some particular aspects concerning electre method applications

SOME PARTICULAR ASPECTS CONCERNING
ELECTRE METHOD APPLICATIONS
Gheorghe CONDURACHE, Professor, Ph.D., Eng.
Romeo-Mihai CIOBANU, Associate Professor, Ph.D., Eng.
« Gh. Asachi » Technical University of Iasi, ROMANIA
Department of Management & Productions Systems Engineering
Tel: +40 232 277736
Fax: +40 232 213708
E-mail: condur@cetex.tuiasi.ro
romeo.ciobanu@personal.ro
Abstract
After the appearance of the ELECTRE genuine method, conceived by the French professor
Bernard ROY, some of the practitioners and theoreticians in the decision making process have appreciated
the incontestable value of this method and they have tried to develop it.
Thus, this paper presents some particular aspects of the authors experience regarding on the
ELECTRE applications. The authors have tried to identify and to present in a comparative study, some
different ways to reach the final hierarchy of the decision alternatives: ELECTRE, ELECTRE II,
normalized ELECTRE, modified ELECTRE and two personnel propositions.
The main feature of the first personnel proposition consists in a new overtaking relationships
between the decision alternatives, based on the elimination of the threshold values.
The second proposition represents an ELECTRE II development by multiplication the number of
the overtaking relationships.
The authors are hopping to contribute with their propositions to the development of the
multicriteria decision methods and they launch a proposition for future collaborations.
Introduction
Ever since the ELECTRE [1] method occurred, both the practical and theoretical
experts in decisions making obviously appreciated the indubitable value of this method
and tried their best to improve its flaws.
They found varieties like: ELECTRE – II [2], rate-set ELECTRE [3] etc.
This paper presents a comparative analysis between some alternatives of
ELECTRE methods and new ways to draw out the final classification, with the great
advantages of being simple and logical. The authors also present a numerical example for
these alternatives.
1

1.The first original proposition (ELECTRE IV)
In [4] the authors have proposed the next hierarchical relationship:
If: c hg . ≥ c hg
d gh ≤ d hg
↔ A g is better than A h . ( A g P A h )
where :
c gh - the concordance indicator between the A g and A h alternatives;
d gh - the discordance indicator between the A g and A h alternatives;
This method has an inconvenience: even if both the alternatives (A g and A h ) have
a major flaw, one of them will be accepted anyway, which is contrary to the principle of
the original method, that doesn’t agree with accepting an alternative with a major flaw.
Comparing our solution with the ELECTRE II method solution we can see that
the hierarchical relationship we proposed:
c gh ≥ c hg
is identical with the ELECTRE II relationship:
P + gh/ P - gh ≥ 1
where:
P + gh – is the amount of better criteria in favor of the A g alternative as comparing with the
A h
alternative.
P - gh – is the amount of better criteria in favor of the A h alternative as comparing with the
A g alternative.
Our suggestion, which we can name the ELECTRE IV, is based on the following:
the second relationship:
d gh ≤ d hg
can be completed by a third relationship, like d gh ≤ d, thus getting rid of the
inconvenience; d is a discordance threshold, whose value is imposed by the decision
maker (over 0,5 in our opinion).
2. The second original proposition
ELECTRE II method has proposed a concept of tough and mild hierarchy, which
we can generalize, using the “hierarchical rank” – meaning the order in which we’ve
done the hierarchy. How could we show this using a calculus?
A suggestion might be the following: (ELECTRE V). In the hierarchical graph we
can add an arrow every time the concordance or discordance threshold respectively
changes. This may lead to the selection of the alternative for which we obtain a “better
hierarchical difference” as comparing to the alternatives for which we get “mild
hierarchical differences”.
2

Issue Method Overtaking
relationships
1. ELECTRE I If : c gh ≥ c; d gh ≤ d
↔ A g P A h
2. ELECTRE II If : c gh ≥ c; d gh ≤ d
↔ A g P A h
P + gh /P - gh ≥ 1;
3. ELECTRE
III
4. ELECTRE
IV (original
alternative)
5. ELECTRE V
(original
alternative)
6. Modified
ELECTRE
7. Rate –set
ELECTRE
If : c gh ≥ c; d gh ≤ d
↔ A g P A h
P gh + /P gh - ≥ 1;
If c gh ≥ c hg ; d gh ≤
d hg ; d ≤ 1
↔ A g P A h
If : c gh ≥ c; d gh ≤ d
↔ A g P A h
If: c gh – d gh ≥ c – d
↔ A g P A h
The
discordance
indicator:
d gh = ∑ j (u hj – u gj ) · k j
where :
k j – the importance
level of C J criteria
Table no.1. ELECTRE Methods
Decision algorithm
Aforementioned algorithm
It uses two pairs of threshold values: one pair for
tough overtaking and one pair for mild
overtaking. We consider the both directly an
indirectly hierarchies. The tough classification is
completed by the mild classification..
It proposes the concept named insensbility for
the discordance indicators less then threshold
value. It makes directly and indirectly
classification for the alternatives.
The threshold values disappear, the comparing it
makes between the values from matrix. The result
is getting by the ELECTRE II method.
Each overtaking relationship is marked every time
when are modified the threshold values. Hereby,
the alternative which have bigger values of
concordance indicators or/and less values of
discordance indicators will obtain more
overtaking relationships than all of others.
It subtractions the discordances matrix from the
concordances matrix and the line which have
more positives values indicates the optimal
alternative.
This way, an alternative with lots of small
disadvantages can be defeated by another one
with only one big disadvantage.
We illustrate our suggested solutions with the following numericalal example. In
the following application there are presented some of the methods.
3

3. Example of ELECTRE methods application
We propose to settle the optimum strategy for a firm, wich has more investment
projects, and its efficiency indicators for macroeconomics conditions (the consequences
matrix), more probable (considerates safes ) are presented in the table no. 2.
Decision C 1
criteria Net Present
C j Value
Alternative [mil. lei]
A I
C 2
Payback
period of
investment
[year]
Table no.2. Consequences Matrix
C 3
C 4
Minimal Life Internal Rate
Cycle of Return
[year] [ % ]
A 1 5.500 ∗ 5,0 ο 3,7 40
A 2 5.000 4,7 4,2 ο 50 ∗
A 3 4.800 4,5 3,6 38
A 4 4.300 4,3 3,0 ∗ 30 ο
A 5 4.000 ο 4,0 ∗ 3,6 40
K j 0,4 0,3 0,2 0,1
Note: it has been marked with * the best solution for the respective criteria and with °
the poor solution for the respective criteria.
We constate that doesn’t exist a solution which can be the best in evidently and a
solution which can be the powerless than all others.
In table no.3. there are calculated the utilities, if the references values X j , Y j
are those from the table no.2, marked with *, respective with °.
C j
Table no.3. Utilities Matrix
A I
C 1 C 2 C 3 C 4 U i Classif.
A 1 1,00 0,00 0,41 0,50 1,91 IV
A 2 0,67 0,30 0,00 1,00 1,97 II
A 3 0,53 0,50 0,50 0,40 1,93 III
A 4 0,20 0,70 1,00 0,00 1,90 V
A 5 0,00 1,00 0,50 0,50 2,00 I
K j 0,4 0,3 0,2 0,1
The concordance and discordance indicators are shown in the table no.4 şi 5.
Table no.4. Concordance Matrix (c gh )
c gh A 1 A 2 A 3 A 4 A 5
A i X 0,6 0,5 0,5 0,5
A 2 0,4 X 0,5 0,5 0,5
A 3 0,5 0,5 X 0,5 0,5
A 4 0,5 0,5 0,5 X 0,6
A 5 0,6 0,5 0,6 0,4 X
4

Table no. 5. Discordance Matrix (d gh )
d gh A i A 2 A 3 A 4 A 5
A i X 0,5 0,5 0,7 1,0
A 2 0,41 X 0,5 1,0 0,7
A 3 0,47 0,6 X 0,5 0,5
A 4 0,8 1,0 0,4 X 0,5
A 5 1,0 0,67 0,53 0,5 X
ELECTRE I: The minimum threshold value of the concordance indicator which
can be totally overtake by an alternative is c = 0,5. The maximal value of the discordance
threshold which can be totally overtake by an alternative is d = 0,6. In table no.6 there
are presented the overtaking relationaships between the alternatives, for this two
threshold values.
Table no.6. ELECTRE I
A (0,5; 0,6) A 1 A 2 A 3 A 4 A 5 Classif.
A 1 X Yes Yes No No II
A 2 No X Yes No No III
A 3 Yes Yes X Yes Yes I
A 4 No No Yes X Yes II
A 5 No No Yes No X III
The classification it made by the summation of the overtaking relationships. The
alternative A 3 is preferates, because this, without have the performances, it is equilibrate,
it not has the majore handicaps and it’s preferates by 1/2 from criterias.
ELECTRE II: The Matrix of concordance indicatores is decomposed in: the
overtaking nett matrix ( P gh + ) and the equivalence matrix (P gh = ), as: u gj > u hj , respective:
u gj =u hj . These two matrix are presented in the tables no.7 and 8.
Table no.7. Overtaking nett matrix (P + gh)
+
P gh A 1 A 2 A 3 A 4 A 5
A 1 X 0,6 0,5 0,5 0,4
A 2 0,4 X 0,5 0,5 0,5
A 3 0,5 0,5 X 0,5 0,3
A 4 0,5 0,5 0,5 X 0,6
A 5 0,5 0,5 0,4 0,4 X
5

P gh
=
Table no.8. Equivalence matrix (P gh = )
A 1 A 2 A 3 A 4 A 5
A 1 X 0 0 0 0,1
A 2 0 X 0 0 0
A 3 0 0 X 0 0,2
A 4 0 0 0 X 0
A 5 0,1 0 0,2 0 X
For example, the classification for the threshold values: c= 0,5; d = 0,5 is
presented in the table no.9.
Table no.9. ELECTRE II
A(0,5; 0,5) A 1 A 2 A 3 A 4 A 5 Classif.
A 1 X Yes Yes No No I
A 2 No X Yes No No II
A 3 Yes No X Yes No I
A 4 No No Yes X Yes I
A 5 No No No No X III
The mild classification can be achieved for the pair c=0,5; d=0,6. This contains,
more, overtaking relationships: A 3 P A 1 ; A 5 P A 3 .
The tough overtaking drive us to un inserting result, because three alternatives are
equally.
The second classification decides for alternative A 3 , which realizes the overtaking
of A 1 .
ELECTRE IV: It compares the indicators’ value c gh and c hg , respective d gh and
d hg , alternative which are satisfying the both comparing, being better than other. Thus, we
can constat :
c 12 >c 21 ; d 12 >d 21 , as a consequence we can’t satisfy the both relations for each
relations between the alternatives;
c 13 =c 31 ; d 13 >d 31 , alternative A 3 are satisfying at limits the conditions, so it
overtakes the A 1 alternative;
c 15 < c 51 ; d 15 =d 51 = 1,0 in this case not even one of the alternatives can be declared
eligible. The overtaking matrix is show in the table no.10.
Table no.10. ELECTRE IV
ELECTRE IV A 1 A 2 A 3 A 4 A 5 Classif.
A 1 X No No Yes No II
A 2 No X Yes No No II
A 3 Yes No X No No II
A 4 No No Yes X Yes I
A 5 No Yes No No X II
6

So, the optimal alternative is A 4 , being the only one which are overtaking two
alternatives. The others have each one overtaking.
Modified ELECTRE: It subtractions the discordance indicators matrix from
the concordance indicators matrix: c gh – d gh .The resulted are presented in the table
no.11.
Table no.11. Modified ELECTRE
c gh – d gh A 1 A 2 A 3 A 4 A 5 Class
A 1 X 0,1 0 -0,2 -0,5 III
A 2 -0,01 X 0 -0,5 -0,2 IV
A 3 0,03 -0,1 X 0 0 I
A 4 -0,3 -0,5 0,1 X 0,1 V
A 5 -0,4 -0,17 0,07 -0,1 X II
The alternative A 3 stands out in top . The other three alternatives have the values
very close.
Ascertainment: Generally speaking, the decisions making methods don’t offer
the same results (only in a less measure). In the table no.12 are centralized the
classements obtained by applying the previous methods.
Method
A i
ELECTRE
I
ELECTRE
II
Table nr.12. The alternatives classification
ELECTRE
IV
Modified
ELECTRE
Total
Final
classification
A 1 2 1 2 3 8 II
A 2 3 2 2 4 11 V
A 3 1 1 2 1 5 I
A 4 2 1 1 5 9 III
A 5 3 3 2 2 10 IV
In the last columns of the table we made a sum of the partial classification,
respective last order, applying the rule of the simple sum method of the ranges. The idea
is the alternative which is more close to the first place is the best alternative. But this
conclusion is not compulsory. As there is a method of dictator, in which the decision
maker can choose a single criteria from many others, same it is possible to choose by a
single criteria or a single decision method group and is not necessarily to choose all the
methods
7

Conclusion
In this paper, the authors have presented some particular aspects of their
experience regarding on the ELECTRE method application. They have tried to identify
and to present in a comparative study, some different ways to reach the final hierarchy of
the decision alternatives: ELECTRE, ELECTRE II, modified ELECTRE and two
personnel propositions.
The main feature of the first personnel proposition consists in a new overtaking
relationships between the decision alternatives, based on the elimination of the threshold
values.
The second proposition represents an ELECTRE II development by multiplication
the number of the overtaking relationships.
The authors are hopping to contribute with their propositions to the development
of the multicriteria decision methods and they launch a proposition for future
collaborations.
Bibliography
[1] Roy, B. – Classement et choix en présence de points de vue multiples (la méthode
ELECTRE), in RIRO (Revue Internationale de Recherche Opérationnelle), no. 8, marsavril,
1968.
[2] Godet, M. – De l’anticipation à l’action, Edition Dunod, Paris, 1991.
[3] Teodorescu, N., ş.a. – Metode ale cercetării operaţionale în gestiunea
întreprinderilor, Editura Tehnică, Bucureşti, 1972.
[4] Ştirbu, C., Condurache, Gh. – Consideraţii privind aplicarea metodei ELECTRE. În
Studii şi cercetări de calcul economic şi cibernetică economică, nr. 4/1974.
[5] Condurache, Gh. – Din nou despre ELECTRE. În Conferinţa de management, vol.
II, Iasi, Romania, 23-25 noiembrie 1995.
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