MULTICRITERIA SELECTION OF AN AIRCRAFT WITH

NAIADE

João Carlos C. B. Soares de Mello

, João Erick M. Fernandes

and Luiz Flávio Autran M. Gomes

Departamento de Engenharia de Produção, Universidade Federal Fluminense, Rua Passo da Pátria 156, Niterói, Brazil

Costa do Sol Táxi Aéreo, Maricá, Brazil

Ibmec/RJ, Rio de Janeiro, Brazil

Keywords: Fuzzy sets, Regional Aviation, Stochastic evaluation, Multicriteria Decision Aiding, Entropy, NAIADE

method.

Abstract: This article deals with the problem of multicriteria selection of an aircraft. The problem has eight

alternatives to be evaluated under eleven different criteria, whose measurements can be exact, stochastic, or

fuzzy. The technique chosen for analyzing and then finding a solution to the problem is the multicriteria

decision aiding method named NAIADE (Novel Approach to Imprecise Assessment and Decision

Environments). The method used allows tackling the problems by working with quantitative as well as

qualitative criteria under uncertainty and imprecision. Another considerable advantage of NAIADE over

other multicriteria methods relies in its characteristics of not requiring a prior definition of the weights by

the decision maker. As a conclusion it can be said that the use of NAIADE provided for consistent results to

that aircraft selection problem.

1 PROBLEM DEFINITION

Decisions form part of our day-to-day routine. Some

are simple and do not require great developments,

others are more complex, requiring a greater degree

of expertise and a methodology which is coherent

with the approach to the problem. This work

essentially deals with a decision making problem of

the more complex type, whose importance requires a

theoretically structured approach.

The problem presented in this article is faced by

a non-regular aerial transport company. The

company under study is a start-up company, derived

from an economic group whose principal activity is

logistics. Founded in 1969, the group is noted for its

capacity for diversification, in 2005, possessing 12

companies acting in diverse sectors, varying from

hotel services to agro-business. During the process

of qualifying as an airline operator, the managers of

the company studied analyzed the opportunity of

acting in the market of non-regular public flights,

known as charter flights, within routes typically

characterized as regional. In this modality, the public

are generally offered seats to destinations which may

or may not be attended by regular airline companies.

Among the analyses necessary for the formatting of

the new product to be offered, the managers

identified a factor of vital importance to the success

of the new service, the correct choice of airplane to

be used in this type of operation.

The company under study came into being in

1983 with the aim of producing ultra-light planes for

the practice of aerial sports. Since its foundation, the

company has been based at the Maricá aerodrome in

the Brazilian State of Rio de Janeiro. After being

acquired by a highly diversified group in 1991, the

organization suffered from lack of investment, later

ceasing its activities. The company remained

inactive until 2007, maintaining its assets by means

of renting its facilities. At the end of that year,

studies were initiated to reactivate the company with

a view to making use of the buildings available to

install a company in the aeronautic sector; the

decision being made for an air-taxi company. The

regulations for the creation of an air-taxi service

permit the exploitation of passenger flights on

demand, a modality known as charter flights. Based

on this, the managers of the company proposed an

evaluation, with the aim of formulating an economic

plan for the addition of this type of operation.

The critical problem encountered in this

evaluation was the choice of an aircraft, as this

427

Carlos C. B. Soares de Mello J., Erick M. Fernandes J. and Flávio Autran M. Gomes L..

MULTICRITERIA SELECTION OF AN AIRCRAFT WITH NAIADE.

DOI: 10.5220/0003758804270431

In Proceedings of the 1st International Conference on Operations Research and Enterprise Systems (ICORES-2012), pages 427-431

ISBN: 978-989-8425-97-3

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

represents the main part of the investment necessary,

surpassing even the initial investment calculated for

the operations. This amount can be vital for a

company of the scale of the one studied (Bercovitz

and Mitchell, 2007). In addition to this, the selection

process was also shown to be complex at the

beginning, given the number of criteria and their

variations of measurement as well as the quantity of

alternatives to be chosen.

The adoption of a multicriteria decision aiding

tool, providing the managers with well-grounded

decision making, is justified therefore by the

importance for the company and the complexity of

the decision making problem. As it belongs to an

economic group, the decision was the responsibility

of the president of the group. The information

passed on to the decision analyst originates above all

from internal research, with the director of

operations also responsible for the evaluation of the

value of the qualitative variables necessary to the

process and which would be treated by means of

fuzzy logic (Zadeh, 1975).

It fell to these two agents, assisted by the

decision analyst, to make the definition of the set of

alternatives and the family of criteria. To help in

solving the problem, a multicriteria decision aiding

method was chosen with qualities more aligned to

those which the problem required. The actors that

participated in the process were the managers of the

company. The multicriteria method chosen is the

NAIADE method, created by Munda (1995). This

method encompasses, to a greater or lesser degree,

characteristics of resistance to trade-offs – in

contrast, for example, to MAUT, in which there is

an explicit exchange between values in a

multiattribute utility function (Keeney and Raiffa,

1976) – and the possibility of the application of

variables of diverse types. According to Munda

(1995), the application of the NAIADE method

consists of three steps: pair comparison, aggregation

of the criteria and the analysis of the alternatives.

For the application of the first step, the

difference of values between the alternatives must be

obtained. The way in which this difference is

obtained constitutes the larger part of the foundation

of the method. For this reason, even before knowing

how each one of the three steps is executed,

attention must be given to the functioning of this

mechanism.

In the literature there are already some uses of

MCDA in Air Transportation. For instance, a high

density route, the Belgrade – Zagreb air shuttle

service was evaluated by Teodorović (1985) using

the TOPSIS method, and another high density route,

the Rio de Janeiro – São Paulo was evaluated by

Soares de Mello et al (2003) using the MACBETH

method (Bana e Costa and Vansnick, 1994).

2 METHODOLOGY

ANAC – the National Agency of Civil Aviation is

the Brazilian authority responsible for the regulation

of air transport. Constituted by Law no. 11.182,

ANAC regulates the sector supported by the

Brazilian Aeronautical Code and specific

regulations, called the Brazilian Regulations of

Aeronautic – RBHA. According to the RBHA 119

and 135, aircraft permitted for regional charter

operations are those with a capacity equal to or less

than 30 passengers, which already significantly

limits the viable alternatives. Also according to these

regulations, some advantages can be obtained by

companies which opt to use aircraft with a capacity

equal to or less than 19 passengers. The main

advantage can be found in RBHA 135.3(b), where

the company is dispensed from more detailed

training of the crew. Another significant advantage

can be found in RBHA 135.107, which dispenses the

company from the need for a qualified steward on

board its flights, which significantly reduces the

operational costs, of training, and of the preparation

and maintaining of the documents necessary for

operations.

With this new cut-off, the universe of choices

was reduced even more. According to the managers

of the company, the alternatives to be evaluated are:

Cessna Caravan, Fairchild Metro, Beechcraft 1900,

Embraer EMB-110 Bandeirante, LET 410, De

Havilland DHC 6, Dornier 228 and the CASA 212.

In relation to the criteria, one of the ways of working

with the definition of the criteria is by creating a

hierarchy in the form of a tree, in this way becoming

very similar to the AHP method (Saaty, 2005). At

the higher levels are the more wide ranging criteria

which are subdivided in other more detailed criteria

until a sufficiently specific family of criteria is

formed which can be evaluated effectively.

At the first level the criteria are divided into

three groups. In the financial group, there are the

criteria which result in direct expense or which

produce some impact on the financial or economic

administration of the institution. In the group of

criteria linked to logistics are listed the criteria

which are most significant for the operation of the

aircraft and their limitations. Lastly, in the group

linked to quality, the criteria reflect, either directly

or indirectly, the level of relative satisfaction on the

ICORES 2012 - 1st International Conference on Operations Research and Enterprise Systems

428

part of the users of the alternative.

The criteria which will effectively be evaluated

are on the second level. For a better understanding

of the importance of each criterion inside the model,

there follows a list of each of these criteria:

Acquisition Cost; Liquidity; Operating Costs;

Range; Flexibility; Cruising Speed; Replacement

Parts Availability; Landing and take-off distance;

Comfort; Avionics; Availability; Safety (Figure 1).

Figure 1: Subdivision in levels of the Criteria.

3 APPLICATION AND RESULTS

The Impact Matrix summarizes the problem,

showing what is relevant for the application of the

methodology. Munda (2006) suggests that the most

useful information must be present in the impact

matrix and that they should include the alternatives

analysed, accompanied by all the criteria and their

values, as well as the weights practiced for each

criterion.

For the purposes of organization, the impact

matrix for this problem was broken down into two

matrices. The first is a matrix of the information on

the criteria (Table 1), which brings information on

measurement, weights and intersection for each

criterion. The second matrix is the impact matrix

itself (table 2), bringing the values collated for each

alternative in each criterion.

The following stage consists of calculating the

distance of the values and the pair comparison of the

distances calculated, in order to, in this way,

construct a matrix of indices of intensity of

preference for each criterion.

Munda (1995), as previously mentioned, presents

two possibilities for comparing the alternatives. The

first analyses the degree of truth in relation to the

statement “according to the majority of the criteria

...” with the variants “... a is better than b”, “...a is

indifferent to b” or “... a is worse than b”.

Table 1: Impact Matrix – Information on the criteria.

In order to aggregate the criteria, a table of size

N x M is used, where N is half of the number of

pairs of alternatives and M the number of relations

of preference considered. Table 3 presents the result

of the aggregation of the criteria.

Table 2: Impact Matrix – Values for the Criteria.

The second possibility is the ranking of the

alternatives by means of the intersection of two

flows adapted from the PROMÉTHÉE method. As

the first case is related by Munda (1995) merely as a

complement, the analysis will be carried out by

means of the flows, presented in table 4.

The order of preference of the alternatives for the

pilot application is, according to the flows is

presented in table 5.

Both by the positive flow and the negative flow,

alternative a3 is the optimum alternative, according

to the data supplied by the company and its

managers.

4 CONCLUSIONS AND

LIMITATIONS

The NAIADE method is capable of formatting and

aiding in the solution of decision problems which

MULTICRITERIA SELECTION OF AN AIRCRAFT WITH NAIADE

429

involve criteria of various types. In this problem it

was possible to apply mechanisms of the method

which allowed this property to be used.

In meeting the primary objective of this work, it

was possible to apply the NAIADE method to the

problem, even though the usual applications of this

method do not correspond to the profile of this work.

Therefore, it was possible to define the alternative

which best reflects what was being sought by the

administration of the company under analysis.

The option for the LET-410 aircraft was

therefore recommended to the decision maker, as

this stood out as the one which best met the

specifications and values sought in the equipment

for the carrying out of the intended activities.

Table 3: Aggregation of the Criteria.

One of the weak points detected during the

application of the methodology is the lack of

simplicity when approaching variables of diverse

types. Although conceptually the method is simple,

when the component of uncertainty of the variables

is added, the mathematical calculations begin to

acquire undesirable levels of complexity, which

could compromise the transparency of the

recommendations of this work to the decision

maker.

Table 4: Analysis of the Alternatives.

In relation to the results obtained, it is also

important to comment on the difference between the

rankings supplied by the negative and positive

flows. Although some inversion is expected, the

rankings in the greater part were very different. This

phenomenon simply demonstrates how close the

alternatives are, according to the values practiced by

the decision maker. Nevertheless, it can be observed

by the value of the positive and negative flows that

the optimum alternative is found to have a

comfortable difference in relation to the other

alternatives. Therefore, observing this phenomenon,

the recommendation becomes clear for the choice of

this aircraft as the best placed in the ranking of the

alternatives.

Table 5: Ranking of the Alternatives.

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430

In relation to the alternatives, as an option for

these, the decision was made to select aircraft with a

maximum capacity of nineteen passengers, which

significantly reduced the universe of possible

alternatives. The choice of this cut arose solely due

to the strategy adopted by the company, therefore,

no study in greater depth was carried out on the

alternatives which exceed this level of cut. It is

possible that a wider ranging study in terms of the

number of alternatives would point to greater

viability with larger aircraft.

The criteria were defined according to the values

of the managers of a pre-operational company. Even

though they have been defined with the greatest

rigor possible, it is possible that the cast of important

criteria is modified when the operation becomes

effective. Obviously, the same would occur with the

weights and intersection points. A valid suggestion

for a future study is to repeat this analysis after the

operations have begun, so that it becomes a useful

tool when the decision is made to increase the fleet.

The method used was the fruit of a choice

oriented by some characteristics observed above all

by the decision analyst. This does not mean that no

other method can be used to attempt to solve the

same type of problem. The comparison of this work

with another which seeks to solve the same problem

with another methodology would be interesting, as it

would make it possible to verify the mathematical

model practiced in this work.

ACKNOWLEDGEMENTS

For CNPq, for its financial support.

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