Implementation of Elimination and Choice Expressing Reality (ELECTRE) Method in Selecting the Best Lecturer (Case Study STMIK BUDI DARMA)

Implementation of Elimination and Choice Expressing Reality (ELECTRE) Method in Selecting the Best Lecturer (Case Study STMIK BUDI DARMA)

Mesran1

Department Computer Engineering, STMIK Budi Darma Medan,

Jln. Sisingamangaraja No. 338 Telp 061-7875998,

Garuda Ginting 2

Dosen Tetap STMIK Budi Darma Medan

Jln. Sisingamangaraja No. 338 Telp 061-7875998,

Suginam3

Department Computer Engineering, STMIK Budi Darma Medan,

Jln. Sisingamangaraja No. 338 Telp 061-7875998,

Robbi Rahim4

Departement of Computer Engineering Medan Institute of Technology

Jl. Gedung Arca No.52 Kota Medan, Sumatera Utara,

Abstract Measurement of the performance index lecturer at a college should be obliged to do. Performance indexes the basis

1. Lecturer

   1. THEORY

      for university lecturer in determining the best lecturer owned by the university. The right solution to the problems faced by university leaders as a decision maker to consider several criteria relating to the determination of the best computer lecturer, in this case the determination of best computer lecturer using ELECTRE method

      Keywords Decision making, Multi-Criteria Decision Making, Multi-Criteria Decision Making, Best Lecturer, ELECTRE

      1. INTRODUCTION

         The lecturer is the one resource that must have either PTN or PTS. Lecturers who have a good performance will improve the quality of universities. For faculty performance can be enhanced, it is no doubt anymore that universities must be able to assess the extent to which performance of the lecturers, so they know the performance generated by faculty lecturer at the college. For lecturers who earn top performance ratings. Certainly, the senior lecturers are the best that have high ratings on performance

         accomplishments. In conducting the selection of best lecturers can use decision support system, which has many

         Under Law 14, 2015, which referred to the lecturers are professional educators and scientists with the primary task of transforming, developing and disseminating science, technology, and the arts through education, research, and community service [7].

2. Elimination and Choice Expressing Reality (ELECTRE) ELECTRE methods introduced by Roy (1966), which uses a comprehensive evaluation approach by trying to create a ranking of the number of each alternative described on some criteria [8].

The steps of the method ELECTRE can see as below [6] [9] [10]:

Step 1: Preparing for Decision Matrix

In the column, there is a decision matrix criteria (n) and the row in the form of alternative (m). The initial stage and the base for processing to decision support

x11 x12 x13 … x1n

methods that can apply to Weight Product (WP), Analytics Hierarchy Process (AHP), Simple Addictive Weighting (SAW) and some other methods [1] [2]. Decision support

x

x 21

ij .

x

m1

x21

.

xm2

x22

.

xm3

…

…

…

x2n

.

x

mn

(1)

systems should have some alternative, criteria, and weighting that is a crucial factor in the decision support system [1] [3] [4].

Step 2: Normalizing the Decision Matrix

Decision matrix will be normalized by using the following formula and produces the normalized model.

Based on the above, this research is to apply the method Elimination and Choice expressing Reality (ELECTRE) in making decisions for determining best computer lecturer of STMIK Budi Darma with the criteria used, ie rank (C1), research (C2), scientific publications (C3) , dedication (C4), supporting element (C5). Another variant of the ELECTRE approach is TOPSIS method [5] [6].

rij

xij

x

m

2

ij

i1

i=1,2,,m (2)

j=1,2,,n

For cost parameters using the following equation.

max{| v v |}

d kj lj jDkl

kl

(11)

1 max{| vkj vlj |} j

rij

rij

m 2

i=1,2,,m (3)

d matrix is also a dimension of m x m and did not take the value of the l column and k row, d array as below.

1

i1 rij

j=1,2,,n

d12

…

d1n

d

… d

The results of processing the normalized decision matrix, as shown below.

d 21

.

d

m1

.

dm2

2n

.

…

(12)

r11

r21

rij

r12 r21

r13 r22

…

…

r1n

r2n

(4)

Step 6: Determine the dominant concordance matrix and discordance

. .

r r

. … .

r … r

This array could construct with the aid of a threshold value (threshold) c. The formula can obtain c value.

m1 m2 m3 mn

Step 3: Giving weight value

Furthermore, decision makers provide interest factor

m m

c

kl (13)

c k 1 l 1

(weight) on each of the criteria which express its relative importance (wj).

m(m 1)

W= (w1, w2, … , wn) ;

n

wj 1

j 1

(5)

The alternative Ak can have the opportunity to dominance A1 if the concordance index ckl exceed the threshold c with ckl c and elements of the dominant F concordance matrix defined as:

Step 4: Calculate the normalized weighted matrix

Each column of the r matrix multiplied by the weights (wj)

fkl

1 , if ckl c

0

, if ckl < c (14)

determined by the decision maker, can be seen below.

The same also applies to the dominant discordance matrix G with threshold d. The following formula can obtain d value:

vij wj .rij

(6) m m

Where v is

dkl

d k 1 l 1

(15)

v11 v12

…

v1n

m(m 1)

vij

v

21

.

v

v22

.

v

…

.

…

v2n

.

v

(7)

The elements of the dominant F discordance matrix defined as:

m1 m2

mn

1 , if d d

Step 5: Determining the set of concordance and discordance index

The set of concordance index {ckl} indicates where the sum of weighted criteria Ak alternatively is better than the alternative A1.

Ckl={j|vkj vlj} with j=1,2,..,n (8) The set of discordance index {dkl} given as follows: Dkl={j|vkj<vlj} with j=1,2,..,n (9)

Step 5: Calculating concordance and discordance matrix

To calculate or determine the value of the elements in the concordance model is by adding weights are included in the set of concordance

gkl kl

0 , if dkl < d (16)

Step 7: Determining aggregate dominance matrix

The model e as total dominance matrix is a matrix which each element is the multiplication between the matrix elements f, and g corresponding form elements.

ekl=fkl x gkl (17)

Step 8: Elimination of the less favorable alternative

The matrix e gives the preferred order of each option, ie when ekl = 1 then the alternative is Ak better alternative than the A1. That the rows in a matrix e which has a total of at least ekl = 1 can be eliminated.

1. RESULT & DISCUSSION

ckl wj

jCkl

(10)

The initial step to find the best lectures which provide 5

criteria and three alternatives. The criteria and the weights show in Table and choices could see in Table II.

To determine the value of the elements in the discordance

matrix is by dividing the maximum difference of criteria including into subsets discordance with the highest difference between the value of all existing criteria

Table I. The Criteria and Weights

k=2 i=1 c21

Criteria (C)	Weights(W)
Rank (C1)	0.35
Research (C2)	0.15
Scientific Publications (C3)	0.2
Dedication (C4)	0.2
Supporting Element (C5)	0.1

j=1 if v21 v11 0.1485 0.1980 no j=2 if v22 v12 0.0739 0.0923 no j=3 if v23 v13 0.1193 0.1491 no

j=4 if v24

v14

0.0970 0.1455 no

Table II. Alternative of Lecturer

Name of Lecturer (A)	C1	C2	C3	C4	C5
	5	3	4	4	2
A1	4	5	5	3	4
A2	3	4	4	2	4
A3	5	5	2	2	2

By using equation (2), then in the process of normalization matrix.

j=5 if v25 v15 0.0667 0.0667 yes then j=5 c21={5}

i=2 c22 = identity j=1,2,3,4,5 i=3 c23

j=1 if v21 v31 0.1485 0.2475 no j=2 if v22 v32 0.0739 0.0923 no

j=3 if v23 v33 0.1193 0.0596 yes then j=3 j=4 if v24 v34 0.0970 0.0970 yes then j=4 j=5 if v25 v35 0.0667 0.0333 yes then j=5

x1

42 32 52 7.7011

x2

52 42 52 8.1240

c23={3,4,5}

r x11 4 0.5657

r12 x12 5 0.6155

k=3 i=1 c

x

1

11 7.7011 x2

8.1240 31

r x21 3 0.4243

r x22 4 0.4924

j=1 if v31 v11 0.2475 0.1980 yes then j=1

21

r31

x1

x31

x1

7.7011

5

7.7011

0.7071

22

r32

x2 x32 x2

8.1240

5

8.12401

0.6155

j=2 if v32 v12 0.0923 0.0923 yes then j=2 j=3 if v33 v13 0.0596 0.1491 no

j=4 if v34 v14 0.0970 0.1455 no

So on the same way, it will get normalized r matrix :

j=5 if v35 v15 0.0333 0.0667 no

c31 = {1,2}

0.5657

r 0.4243

0.7071

0.6155

0.4924

0.6155

0.7454

0.5963

0.2981

0.7276

0.4851

0.4851

0.6667

0.6667

0.3333

i=2 c32

j=1 if v31 v21 0.2475 0.1485 yes then j=1 j=2 if v32 v22 0.0923 0.0739 yes then j=2

Matrix V is calculated based on the equation (6) as follows: v11 = w1r11 = (0.35) (0.5657) = 0.1980

v12 = w2r12 = (0.15) (0.6155) = 0.0923

v13 = w3r13 = (0.2) (0.7454) = 0.1491

v14 = w4r14 = (0.2) (0.7276) = 0.1455

v15 = w5r15 = (0.1) (0.6667) = 0.0667

From the above results obtained matrix v as follows:

j=3 if v33 v23 0.0596 0.1193 no

j=4 if v34 v24 0.0970 0.0970 yes then j=4 j=5 if v35 v25 0.0333 0.0667 no

c32 = {1,2,4}

i=3 c33 = Identity j=1,2,3,4,5

Then for dkl value can synchronize with a value that is not contained in ckl to set of dkl

0.1980

v 0.1485

0.2475

0.0923

0.0739

0.0923

0.1491

0.1193

0.0596

0.1455

0.0970

0.0970

0.0667

0.0667

0.0333

d12={} d23={1,2}

d13={1} d31={3,4,5}

d21={1,2,3,4} d32={3,5}

Next calculate the set of concordance index:

k=1 i=1 c11=identity j=1,2,3,4,5 i=2 c12

j=1 if v11 v21 0.1980 0.1485 yes then j=1 j=2 if v12 v22 0.0923 0.0739 yes then j=2 j=3 if v13 v23 0.1491 0.1193 yes then j=3 j=4 if v14 v24 0.1455 0.0970 yes then j=4 j=5 if v15 v25 0.0667 0.0667 yes then j=5 c12={1,2,3,4,5}

i=3 c13

j=1 if v11 v31 0.1980 0.2475 no

j=2 if v12 v32 0.0923 0.0923 yes then j=2

The member states set of dij columns on vij

Then the concordance matrix is formed. ckl element is calculated by equation (10)

c12 = w1+w2+w3+w4+w5 = 0.35+0.15+0.2+0.2+0.1=1 c13 = w2+w3+w4+w5 = 0.15+0.2+0.2+0.1 = 0.65

c21 = w5 = 0.1

c23 = w3+w4+w5 = 0.2+0.2+0.1 = 0.5 c31=w1+w2 = 0.35+0.15 = 0.5

c32 = w1+w2+w4 = 0.35+0.15+0.2 = 0.7

The concordance matrix is:

j=3 if v13 v33 0.1491 0.0596 yes then j=3 j=4 if v14 v34 0.1455 0.0970 yes then j=4 j=5 if v15 v35 0.0667 0.0333 yes then j=5 c13={2,3,4,5}

1

C 0.1

0.5 0.7

0.65

0.50

At concordance model the elements of dkl are calculated

0

0 A1

based on the equation (11) as follows:

E 0

0 A

2

d12

max{0} 0 0

0

1

A3

max{0.0495;0.0185;0.0298;0.0485;0}

0.0495

With the ELECTRE methods of calculation indicated ekl=1 then the alternative is better than the A1. Alternative A3

d13

max{0.0495}

max{0.0495;0;0.0894;0.0485;0.0333}

0.0495

0.0894

0.5534

better than A2, but not necessarily be able to draw connections between A1 to A2 and the A1 and A3.

1. CONCLUSION

   In this case using ELECTRE method to solve the problem of

   d21 max{0.0495;0.0185;0.0298;0.0485} 0.0495 1

   selecting the best computer lecturer. The results of the study

   d23

   max{0.0495;0.0185;0.0298;0.0485;0}

   max{0.0495;0.0185}

   max{0.0990;0.0185;0.0596;0;0.0333}

   0.0495

   0.0495 0.5

   0.0990

   are expected to be useful for decision makers in STMIK Budi Darma, especially for policy makers. Selection of the best computer lecturer believed to be able to motivate the lecturers at the university, so the faculty performance becomes better. Application of this method by using data

   d31 max{0.0894;0.0485;0.0333} 0.0894 1

   from a sample of cases contained in STMIK Budi Darma.

   d32

   max{0.0495;0;0.0894;0.0485;0.0333}

   max{0.0596;0;0.0333}

   max{0.0990;0.0185;0.0596;0;0.0333}

   0.0894

   0.0596 1

   0.0596

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   3(3 1)

   4.0534

   6

   0.6756

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   1

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   0.65

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   1 1

   0

   F 0

   0 1

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   D 1

   1

   0 0.5534

   0.5000 1

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   0 0

   0

   G 1

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1

1

Aggregation dominant matrix obtained from the

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