Evaluation of Efficiency of Brazilian Airlines using the

MCDEA-TRIMAP Model

Eliane Ribeiro Pereira

, Maria Cecília de Carvalho Chaves

and João Carlos C. B. Soares de Mello

Accounting Department, Universidade Federal do Rio de Janeiro, Av. Pasteur, 250, Urca, RJ, Brazil

Production Engineering Department, Universidade Federal Fluminense, R. Passo da Pátria, 156, Niterói, RJ, Brazil

Keywords: Data Envelopment Analysis (DEA), TRIMAP, Air Carriers.

Abstract: The deregulation of the domestic airline industry brought a significant increase in competition between

airlines, pushing them to continuously update their strategies. This article reviews the operating

performance of these companies, from the contrast in the results of the DEA classic model and MCDEA-

TRIMAP efficiency indicators. The use of such methodology allows the increase of discriminatory power of

the productive units evaluated and a better evaluation of them. The application of the DEA model to the data

from the Brazilian Airline industry for the year 2008 indicated three companies as efficient, while the use of

MCDEA TRIMAP index allowed the identification of the most efficient company in 2008. The index

provided better discrimination of the production units in the study.

1 INTRODUCTION

The continued development of commercial aviation

has led to it being one of the main means of

transportion for both passengers and cargo, when it

comes to medium and long distances. Governments

and analysts often highlight the airline industry as

playing an essential and strategic role for the country

(Pasin and Lacerda, 2003). In Brazil, which has

large territorial dimensions, the use of commercial

aviation is highlighted as an element of integration

between its farthest points. Its unquestionable

importance can be measured by it being the largest

market in Latin America, accounting for 3% of

national GDP (Araújo et al., 2006).

The Brazilian air transportation sector has

undergone profound changes over time, mainly due

to the deregulation of the sector, (Soares de Mello et

al., 2003), which brought increased competition into

the air transportation industry. The entry into the

market of GOL Airlines, the first LCC (low cost

carrier) airline in Latin America in 2001, further

intensified competition (Evangelho et al., 2005). To

ensure competitiveness, the airlines have been

forced to aim for better use of their resources. New

transformations occurred due to both physical

infrastructure problems and operational issues,

brought to light by the occurrence of serious

accidents in the years 2006 and 2007. The domestic

airline industry was then placed in check and has

slowly been recovering from this period, marked by

insecurity and mistrust.

This article aims to investigate the performance

of Brazilian airlines within the scenario described.

The analysis carried out took into account the staff

involved in the operation of the means of

transportation, and the use of the fleet to transport

cargo and passengers within national territory and

internationally, as done by Silveira et al. (2008).

Other studies regarding operational efficiency can be

found in Soares de Mello et al. (2003) and Araújo et

al. (2006). Fernandes and Capobianco (2001) and

Fernandes and Capobianco (2004) used the DEA

tool to study the capital structure of companies.

Lopes et al. (2006) investigated the pricing of

airlines in domestic long-distance flights. The DEA

methodology is widely used in the study of air

transportation and the efficiency of airports.

(Fernandes and Pacheco, 2002); (Pacheco and

Fernandes, 2003); (Soares de Mello and Gomes,

2004); (Pacheco et al., 2006).

To measure the effectiveness of airlines, the

model MCDEA created by Li and Reeves (1999)

was applied, which allows the ordination of efficient

units, with the use of two objective functions in

addition to the classic DEA. Next, the TRIMAP tool

(developed by Clímaco and Antunes 1987) was

Pereira E., Chaves M. and Mello J..

Evaluation of Efﬁciency of Brazilian Airlines using the MCDEA-TRIMAP Model .

DOI: 10.5220/0004310302130221

In Proceedings of the 2nd International Conference on Operations Research and Enterprise Systems (ICORES-2013), pages 213-221

ISBN: 978-989-8565-40-2

 2013 SCITEPRESS (Science and Technology Publications, Lda.)

used, which allows investigation of the decomposing

of the area of the weights space of the objective

functions. Finally, by calculating the values of

objective functions for each region of weight space,

the efficiency index MCDEA-TRIMAP was

determined proposed by Soares de Mello et al.

(2006) in order to assess each airline.

This article is organized as follows: section 2 is a

brief summary of the evolution of the Brazilian

airline industry. Section 3 presents a review of the

tool and the DEA model created by Li and Reeves.

Section 4 discusses the use of the TRIMAP tool in

the solving of the MCDEA model, and Section 5

presents the characterization and modeling of the

problem. Section 6 discusses the results of applying

the MCDEA model, together with the calculation of

the efficiency index, as well as conducting a

comparison of them with the results obtained from

the classic DEA. Finally, Section 7 describes the

conclusions of the study.

2 AIR TRANSPORT SECTOR

The first big boost for the airline industry took place

in World War I when aircrafts were used in military

strategies. However, it was only after World War II

that air transportation began to be used on a larger

scale.

The large extension of Brazilian territory and the

precarious nature of other means of transportation

favored the expansion of commercial aviation in the

country, which began in 1927 with the founding of

the Airline Rio-Grandense (VRG). In 1933 another

major company was founded: VASP Airlines, which

three years later inaugurated a regular flight between

Rio de Janeiro and São Paulo, which remains until

today the largest line of domestic aviation traffic,

(Oliveira, 2005).

In the 40s, the market gained tremendous

momentum with the purchase of American aircrafts

from the World War II surplus (Novais and Silva,

2006) sold at low prices and financing, which

favored the emerge of airlines. The poor

administrative and financial structure of companies

at that time resulted in the realization of many

mergers and bankruptcies in the 50s, and few

Brazilian companies were maintained, operating

mainly regionally.

The 60s were marked by the search for solutions

to the problems the sector faced. The government

created the National Aviation Conference

(CONAC), with the aim of defining strategies to

reverse the crisis which the airline industry was

engulfed in. Defined policies and guidelines, which

remained in place until the late 80's, encouraged the

merger of companies, improving their financial

situation. The industry began to operate under a

model of "managed competition" in which the

government controlled both the entry of airlines into

the domestic market, as well as the defining of fees

to be charged (Guimarães and Salgado, 2003).

The early 90s brought the introduction of a new

policy for the Brazilian air transportation industry,

resulting in the loosening of regulations in the

sector. Companies were able to start working with

different rates, due to tariff bands, controlled by the

government. In 1992, the abolition of regional

monopolies contributed to increased competition in

the sector. At the end of the decade, the competition

received a new impetus - the tariff bands were

extinguished and exclusivity in the operation of

some airlines to regional companies was removed,

(Lima and Soares de Mello, 2009). All companies

became domestic, ending the classification of

regional and national companies.

With the absorption of the company Cruzeiro,

VARIG became, at the beginning of the XXI

Century, the largest carrier in Latin America. During

this same period, the DAC (Civil Aviation

Department), currently the ANAC (National Civil

Aviation Agency) promoted the freedom to set rates,

allowing each company to define their marketing

strategy. TAM which had been a regional airline,

became the second largest company in the South

American continent, while Transbrasil ceased

operations in 2001.

The process of creating new companies and

airlines, and the frequency of flights and aircrafts

was made more flexible, which enabled the creation

of GOL Airlines in 2001, the first Brazilian

company to apply the model LCC (Low Cost

Carriers). In this model, lower rates are charged,

with high use of the aircrafts, increased use of the

internet for sales, service on board reduced and

better use of the maximum takeoff weight

(Evangelho et al., 2005).

The year 2005 was marked by change. VASP

operations ceased, while new companies started

regular operations. Some companies that were

traditionally part of the irregular segment became

concessionary companies and started to operate

regular airlines. TAF Airlines, for example, returned

to the market and to this field of work from which it

had retired in 2002.

In September 2006, the positive momentum

gained by a sector seen as having excellence in

safety, quality and punctuality was shaken by the

ICORES2013-InternationalConferenceonOperationsResearchandEnterpriseSystems

early indications of serious problems. Air disasters

revealed the serious lacks in the physical

infrastructure of the Brazilian airline industry. Flight

controllers were removed, others went on strike;

flights were continually canceled and airlines who

could not meet the scheduled times for their flights

aggravated the crisis by overselling tickets,

outnumbering the seats available. In July 2007, yet

another accident resulted in further uncertainty for

air travelers.

After the heavy crisis the airline industry had

faced in 2006 and 2007, 2008 came as a year of

recovery for the sector, which sought to adopt new

measures to restore the confidence and credibility

they had previously enjoyed. Even so, Visagio

(2008) cautions that although the symptoms of the

crisis have been reduced, consequences generated by

the global financial crisis can bring difficulties for

the sector, due to decreased availability of credit.

Few companies dominated the domestic market

between 2003 and 2008. The Statistical Yearbook of

Air Transport for the year 2008 highlights the

presence of four major companies that year: Tam,

Gol, VRG and Oceanair, the first 3 being considered

the biggest of the year. In October of that year, Gol

merged with VRG, resulting in the VRG Linhas

Aéreas S.A. , (VRG Airlines) leaving the domestic

market basically divided between two companies.

3 DATA ENVELOPMENT

ANALYSIS AND LI AND

REEVES’ MODEL

The Data Envelopment Analysis (DEA), developed

by Charnes, Cooper and Rhodes (1978), uses

mathematical optimization in order to estimate the

technical efficiency of production units (Decision

Making Units - DMUs) without have to arbitrate the

weights for each input variables (available

resources) or output (results obtained) or consider

financial matters to make comparative analyses

(Estellita Angulo-Meza and Lins, 2000).

Multiobjective Linear Programming (PLMO)

and DEA have in common the concept of Pareto

efficiency, since both approaches consider that

production units are efficient, if, and only if, it is not

possible to improve one of its features without

worsening any of the others.

The DEA metholdology constructs an efficient

frontier, which vertices are formed by DMUs

deemed efficient (Pareto efficient) because they

have a better input/ output ratio, while the others are

located in a region below the boundary (Gomes et

al., 2003). Since each DMU chooses its own set of

multipliers, so that the effectiveness is the best

possible in relation to others, it is possible that a

large number of DMU's are located on the efficient

frontier, revealing the benevolent structure of the

method and its low discriminatory power. According

to Leta et al. (2005) for empirical determination, the

tie of production units happens when the number of

DMU's is not very large compared to the total

number of inputs and outputs.

The MCDEA model, by Li and Reeves (1999),

uses Multiobjective Linear Programming in order to

solve the problems of discrimination of the DMU's

and promote a better distribution of the multipliers

for the variables. It proposes a multicriteria approach

to DEA, including two other objective functions, in

addition to the traditional objective function of the

DEA model, each representing a new criterion to

measure the efficiency (maximum deviation and

sum of deviations). Since the criteria provides less

flexibility for optimization, it tends to restrict the

freedom of DMU's in the quest for efficiency.

It should also be noted that the MCDEA model

can be considered a method of joint evaluation

(Angulo-Meza et al., 2003) because it is a

multicriteria method which presents non-dominated

solutions, taking into account all the objective

functions without being limited by the solutions

obtained from the individual optimization of each

function.

The model originally defined as CCR, considers

the maximizing of the efficiency of the production

unit, which is calculated according to the model (1)

where v

and u

are the multipliers of inputs i, i =

1,...,m, and outputs r, r = 1, ..., s, respectively; x

and y

are the inputs i and outputs r of DMU j, j =

1,..., n; x

and y

are the inputs i and outputs r of

DMU 0.

Max h





r 1

Subject to





i 1

= 1 (1)





r 1





i 1



0 , j=1,...,n

r ,



0 ,



r, i

A DMU is efficient when h

= 1, which means

that the restriction relating to the DMU is active and

therefore has to be equal to zero. The MCDEA

EvaluationofEfficiencyofBrazilianAirlinesusingtheMCDEA-TRIMAPModel

model proposes the use of the variable d, as the

measurement rather than h. Thus, in this model the

DMU is efficient if, and only if, d = 0. Therefore, it

could be assumed that this formulation minimizes

the inefficiency of the DMU with the restriction that

the weighted sum of outputs be less than or equal to

the weighted sum of inputs of each DMU. Thus, the

CCR model is reformulated as shown in (2):

Min d

Subject to

Max h

= u





i 1

= 1 (2)





r 1





i 1

i j

+ d

0 , j=1,...,n

r ,

i ,



0 ,



r, i

From the model presented in (2), and in order to

restrict the freedom of choice of the multipliers, the

MCDEA model adds two objective functions:

minimization of the sum of deviations ("general

benevolence") and minimizing the maximum

deviation ("equity "). According to Li and Reeves

(1999), each of the three objective functions is

independent of the others, since there is no order of

priority among the criteria of efficiency. The

MCDEA formulation is shown in (3):

Min d

Min Max d

Min





j 1

Subject to





i 1

= 1 (3)





r 1





i 1

i j

+ d

0 , j=1,..., n

r ,

i ,



0 ,



r, i

In evaluating the results, a DMU is minimax if,

and only if, the value of d

corresponding to the

solution that minimizes the second objective

function of the MCDEA is zero. Likewise, a DMU

minisum is efficient if, and only if the value of d

corresponding to the solution which minimizes the

third objective function of the model is zero.

When a DMU is minimax or minisum efficient,

it must also be DEA efficient because, by definition,

the efficiencies minisum and minimax require d

0. It can be concluded, as a result, that the minimax

and minisum objectives do not, as a general rule,

favor the classical efficiency of DMU under

evaluation.

To solve the model being studied, a decision

support tool for TRIMAP was used, which has an

excellent graphic interface for analysis and is

suitable for linear programming problems which

have three objective functions.

4 TRIMAP AND MCDEA

The TRIMAP method (Climaco and Antunes, 1989),

combines three fundamental procedures:

decomposition of the weights space, introduction of

restrictions in objective space, and introduction of

restrictions in the weights space. The interactive

environment enables the decision-maker to research

efficient solutions, based on past progressive

learning findings of efficient solutions. The

combination of reduced permissable space, along

with the reduction in the weights space of objective

functions, allows the agent to specify lower

constraints for the values of the objective function,

and/or restrictions in the weights space (Climaco et

al., 2003).

The TRIMAP calculates efficient solutions that

optimize each objective function and the efficient

solution that minimizes a weighted Tchebycheff

distance to the ideal solution. During the

interactions, as unwanted solutions are eliminated,

the preferences of the decision maker are perceived.

The development of the method enables the

reduction of permissible space, saving

computational effort and progressively increasing

the focus on the sub-region of greatest interest to the

efficient decision maker, facilitating the decision

making.

The use of this tool allows for key graphcs to be

obtained for the study of the MCDEA model. The

graph obtained shows the weights space

decomposed in indifferent regions - regions where

the weights of the objective functions may vary

without changing the value of the solution obtained -

that correspond to the basic non-dominated solutions

obtained. In addition, the chart can show direct

restrictions on weights and permissible values of

objective functions. The TRIMAP also offers a

summary of the numerical results obtained,

providing for each nondominated basic solution, the

value of the basic variables, the objective functions,

the percentage of area occupied by the region of

indifference, among other data. In this study

ICORES2013-InternationalConferenceonOperationsResearchandEnterpriseSystems

TRIMAP was used to generate solutions and served

as an analysis tool for studying the weighting space,

as in Soares de Mello et al. (2006).

The TRIMAP is a tool that is well suited for the

study of the MCDEA model, once it calculates all

the solutions of the optimal objective function of the

classic DEA, identifying the nondominated

solutions. Soares de Mello et al. (2006) highlights

the importance of this result, because the knowledge

of the existence of alternative multipliers and the

identification which corresponds to basic solutions

enables the realization of further analysis. In

addition, knowledge of the decomposition of

weighting space allows the investigation of the

stability of the efficient solutions, as well as the

identifying of combinations of weights which, while

not giving maximum efficiency to a DMU, enable

them to be considered a good solution, as they don’t

excessively reduce the efficiency, and by providing

better values to other objective functions, are more

in line with the preferences of the decision-maker.

In Climaco et al. (2008) one can find discussions

on how to do qualitative analysis of the MCDEA

model with TRIMAP. Soares de Mello et al. (2006)

proposed an MCDEA- TRIMAP evaluation index,

which considers the properties derived from the use

of the TRIMAP in the Li and Reeves model.

Considering that the calculation of efficiency in this

model requires the consideration of all the possible

combinations of the weights of objective functions

and that the values assumed by the classical

objective function undergo continuous variation, this

objective function is integrated when the weighted

sum of three objective functions is optimized. This

integration must be done in the entire space of

possible weights and, the result divided by the size

of this space, provides the average value of the

classic objective function in this space. The

complement of this average value represents the

efficiency ratio, as detailed in (4):

I (Ef

MCDEA- TRIMAP

) = 1- ((



FO1 (λ

, λ

)

dS)/área ∆) (4)

As the integration is continued by parts in the

weights space, assuming a constant value in each

region of continuity, the calculation of the index can

be simplified by making the weighted sum of the

first objective function, using as a measure the

percentage area in each valid solution. It is important

to note that all these values are easily obtained

through TRIMAP. To avoid distortions in the

integration of the weights space the expression on

the objective function minisum must be divided by

the total number of DMU's under analysis (Soares de

Mello et al, 2006). In accordance with the model

properties of Li and Reeves, MCDEA index is less

than or equal to the classic DEA efficiency. In this

study the evaluation of the efficiency is performed

by comparing the index with the results obtained by

classic DEA.

5 CHARACTERIZATION AND

MODELING OF THE

PROBLEM

Annually, the ANAC (National Civil Aviation

Agency) publishes the Statistical Yearbook of Air

Transport, which contains statistical data on the

national air transportation sector. Silveira et al.

(2008) investigated the efficiency of the national

airlines, considering the data for the year 2005,

using a methodology similar to that used in this

study. The big changes that occurred in the scenario

of the air transport industry in recent years

motivated the realization of this study, which

considers the data for the year 2008, available at

www.anac.gov.br. The recent scenario in the airline

industry shows significant changes from one year to

another with mergers, creation, and closure of

companies. Therefore, it was not possible to perform

a comparative analysis of the results obtained from

the previous years.

Data provided by ANAC is made available at the

end of the year, and therefore not considered for

purposes of analyzing any possible variations

throughout the year. In October 2008, Varig was

bought by Gol and the national market was basically

divided between two companies: Gol/VRG and

TAM. In order to simplify things, this study

considered only one company (GOL/VRG), taking

into account the sum of each company’s information

during the period.

The companies AZUL, MASTER TOP,

SKYMASTER and VARIG LOG did not present

their data in the time frame for disclosure and are

not included in this study. The company ABSA -

Aerolineas Brasileiras, used only for cargo

transportation, was also not considered.

In 2008, the serious challenges the airline

industry faced in 2006 and 2007 were, if not solved,

at least softened. The government adopted a series of

measures throughout this time, with the objective

being to solve the problems of the infrastructure and

other particular problems which unfolded during the

crisis.

EvaluationofEfficiencyofBrazilianAirlinesusingtheMCDEA-TRIMAPModel

The evaluation of Brazilian airlines was done

from a comparative analysis of the results obtained

by applying the DEA methodology and the indexes

obtained by applying the MCDEA model.

Air transport is characterized by the transport of

passengers and cargo over long distances. Therefore,

for this study two outputs related to these variables

were chosen: number of paid seats used, and the

metric tons used per kilometer. The choice of inputs

considered the main capital asset of these

companies: airplanes. Since the aircraft from each

company has distinct characteristics, the maximum

takeoff weight input was used, being a variable that

is linked to the ability to transport both passengers

and cargo. On the other hand, staff is needed to

operate the aircraft, perform services, and manage

the company. For that reason, the other input used

was the total staff amount of each company.

Each individual company was considered a

DMU. As mentioned, Gol and Varig were

considered as a single DMU, due to the purchase of

the latter in October 2008. As the study aims to

evaluate the performance of airlines in terms of their

operational management, an input- oriented model

was used to evaluate companies that have the ability

to reduce their fleet and manage their workforce

without causing damage to the total transported.

Despite the difference in size between airlines,

there is no guarantee of disproportionality between

the inputs and outputs. Silveira Soares de Mello

(2009) formulated the MCDEA-BCC model and

applied it to the airline industry, with the data

pertaining to the year 2005. However, due to the

formulation of classic BCC, the MCDEA-BCC can

generate slacks larger than 1, which means negative

efficiencies. According to Soares de Mello et al

(2002), this phenomenon occurs especially when a

DMU has an increasing return to scale. Thus, the

CCR model was adopted for comparison with the

model used by Reeves and Li (1999), which is based

on this model.

6 RESULTS

The classic DEA-CCR was applied to the 17 DMU’s

that represent regular Brazilian air transport

companies, with the movement of cargo and

passengers in 2008.

According to ANAC, the year 2008 was marked

by the presence of four companies who represented

80% of the total number of stages performed: TAM,

GOL, VRG, and OCEANAIR, the first considered

the top three of the year.

In October 2008 the merger of GOL and VRG

companies took place which resulted in the

continuation of a single company, VRG Linhas

Aereas SA. For simplicity sake, this study

considered conjunctively the data for both

companies, as GOL/VRG.

The 2008 report of the ANAC featured a

retrospective perspective of the information

disclosed in the period 2000/2008, noting that

between the years 2003 to 2008, the domestic

market share had the predominance of few

companies in the sector. In 2008, TAM had a 50%

stake, Gol 29%, and VRG, 14%.

The first step of the study was to apply the DEA-

CCR model to the DMU’s investigated, using the

software SIAD of Meza Angulo et al. (2005). The

results are summarized in Table 1.

Table 1: Classical Efficiency for Airlines.

DMU Airline

Classical

Efficiency

DMU1

Abaeté Linhas Aéreas 0,098966

DMU2

Gol Transp. Aéreo

Ltda/VRG Linhas Aéreas

1,000000

DMU3

Meta Mesquita 0,414240

DMU4

Oceanair 0,619809

DMU5

Puma Air 0,091950

DMU6

Passaredo Transp.Ae.S/A 0,384954

DMU7

Pantanal L.A.Sul-

Matogrossense

0,255394

DMU8

Rico Linhas Aéreas S/A 0,378091

DMU9

Tam Linhas Aéreas S/A 1,000000

DMU10

Trip T. A. R. Interior

Paulista

0,431652

DMU11

Taf Linhas Aéreas S/A 1,000000

DMU12

Total Linhas Aéreas S/A 0,713920

DMU13

Webjet 0,694577

DMU14

Air Minas 0,192657

DMU15

Nht 0,129612

DMU16

Sete 0,150975

DMU17

Team 0,078830

The classic DEA-CCR model provided 3

efficient DMU's - Gol Transportes Aereos

Ltda/VRG Linhas Aereas, TAM Airlines S/A, and

TAF Linhas Aéreas S/A, without it being possible to

make any distinctions between them. At this point,

the model MCDEA was applied in order to increase

the power of discrimination between the units

studied and the TRIMAP was used in order to assess

the weights space.

ICORES2013-InternationalConferenceonOperationsResearchandEnterpriseSystems

Figure 1: Gol/VRG. Figure 2: TAM.

Figure 3: TAF.

Figures 1, 2 and 3 show the decomposition of the

weight space for the DMU's effective in the classical

model. The analysis (details in Clímaco et al., 2008)

shows that the DMU TAM was the only efficient

minisum and minimax. Since the solutions that

optimize the objective function related to the DEA

CCR model cover the entire weights space, the latter

is better assessed by the MCDEA model.

The DMU GOL/VRG is minimax efficient but

not minisum efficient. However, the DMU TAM is

only minisum inefficient in a small area. The DMU

TAF was only efficient achieving this efficiency

with very specific multipliers.

The calculation of the evaluation index for

MCDEA-TRIMAP DMU's considers the weighted

sum of the solutions of the first objective function

which weighting space is the percentage of the areas

where each solution is valid, using the data provided

by TRIMAP.

From these results, it was discovered that the

only DMU which remained efficient was the

company TAM, followed by GOL/VRG, confirming

the graphical analysis carried out and the fact that

the model restricts the optimization of MCDEA

DMU's.

In addition, the analysis of the results show the

benevolence of the Classic DEA model, which

identified the company TAF Airlines as efficient,

while the MCDEA model showed the same

company as having very low efficiency ratios,

0.2568.

7 CONCLUSIONS

The application of the DEA model to the data from

the Brazilian Airline industry for the year 2008,

provided by ANAC, indicated three companies as

efficient - Gol Transportes Aereos Ltda/VRG Linhas

Aereas, TAM Airlines S/A, and TAF Linhas Aéreas

S/A, without it being possible to make any

distinctions between them. The use of MCDEA

TRIMAP index allowed the identification of the

most efficient company in 2008 - TAM airlines.

Therefore, the index provided, once again, better

discrimination of the production units in the study.

It is important to note that GOL, shown as

efficient in the application of the DEA model,

obtained a very similar index in the application of

MCDEA. However, TAF reached a much lower

index. This difference can be seen in the qualitative

analysis of Figure 3, where TAF barely achieved

being efficient, and even then, in a very small area.

The decomposition of the weight space for the

DMU's effective in the classical DEA model is

illustrated in Figures 1, 2 and 3. It shows that the

DMU TAM was the only efficient minisum and

minimax, being considered the company more

efficient. This result could be expected, since the

solutions which optimize the objective function for

the DEA CCR model overlying the entire space of

weights. The DMUs GOL / VRG is only minimax

efficient, while TAF is only efficient DMU, which is

not getting thus able to overcome the result of the

first DMU.

It should be noted that since the departure from

the market of VARIG, in 2006, TAM has been

responsible for the largest share of the Brazilian

market. The result obtained in this study is quite

consistent, since efficiency is crucial for a company

that wishes to remain an industry leader. The merge

of GOL/VRG, which occurred at the end of 2008,

will undoubtedly bring dispute in the near future and

generate strong reactions in the market.

The MCDEA model (Li and Reeves, 1999) was

developed for DEA-CCR models. Future studies

may investigate the use of MCDEA with DEA-BCC

models (Banker et al., 1984). Future studies may

also explore the potential interactivity of TRIMAP

and DEA models, with constrains to the values of

the objective functions, and constraints with values

of the multipliers.

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EvaluationofEfficiencyofBrazilianAirlinesusingtheMCDEA-TRIMAPModel