on
flight numbers, posted fares and the seats available at those fares
on originating and connecting flights, in-flight and layover times.
Pðy
i
¼0Þ¼11þexphP
j
b
j
x
ij

m
0
i
Pðy
i
¼1Þ¼n1h1þexpP
j
b
j
x
ij

m
1
ion1h1þexpP
j
b
j
x
ij

m
0
io
Pðy
i
¼2Þ¼n1h1þexpP
j
b
j
x
ij

m
2
ion1h1þexpP
j
b
j
x
ij

m
1
io
::::::::::::::::::::::::::::
Pðy
i
¼iÞ¼1n1h1þexpP
j
b
j
x
ij

m
i1
io
9
>
>
>
>
>
>
>
>
=
>
>
>
>
>
>
>
>
;
(8)
5
Initially, we used the arithmetic mean and did not get good results.
6
The rationale for studying this market is to capture fare dispersion in non-hub
airports where the absence of low-cost carriers makes established airlines charge
premium fares.
7
The data were collected between 4pm and 6pm each weekday during the three
weeks prior to the trip.
K. Obeng, R. Sakano / Journal of Air Transport Management 24 (2012) 42e48 45

The posted fares are interpreted as the discount fares because some
seats are unavailable at these fares. Data were also collected on
seats on originating and connecting flights, direct service, and
number of carriers involved in connecting flights, airline name, and
departure time among others. These data were supplemented by
service factors at the airport such as airline load factors, on-time
performance and departure delays available from the website of
the US Bureau of Transportation Statistics (2008). Multiple-carrier
flights are treated as if offered by separate carriers, and we
assume symmetry so that Delta-US Airways or US Airways-Delta
flight for example is the same.
8
Because the on-line data did not
include passenger load, that information is obtained by multiplying
the capacity of each aircraft used by an airline to provide the service
by the corresponding load factor of that airline at the airport the
month of the trip. For all flights the geometric mean of the calcu-
lated passenger loads on both flights was used in our equation.
With these modifications the data are an unbalanced panel of 604
itineraries whose characteristics show that the average fare is
$812.69 for a round trip, originating flights use aircrafts with 64
seats per flight and connecting flights 107.5 seats per flight. On the
average there are 17.3% discount seats on originating flights
compared to 38.6% on connecting flights, while average in-flight
and layover times are 2.9 h and 1.4 h.
5. Results
Because the dataset is large we use the FASTCLUS procedure in
SAS (1985) to perform the cluster analysis with normalized vari-
ables: days before flight, geometric mean of passengers, fare, seats
on originating plane; seats on connecting plane, layover time in
hours, direct flight times, and trip time. Several cluster solutions
were obtained and compared in terms of pseudo F-statistic and the
cubic clustering criterion. These statistics peaked when there were
three-clusters and five-clusters suggesting that either of them
could be a solution. Further analysis, however, showed that in both
solutions a cluster had very few observations. Consequently, a four-
cluster solution is used. Table 1 shows cluster characteristics in
terms of the means of the variables used and progressively large
fares from Cluster 1 to Cluster 4 permitting an ordering of the
strategies from the least to the most expensive in terms of fares.
Comparing the clusters, Cluster 2 is the base to which the others
may be compared because it is where airlines sell at the average
(discount) price and reserve the average number of discount seats
for their passengers. When demand is small relative to capacity,
there are many vacant high fare seats making airlines increase the
number of discount seats they offer. If demand is less elastic, deep
fare discounts must be used to sell more discount seats than the
average as in Cluster 1. Alternatively, if demand is much more
elastic and capacity is slightly more than demand, a small fare
discount can be used to sell more discount seats than the average.
However, if demand is less elastic a large fare discount than the
average only leads to a small increase in the number of discount
seats demanded above the average. For the case where capacity is
less than demand, competition for seats makes an airline offer
more high fare seats and fewer discount seats than the average. It
does so by charging premiums above the average fare. Here, if
demand is elastic, a small fare increase over the average reduces the
number of discount seats below average as in Cluster 3. And if
demand is less elastic a large premium on discount seats makes
their fares higher than the average resulting in fewer number of
discount seats than the average as in Cluster 4. The four clusters
thus represent different demand, elasticity, and aircraft capacity
situations and offer strategies for airline management.
Using the ordered clusters, we modify Eq. (6) to account for
airline fixed effects. If there are m¼1,2,3,.,Mairlines and
n¼1,2,3,.,N, observations then considering each row of the data
the probability that an observation belongs to a particular airline is
P
nm
¼F(m,
m
,
b
0
þP
j
b
j
x
jn
þε
n
þ
y
m
>0) where
m
is a threshold
parameter,
y
m
is airline fixed effect, and
b
0
þ
y
m
is an airline-specific
constant term. To avoid identification in estimating this equation
we impose the constraint P
m
y
m
¼0. This fixed effects ordered logit
model is estimated, and Table 2 shows its results and fit statistics.
All the coefficients are highly significant statistically except that of
the squared layover term.
9
From the cluster analysis and the
ordered logit results we identify the following strategies:
Large fare discount-many discount seats strategy: This strategy
characterizes Cluster 1 because its average discount fare of
$556 is far smaller than the mean discount fare of $812.69, and
originating planes have 44.2% discount seats and connecting
planes 51.4% discount seats. This strategy could represent
where demand is less elastic, plane capacity is average and
loads factors are relatively low; i.e. it represents weak high-fare
seat demand requiring increasing the number of discount seats
and offering a large fare discount to fill them (i.e., a shift to the
right of discount-seats supply). From the marginal effects of the
statistically significant coefficients in Table 2 the probability of
using this strategy reduces by 6.5% when fares increase
compared to a 21.9% increase when discount seats on origi-
nating and connecting flights increase. In addition, the proba-
bility of using this strategy increases by 6.3% for an increase in
the number of days in advance when a ticket is purchased.
Comparatively, the probability of using it reduces by 24.4% and
12.2% when trip time increases, and when there is an increase
in the number of days when direct flights are available. Other
results in Table 1 show that there are no direct flights for this
strategy; tickets are offered on the average 13.0 days in
advance; and the average trip takes 4.58 h including 2.5 h
layover, which may contribute to lower demand. Additionally,
42.5% and 30.5% of the flights affected by this strategy are from
5:30ame6:30am and 10:30ame11:30am and medium-size
planes seating approximately 132 passengers on the average
are used on connecting flights.
No fare discount-moderate number of discount seats strategy:
This strategy describes Cluster 2 where small planes seating 52
passengers on average are used to provide service and 33.9% of
the seats are discounted, a percentage close to the overall
average of 35.9% discount seats on connecting flights. All flights
affected by this strategy are direct and airlines charge
a discount fare of $815.24 that is almost the same as the overall
mean discount fare of $812.69 per round trip. Because the fare
is almost the same as the mean discount fare for all observa-
tions, it is described as the no fare discount-moderate discount
seats strategy. Alternatively, we characterize it as the norm to
which others can be compared. The results show that the
probability of airlines using this strategy increases by 10.6%
with each increase in the number of days in advance a ticket is
purchased, and by 36.8% when the number of discount seats
increases. Conversely, the probability of using it reduces by
11.0% as fares increase and by 9.6% with each additional
passenger. The factors that mostly reduce this probability are
8
Further, only flights with available seats on all legs at the offered fares are
considered.
9
In the discussion following the supply of discount seats assumes fixed plane
size. If aircraft size increases, the supply of discount seats shifts to the right, the
reverse being also true.
K. Obeng, R. Sakano / Journal of Air Transport Management 24 (2012) 42e4846

trip time and how many days in advance direct flights are
available. For instance, an increase in trip time reduces this
probability by 41.1%, whereas each additional day a direct flight
is offered reduces the probability of using this strategy by
20.6%. Tickets for these flights are offered on the average
a week in advance; trip time is 2.55 h, 38.1 passengers per
plane take flights affected by this strategy and 92.5% of the
affected flights depart from 6:30ame7:30am
Small fare premium-few discount seats strategy: This strategy
(Cluster 3) is when increased demand from airlines channeling
passengers through their hubs results in flying larger planes,
and offering few discount seats at a very small premium of
$9.10 over the overall mean discount fare of $812.69. The main
characteristics of this strategy include the absence of direct
flights and offering 17.2% and 32.8% discount seats on origi-
nating and connecting flights. The marginal effects of the
variables are the largest here than they are in the other
strategies discussed earlier. For example, the probability of
using this strategy reduces by 16.9% with an increase in the
number of days in advance a ticket is purchased, and by 58.5%
when there is an increase in the number of discount seats.
However, increases in fares, trip time and the number of days in
advance on which direct flights are available increase the
probability of using this strategy by 17.5%, 65.4% and 32.7%.
And, an increase in the number of passengers increases the
probability of using this strategy by 15.2%. From Table 1, the
mean discount fare of $823.79 for flights in this cluster is
offered on the average six days before the flight day, the flights
have 2.9 h layover and as many passengers as in the first
cluster. Additionally, 45.1% of the flights affected by this
strategy depart from 10:30ame11:30am, while 29.2% depart
from 5:30ame6:30am
Large Fare premium-very few discount seats strategy: The final
cluster (Cluster 4) gives the large fare premium-very few
Table 1
Characteristics of clusters.
Variable Mean Mean Mean Mean Overall mean
Cluster 1
(N¼167)
Cluster 2
(N¼120)
Cluster 3
(N¼257)
Cluster 4
(N¼60)
Fare 556.19 815.24 823.79 1474.00 812.69
Days before flight 13.0 8.3 6.0 6.3 8.4
Layover time squared 2.5 N/A 2.9 16.7 3.6
Discount seats on originating flight 27.6 17.7 12.3 9.9 17.3
Discount seats on connecting flight 67.7 N/A 41.7 21.7 38.6
Direct flight days before flight N/A 8.3 N/A 0.0 1.7
Trip time (in-flight time þlayover time þdeparture delay) 4.58 2.55 4.69 8.54 4.62
Geometric mean of passengers on
originating (Q
1
) and connecting flights (Q
2
) i.e., ðffiffiffiffiffiffiffiffiffiffiffiffi
Q
2
Q
1
pÞ
66.0 38.1 65.7 67.8 52.9
Direct flight (%) 0.00% 100% 0.00% 1.67% 20.33%
Capacity of originating plane 62.5 52.1 71.1 58.1 63.7
Capacity of connecting plane 131.7 N/A 127.3 170.2 107.5
Table 2
Maximum likelihood results of fixed effects ordered logit model.
Fixed effects ordered probability model
Log likelihood function 372.261
AIC information criterion 1.2889
AIC finite sample 1.2907
BIC Information criterion 1.4129
Variable Coefficient
Days before the flight 0.4578*
Fare ($) 0.4734*
Discount seats on originating flight 1.3284*
Discount seats on connecting flight 0.2584*
Geometric mean of passengers on originating (Q
1
)
and connecting flights (Q
2
) i.e., ðffiffiffiffiffiffiffiffiffiffiffiffi
Q
2
Q
1
pÞ
0.4129*
Layover time squared 0.1373
Direct flight days before flight 0.8879*
Trip time (in-flight + layover + departure delay) 1.7731*
Mu(1) 1.0687*
Mu(2) 4.9065*
Marginal Effects
Variable Y¼00 Y¼01 Y¼02 Y¼03
Days before the flight 0.0630 0.1062 0.1688 0.0005
Fare ($) 0.0652 0.1098 0.1746 0.0005
Discount seats on originating flight 0.1830 0.3082 0.4898 0.0014
Discount seats on connecting flight 0.0356 0.0599 0.0953 0.0003
Geometric mean of passengers on originating (Q
1
)
and connecting flights (Q
2
) i.e., ðffiffiffiffiffiffiffiffiffiffiffiffi
Q
2
Q
1
pÞ
0.0569 0.0958 0.1523 0.0004
Layover time squared 0.0189 0.0319 0.0506 0.0001
Direct flight days before flight 0.1223 0.2060 0.3274 0.0009
Trip time (in-flight + layover + departure delay) 0.2442 0.4114 0.6538 0.0019
Note: * is 1% significant.
K. Obeng, R. Sakano / Journal of Air Transport Management 24 (2012) 42e48 47

discount seats strategy because there is indeed a large
premium of $661 when its mean discount fare of $1474 is
compared to the overall mean discount fare of $812.69. And, its
17.0% and 12.3% discount seats on originating and connecting
flights are far lower than the mean reported earlier despite
airlines flying larger planes on connecting flights which have
170.2 seats on the average. An explanation for this strategy is
that both high-fare seats and discount-fare seats are substi-
tutes in production, especially on connecting flights which fly
near capacity without discounts due to less elastic high
demand relative to capacity. With this less elastic demand
a large fare premium over the mean is needed making few
discount seats available at regular fares. Thus, if the number of
high-fare seats increases to meet increased demand, the supply
of discount seats decreases because with fixed capacity fewer
discount seats become available at each discount-fare level. If
the demand for discount seats is relatively less elastic, then this
decrease in supply would result in high fares and fare
premiums. However, the very small marginal effects of the
variables on the probability of choosing this strategy show that
they do not affect this strategy much. For example, increases in
fares, trip time and the number of days in advance when direct
flights are available increase the probability of using this
strategy by 0.1%, 0.2% and 0.1%. Comparatively, an increase in
discount seats reduces this probability by 0.2% whereas an
increase in passenger load increases it by 0.04%. In Table 1 most
of the flights in this strategy connect with others and only 1.7%
are direct. Because of these connections travel time and layover
time are long; 8.5 h and 4.1 h. Also, only 60 flights are affected
by this strategy with 51.7% departing between 6:30am and
7:30am
6. Conclusion
This paper classifies the fare discount-discount seats strategies
which airlines use in yield management into stylized groups and
identify the characteristics of each group to inform decision
making. At least five such strategies are conceptualized: small fare
discount-many discount seats, small fare discount-few discount
seats strategy, large fare discount-few discount seats, large fare
discount-many discount seats strategies and fare premium-no
discount seats strategies. It was argued that these strategies are
chosen on the basis of elasticity of demand and plane capacity
relative to demand. Using a constrained revenue maximization
model in which switching is explicitly considered a marginal
revenue equalization rule is derived and used to show that the
strategies to adopt are the small fare discount-few discount seats
and large fare discount-many discount seats. While the revenue
maximization rule is standard, because both demands shift down
and discount-fare seats demand is more elastic than high-fare seats
demand when there is switching, marginal revenue equalization is
reached where there are more discount seats. Additionally, alter-
nate derivation of Littlewood’s rule are presented, which is that the
discount fare is the product of the high-fare and the probability that
there are more high-fare seats than there are discount-fare seats.
An approximation for this probability based on price elasticities of
demand, cross-elasticities of demand and the seats allocated to
high- and discount-fares is estimated.
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