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1. D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCS 4113, pp. 1003– 1011, 2006.
© Springer-Verlag Berlin Heidelberg 2006
A Case-Based Seat Allocation System
for Airline Revenue Management
Pei-Chann Chang1, Jih-Chang Hsieh2
, Chia-Hsuan Yeh3
, and Chen-Hao Liu1
1
Department of Industrial Engineering and Management, Yuan-Ze University,
Ne-Li, Tao-Yuan, Taiwan, R.O.C
iepchang@saturn.yzu.edu.tw,
s929510@mail.yzu.edu.tw
2
Department of Finance, Vanung University, Chung-Li, Tao-Yuan, Taiwan, R.O.C
hjc@vnu.edu.tw
3
Department of Information Management, Yuan-Ze University,
Ne-Li, Tao-Yuan, Taiwan, R.O.C.
imcyeh@saturn.yzu.edu.tw
Abstract. Airline companies usually implement revenue management to increase
profits. The revenue management can be performed through seat inventory man-
agement. The current system to book seats is first-come first-served. This ap-
proach tends to sell low-price seats because low-price requests often appear ear-
lier. It also results in low revenue. In this paper, an expected dynamic probability
method and a case-based seat allocation system are proposed to enhance the per-
formance of the seat inventory management. Extensive studies are conducted to
compare the performance of first-come first-served method, expected dynamic
probability method, and case-based decision support system. The result indicates
that the case-based seat allocation system outperforms the other methods.
1 Introduction
Revenue is one of the most important indices for the management of airline industry.
The practical situations of the revenue management in airline companies are compli-
cated. Many dimensions have to be considered such as customer behavior, demand
forecasting, control system, revenue factors, variable cost factors, fare products, prob-
lem scale, and problem interfaces. Besides these dimensions airline companies also
own two characteristics, i.e. high fixed cost and perishable products. However, seat
selling is nearly the only revenue. Therefore every airline is dedicated to develop
various strategies to raise the performance of seat selling. Donaghy et al. (1995) re-
ported that revenue management has been successfully adopted by the airline industry
after deregulation in the late 1970’s. With introducing revenue management airline
companies actually raised the net profit. For example, American Airline earned a net
profit of 450 million to 500 million in 1989 and United Airline made 100 million to
200 million net profits in 1990.
In the open literature, airline revenue management problems can be classified as
forecasting, overbooking, pricing and seat inventory control. In this paper, we concern
the issues on seat inventory control to implement the revenue management. Seat in-
ventory control is to allocate the seats with respect to several fare classes in order to
reach maximal revenue. The past works were interested in finding the optimal

2. 1004 P.-C. Chang et al.
allocation. Many researchers have proposed their ideas such as Brumelle et al. (1990),
Weatherford (1991), Sun (1992), Wollmer (1992), Weatherford et al. (1993), Shayke-
vich (1994), Young and Van Slyke (1994), Bodily and Weatherford (1995), Robison
(1995), Belobaba and Rpbison (1996), Brumelle and Walczak (1997), Kleywegt and
Papastavrou (1998), Li and Oun (1998), Subramanian et al. (1999), Lautenbacher and
Stidham (1999). These works focused on applying operations research-based tools to
obtain optimal solutions for seat inventory control. Too many mathematical tech-
niques sometimes may be not suitable for the real case applications. Therefore we
intend to propose a heuristic instead of optimal solutions in this paper.
McGill and Van Ryzin (1999) indicated that in the forty years airline revenue man-
agement has evolved from low level inventory control methods to advanced informa-
tion systems. To meet the requirement of advanced information system, an artificial
technique, case-based reasoning (CBR) is applied in this research. Case-based reason-
ing decision support systems lately are applied to many application areas. Malek
(1998) developed a case-based reasoning operation system for the plastic moulding
injection process. Göker et al. (1998) developed a case-based CAD/CAM help-desk
support system, HOMER. Göker and Roth-Berghofer (1999) for computer aided de-
sign in Mercedes-Benz. Although there were some successful applications of CBR
proposed, the application of CBR to seat allocation for the airline industry is still
interesting and no effort was ever done.
2 Problem Definition
It can be mastered for airline companies to make the most effective use of seat alloca-
tion through controlling booking conditions, which involves assigning the total num-
ber of fixed seats with the goal of finding out appropriate passengers to make the
whole benefit maximum. The optimal distribution of seat inventory management is
considered as a booking control strategy to decide whether the request is accepted or
not when the booking demand is achieved. Because the booking requests of different
fare classes can be provided at the same cabin seats, how to allocate the booking
number of passengers from different fare classes is the main problem to be studied in
the research. The booking process has been viewed as a single time period in the past,
in which the total demand quantity of each fare class was considered as a single vari-
able; that is, only the possible accumulated demand sum from a certain fare class
before the close of booking was considered. The existence of the uncertainty hidden
between each different fare class has been ignored. This type of question is dealt
with by dynamic planning in Lee and Hursh’s strategy model, but when the scope
of problems becomes too big, the solutions are usually not so easy to be found.
CBR is used in this research to solve the decision problem of seat allocation. The
decision whether or not to accept the request is based on the booking information in
the past and of the time being. The role of the airline company has been changed from
passively selling tickets to passengers to actively deciding whether or not to sell the
tickets. A decision system of seat allocation has been well built to provide a reference
for solving related problems in realistic cases faced by the airline companies.
The main focus in this research is on the seat allocation problem for a single leg.
When each fare level is fixed and the number of cabin seats is known, the seat alloca-
tion problem is investigated without considering the influences of other competitive
companies. It is hypothesized that the booking demand is of specific environment and

3. A Case-Based Seat Allocation System for Airline Revenue Management 1005
seasons, which does not have periodical changes and the factor of season is excluded
in this research. The hypotheses for controlling the booking for a single leg are:
1. The booking demand of each fare class is independent, and the demand probabil-
ity is known.
2. Only the interior seat allocation planning of a single airline company is consid-
ered; the influences of other competitive companies are not taken into considera-
tion.
3. The influence of passengers’ number is not considered for the changing expenses.
4. If a booking request is declined, it is considered as a benefit loss. The possibility
of rebooking will not be taken into consideration; that is, the rebooking will be
considered as a new booking request.
2.1 Current Operation System
The case study company in this research is a well-known airline in Taiwan. It was set
up in 1989. Up to date this company cooperates with foreign airlines in order to raise
global competition. The current seat allocation policy they are using to deal with the
passenger requests is by the first come first served rule (FCFS). The booking process
is operated by professional staffs. The demand of any passenger, any fare class will be
accepted as long as any available seat remaining. In other words, the current system
rejects the requests only when there is no seat available. This system is able to control
the seat allocation effectively however it is possible to cause loss if the staffs make
the wrong decisions. Moreover, FCFS tends to make low revenue. To prevent from
the man-made errors and low revenue, an expected dynamic probability method and a
case-based seat allocation system are developed in this paper.
3 Decision Model for Airline Seat Management
Two heuristic methods are developed in this research. One is the expected dynamic
probability method (EDP) and the other is the case-based seat allocation system
(CBSAS)
3.1 Expected Dynamic Probability Method
The EDP requires two types of information to accept or reject a request. The first is
the request information of each period and the other is the information of available
seat(s). A formula is used to decide whether each request should be accepted or re-
jected and the formula is as follows:
1
1
1 0 −
−
− +
≥
+ n
s
n
n
s
n
t f
f
F (1)
where
n denotes period,
s denotes a seat,
n
i
F denotes the revenue of request i at period n,
1
−
n
s
f denotes the revenue of seat s is still available at period n-1.

4. 1006 P.-C. Chang et al.
Therefore the formula represents the revenue of a request must be greater than the
revenue of not selling this seat at the next period. The request distribution can be
described by probabilities for each period. Considering fares and probabilities to-
gether produces expected revenue. This formula actually is using the expected reve-
nue to make decisions to accept or reject the requests.
3.2 Case-Based Seat Allocation System
To promote the revenue of seat allocation for the case study company, CBSAS is
developed. The system is depicted as Figure 1. And the procedure of CBSAS is con-
stituted of four steps. The first step is case representation. The second step is cases
retrieve. The third step is case adaptation and the last step is case storage. The detailed
description of the steps is reported as follows.
I. Case representation II. Case retrieve
IV. Case storage III. Case adaptation
Features collection
and data analysis
Market
decision
Cases
Cases Data-base
Similarity
computing
Most three similar
cases finding
Marketing decision
generating
Voting rule
Decision storage
Cases
Cases
List of
candidates
Fig. 1. Configuration of CBSAS
3.2.1 Case Representation
Each case is represented by five features, namely, period, fare class, arrival rate,
available seats, decision. For example a case base is shown in Table 1.
Table 1. Case representation
Period Fare class Arrival rate Available seats Decision
20 3 2 100 Accept
15 2 1 30 Accept
3 1 1 0 Reject
1 3 5 6 Accept
3.2.2 Cases Retrieve
When a request shows, the CBSAS searches similar cases in the case base to make a
decision whether the request should be accepted or rejected. As to how to measure the
similarity, an idea comes from distance is proper. The shorter the distance between
two cases is, the more similar the two cases are. Therefore distance is used to measure
the similarity. Euclidean distance ( )
j
i
ij C
Q
S , between the request case and each case
in the case base is calculated respectively.

5. A Case-Based Seat Allocation System for Airline Revenue Management 1007
( ) ( )
∑
=
−
=
4
1
2
,
k
jk
ik
j
i
ij C
Q
C
Q
S (2)
where
ik
Q the kth feature of request i,
jk
C the kth feature of case j in the case base,
k index of features.
3.2.3 Case Adaptation
Similarities from the request to each case in the case base are calculated in the last
step. The most three similar cases are retrieved. Then the voting rule is used to make a
decision whether the request is to be accepted or not. The request is accepted if at
least two decisions of the most three similar cases are “Accept” and vice versa.
3.2.4 Case Storage
Once the decision of the request has been made, it is also stored into the case base for
the future use.
4 Numerical Experiments
Two scenarios are used to evaluate the proposed EDP and CBSAS. The first scenario
is referred to the example in Lee and Hersh (1993). The second scenario is the real
data from the case study company.
4.1 Scenario 1
The example from Lee and Hersh (1993) assumes four fare classes: 200, 150, 120,
and 80. The number of booking period is 5. The request probability at each period is
given in Table 2.
Ten simulations are executed. The results of each simulation and the average are
shown in Table 3. The performance of current system is used as the benchmark. The
percent improvement of EDP to FCFS and CBSAS are 12.4% and 16.9% respectively.
It is evident that the proposed methods earn more revenue than the current system.
Table 2. Request probability at each period
Period
Pk (t)
1 2 3 4 5
P1
n
0.15 0.14 0.10 0.06 0.08
P2
n
0.15 0.14 0.10 0.06 0.08
P3
n
0.00 0.16 0.10 0.14 0.14
P4
n
0.00 0.16 0.10 0.14 0.14

6. 1008 P.-C. Chang et al.
Table 3. Simulation result by using example of Lee and Hersh (1993)
# FCFS EDP CBSAS EDP(%) CBSAS(%)
1 38410 44110 43740 0.148399 0.138766
2 38050 41530 43820 0.091459 0.151643
3 39010 42770 44570 0.096386 0.142528
4 38310 42720 45150 0.115114 0.178543
5 38040 44290 45250 0.164301 0.189537
6 37800 41500 45350 0.097884 0.199735
7 38790 43230 44490 0.114462 0.146945
8 37070 43130 44480 0.163475 0.199892
9 39140 42710 44990 0.091211 0.149463
10 38080 44060 45440 0.157038 0.193277
Avg. 38270 43005 44728 0.123973 0.169033
4.2 Scenario 2
This example comes from the real data of the flight from Taipei to Hong Kong. There
are two fare classes, 13800 and 10100. The number of booking periods is 6. The re-
quests are summarized from the real data and modeled as four types of probability
distribution.
Type 1: The request probability increases along with the booking period and the
probability at each period is shown in Table 4.
Type 2: The request probability decreases along with the booking period and the
probability at each period is shown in Table 5.
Type 3: The request probability increases first and then decreases. The request prob-
ability of each period is shown in Table 6.
Type 4: The request probability decreases first and then increases. The request prob-
ability of each period is shown in Table 7.
Table 4. Type 1 request probability
Period
Pk (t)
1 2 3 4 5 6
P1
n
0.035 0.071 0.069 0.072 0.067 0.064
P2
n
0.235 0.245 0.262 0.271 0.267 0.265
Table 5. Type 2 request probability
Period
Pk (t)
1 2 3 4 5 6
P1
n
0.051 0.123 0.154 0.134 0.147 0.156
P2
n
0.242 0.232 0.227 0.181 0.179 0.177

7. A Case-Based Seat Allocation System for Airline Revenue Management 1009
Table 6. Type 3 request probability
Period
Pk (t)
1 2 3 4 5 6
P1
n
0.128 0.053 0.048 0.044 0.039 0.036
P2
n
0.243 0.276 0.284 0.284 0.276 0.268
Table 7. Type 4 request probability
Period
Pk (t)
1 2 3 4 5 6
P1
n
0.043 0.002 0.037 0.059 0.053 0.057
P2
n
0.261 0.057 0.198 0.279 0.263 0.281
Table 8. Average revenue of each types of request probability
Average revenue FCFS EDP CBSAS
Type 1 3200940 3273830 3556880
Type 2 3270870 3355600 3594250
Type 3 3397410 3481030 3659000
Type 4 3190580 3246080 3501750
The average revenue of each type is shown in Table 8. Both EDP and CBSAS per-
form better than the FCFS (the current system). In these numbers, it seems that no big
gaps between FCFS v.s. EDP and FCFS v.s. CBSAS. However the result simply
represents one flight. There are six flights each day. Therefore the annual revenue will
be a meaningful number. It also indicates that the proposed EDP and CBSAS are
effective.
In this paper, EDP and CBSAS are proposed to deal with the seat allocation prob-
lem in airline industry. Through the numerical validation, the proposed EDP and
CBSAS are effective. In other words, both two methods earn more revenue than the
current system.
5 Conclusion and Future Directions
Seat allocation directly relates to airline companies’ benefits; therefore, how to pro-
mote passengers’ demands and revenue management skills to increase the company’s
profits is a crucial issue. In order to make the passenger load factor and profit-gaining
capacity higher, it is necessary to analyze the passengers’ demands actively and con-
trol the seat allocation effectively. The research proposes two novel solutions for seat
allocation planning, namely EDP and CBSAS. Through extensive numerical experi-
ments, the proposed EDP and CBSAS are shown to be effective.
Several directions for future investigations can be suggested: 1. This research is
based on a single-leg model; multi-leg problems can be further studied. 2. Only

8. 1010 P.-C. Chang et al.
passengers of personal tickets are studied in the research. For further research, pas-
sengers of group tickets and those who purchase several tickets at the same time are
suggested to be studied. 3. Building a database of passengers for research and analysis
to study the customer’s choice and purchasing model is recommended for effective
airline yield management. 4. Magnificent results can be expected by applying the
process of CBR proposed in the research to other industries.
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