Decision Support System for High Achieving Students Selection Using AHP and TOPSIS

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Decision Support System for High Achieving Students Selection Using AHP and TOPSIS

Yufika Sari Bagi Information System

STMIK Multicom Bolaang Mongondow Kotamobagu, Indonesia yufika@stmikmulticom.ac.id

Suyono Information System

STMIK Multicom Bolaang Mongondow Kotamobagu, Indonesia suyono@stmikmulticom.ac.id

Michel Farrel Tomatala Information Technology STMIK Multicom Bolaang Mongondow

Kotamobagu, Indonesia mikefarrel7@gmail.com Abstract—The selection of high-achieving students is one of

the schools' efforts to determine potential students who will be prepared to participate in the section of high achieving students at the regional, provincial, national, and international levels.

Manual selection activities can have several problems, including it can take a lot of time when many criteria must be used, and many students participate in the selection, and there can be subjective assessments from the selection committee. Based on those problems, a decision support system is proposed using AHP to determine the weight of the criteria and TOPSIS to determine the best alternative. Decision support systems using AHP and TOPSIS can assist the selection committee in selecting high achieving students. The application of a decision support system using AHP and TOPSIS in this study can also resolve problems such as reducing the time required for the selection process and making the selection results more objective.

Keywords—AHP, TOPSIS, DSS, DSS AHP-TOPSIS, High Achieving Student

I. INTRODUCTION

Every educational institution, especially in Junior High School, always has a vision and mission that is oriented towards smart, superior graduates in achievement and insight.

To realize these, every school needs to evaluate, improve the services to students related to teaching techniques, assessment, quality assurance so that the school becomes a competitive, quality, and high achieving school. Schools can participate in student achievement competitions to improve student abilities and have the school's right name. This is also done by SMP Negeri 11 Dumoga, West Dumoga sub-district, Bolaang Mongondow District. The selection of high- achieving students is one of the efforts made by this school to determine potential students who will be prepared to participate in the student achievement competitions at the regional, provincial, national, and international. Some problems arise when the selection is carried out manually, such as it takes a long time when the criteria used are many.

There are also many participating students, and there can be subjective assessments from the committee. To help the school simplify the selection, a decision support system using Analytical Hierarchy Process (AHP) and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is proposed, where AHP is used for determining the weight of criteria and TOPSIS is used for determining the best alternative.

AHP has a unique feature: it provides a significant procedure to determine the relative importance of different attributes concerning the objective [1][2]. Implies structuring several options into a system hierarchy, including the relative values of all criteria, alternatives comparison for each particular criterion and defining the average importance of alternatives are methodology approach of AHP [3], where it is a flexible and powerful analytical tool to solve qualitative and quantitative problems [4][5]. The AHP method is also reliable

in determining the weight of the criteria [6][7]. AHP was applied to determine the appropriate value of standards in selecting students in a dormitory[8].

TOPSIS is related to the problems of discrete alternatives.

This technique is one of the most practical methods for solving real-world problems. The relative advantage of TOPSIS is its capability to rapidly identify the best alternative [9]. TOPSIS is one of the multi-criteria decision-making approaches from a finite set of parameters, which are based upon minimum distance from an ideal solution and maximum distance from non-ideal solution, where this method assures that each criterion has a propensity of continuously increasing or decreasing utility, which easily defines the ideal and negative ideal alternative [10].

AHP and TOPSIS combination has been widely applied to decision support systems. The selection using a combination of the TOPSIS-AHP method is the best-recommended solution to determination tuition fee students[11]. AHP and TOPSIS methods were applied in the selection of state of transformers based on insulation condition, and the results demonstrate their efficiency in the performance assessment of transformers [12].

II. METHODOLOGY

The proposed decision support system using AHP- TOPSIS in this study is shown in Fig. 1.

Determination weights of Criteria using AHP

Database

Determination the best alternatives using TOPSIS Pair-wise comparison

value of criteria

Weights of Criteria Weights of Criteria

Result of Ranking

Alternative’s values of each criteria

User

Fig. 1. Proposed model of DSS for High Achieving Students Selection Using AHP and TOPSIS

A. Analytical Hierarchy Process (AHP)

AHP is a common, multi-criteria decision-making method. It is developed to assist in solving complex decision problems by capturing both subjective and objective evaluation measures. It breaks a complex problem into a hierarchy or level [13]. The steps in the AHP method are [8]:

1. Make pairwise comparison

2. Eigenvector calculation and normalization using (1).

=_∑ (1)

(2)

3. Calculate Consistency Ratio (CR) using (2). If the CR value is less than 0.1, then the eigenvector can be used as weights of the criteria.

= (2)

TABLE I. RANDOM INDEX

N RI 1 0.00 2 0.00 3 0.58 4 0.90 5 1.12 6 1.24 7 1.32 8 1.41 9 1.45 10 1.49 Where CI is calculated using (3), and the RI value is

Random Index that shown in Table I.

= ^_ (3)

B. The Technique for Order Preference by Similarity to Ideal Solution (TOPSIS)

One of the popular techniques in Multi-Criteria Decision Making (MCDM) to solve problems is TOPSIS where. This technique has a core idea that is to choose the best solution by simultaneously measuring the distances of each alternative to the positive ideal solution (PIS) and the negative ideal solution (NIS) [9]. The steps in TOPSIS are [14][15]:

1. Form a normalization matrix

R =

∑ (4)

2. Calculating the weighted normalized values

3. Identify positive ideal solutions and ideal negative solutions using (5) and (6).

= ( , , , … , ) (5)

= ( , , , … , ) (6)

4. Calculate the distance between each alternative with a positive ideal solution and a negative ideal solution using (7) and (8)

= ∑ ( − ) , = 1,2,3, … , (7)

= ∑ ( − ) , = 1,2,3, … , (8)

5. Calculate the preference value of each alternative using (9).

= , = 1,2,3, … , (9)

III. RESULTS AND DISCUSSION A. Criteria

The criteria used in the selection of high achieving students in this study are the average value of report cards, presence, attitude, extracurricular activities, and charter.

Based on interviews with the selection committee, a pairwise comparison matrix was created, shown in Table II.

TABLE II. PAIRWISE COMPARISON OF CRITERIA

Criteria

The Avera ge Value

of Repor

t Cards

Presen ce Attitu

de Extracurricu lar Activities Chart

er

The average value of

report cards 1 3 4 5 7

Presence 1/3 1 3 4 5

Attitude 1/4 1/3 1 2 3

Extracurricu

lar activities 1/5 1/4 1/2 1 2

Charter 1/7 1/5 1/3 1/2 1

The values in Table II are obtained from the results of interviews with the selection committee.

B. Weights of Criteria Determined Using AHP

By employing data from Table I, next, we calculate the eigenvector of the criteria. The result is shown in Table III.

TABLE III. RESULT OF EIGENVECTOR CALCULATION

Criteria

The Average Value of Report

Cards Pres ence

Attit ude

Extrac urricul ar Activit

ies Cha rter

Eigenv ector Values The

average value of report

cards

1 3 4 5 7 0.48

Presence 0.33 1 3 4 5 0.26 Attitude 0.25 0.33 1 2 3 0.125 Extracurr

icular activities

0.2 0.25 0.5 1 2 0.079

Charter 0.142 0.2 0.33 0.5 1 0.049 Amount 1.925 4.78

3 8.83

3 12.5 18 1

Emaks 5.17 CI 0.04 CR 0.03

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CR value calculated using (2). According to Table I, we used 1.12 as the RI value because we have five criteria in this study. Based on Table II, the CR value is less than 0.1 so that the eigenvector values can be used as weights of criteria.

C. Case Study

Sample of student value data obtained from SMPN 11 Dumoga using five samples shown in Table IV.

TABLE IV. SAMPLE OF STUDENT VALUE

N o.

Studen t's Name

The avera ge value

of repor

t cards

de

Extracurric ular activities

Chart er

1 Dewi

W. 75.54 100 73 1 2

2 Freshyl

ia L. 87.09 80 78 2 2

3 Jocheli

n S. 86.54 80 70 2 1

4 Sevalin

o W. 87.36 100 79 4 3

5 Ranti

H. 87.27 100 85 3 2

Then, the value is converted into a predicate based on Table V.

TABLE V. PREDICATE

Criteria Very Goo

d Goo

d Satisfactor y

Less than Satisfactor

y Bad

The average value of report cards

80.50 – 100

70.50 – 80.49

60.50 –

70.49 40.50 – 60.49

0 – 40.4

9 Presence 81 –

100 61 –

80 41 – 60 21 – 40 0 – 20 Attitude 80 –

100 70 –

79 60 – 69 40 – 59 0 – 39 Extracurricula

r activities > 4 3 2 1 0

Charter > 4 3 2 1 0

Then, the predicate score is shown in Table VI.

TABLE VI. PREDICATE SCORE

Predicate Score Very Good 5

Good 4

Satisfactory 3

Less than Satisfactory 2

Bad 1

Based on Table V and Table VI, the alternative score or students' scores are shown in Table VII.

TABLE VII. ALTERNATIVE SCORE

N o.

of repor

t cards

de

Chart er

1 Dewi

W. 4 5 4 2 3

2 Freshyl

ia L. 5 4 4 3 3

3 Jocheli

n S. 5 4 4 3 2

4 Sevalin

o W. 5 5 4 5 4

5 Ranti

H. 5 5 5 4 3

Next, normalizing values using (4) and the result of normalization shown in Table VIII.

TABLE VIII. NORMALIZATION RESULT

N o.

The averag

e value

of report

cards

Presen ce

Attitu de

Chart er

1 Dewi W.

0.3713 91

0.4833 68

0.4239

99 0.251976 0.4375 95 2 Freshyl

ia L. 0.4642 38

0.4833 68

0.4239

99 0.377964 0.4375 95 3 Jocheli

n S.

0.4642 38

0.3866 95

0.4239

99 0.377964 0.2917 30 4 Sevalin

o W. 0.4642

38 0.4833 68 0.4239

99 0.629941 0.5834 60 5 Ranti

H.

0.4642 38

0.4833 68

0.5299

99 0.503953 0.4375 95 Next, calculate weighted normalized by multiplying weights that are determined using AHP with normalized value in Table III. The result is shown in Table IX.

TABLE IX. WEIGHTED NORMALIZED VALUE

N o.

The averag

e value

of report

cards

de

Chart er

1 Dewi

W. 0.1793 82

0.1271 26

0.0534

24 0.019906 0.0214 42 2 Freshyl

ia L.

0.2242 27

0.1017 01

0.0534

24 0.029859 0.0214 42 3 Jocheli

n S.

0.2242 27

0.1017 01

0.0534

24 0.029859 0.0142 95 4 Sevalin

o W.

0.2242 27

0.1271 26

0.0534

24 0.049765 0.0285 90 5 Ranti

H. 0.2242

27 0.1271 26 0.0667

80 0.039812 0.0214 42 Next, determine the ideal solution using (5) and (6), and the result is shown in Table X,

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TABLE X. IDEAL SOLUTION

Ideal Solutio n

The average

value of report

cards

Presenc

e Attitud

e Extracurricul

ar activities Charte r

Positiv e Ideal Solutio

n

0.22422 7

0.12712 6

0.06678

0 0.049765 0.02859 0 Negati

ve Ideal Solutio n

0.17938 2

0.10170 1

0.05342

4 0.019906 0.01429 5

The next step calculates the distance between the alternative's value with the positive ideal solution and the negative ideal solution using (7) and (8). The result is shown in Table XI and Table XII.

TABLE XI. DISTANCE BETWEEN ALTERNATIVE'S VALUE AND POSITIVE IDEAL SOLUTION

Stude nt's Name

of repor

t cards

Prese nce

Attitu de

Extracurri cular activities

Chart er

Amou nt

Dewi W. 0.002

011 0 0.000

178 0.000892 0.000 051

0.055 964 Freshy

lia L. 0 0.000 646

0.000

178 0.000396 0.000 051 0.035

651 Jochel

in S. 0 0.000 646

0.000

178 0.000396 0.000 204

0.037 736 Sevali

no W. 0 0 0.000

178 0 0 0.013

342 Ranti

H. 0 0 0 0.000099 0.000

051 0.012

247

TABLE XII. DISTANCE BETWEEN ALTERNATIVE'S VALUE AND NEGATIVE IDEAL SOLUTION

Stude nt's Name

of repor

t cards

Prese nce Attitu

de

Extracurri cular activities

Chart er Amou

nt

Dewi

W. 0 0.000

646 0 0 0.000

051 0.026

401 Freshy

lia L.

0.002

011 0 0 0.000099 0.000 051

0.046 487 Jochel

in S.

0.002

011 0 0 0.000099 0 0.045

935 Sevali

no W.

0.002 011

0.000

646 0 0.000892 0.000 204

0.061 262 Ranti

H.

0.002 011

0.000 646

0.000

178 0.000396 0.000 051 0.057

289 Next, calculate the preference value using (9) and then ranking the alternative by the preference value. The final result of alternative ranking using TOPSIS is shown in Table XIII.

TABLE XIII. FINAL RESULT

No. Student's

Name Preference

Value Rank

1 Dewi W. 0.320537 5

2 Freshylia L. 0.565962 3

3 Jochelin S. 0.548995 4 4 Sevalino W. 0.821162 2

5 Ranti H. 0.823875 1

In Table XIII, we can see that Ranti H. is in the first place, so the best student in this selection using DSS AHP- TOPSIS is Ranti H.

D. Comparison of Manual System Result and AHP-TOPSIS Decision Support System Result

A comparison of results is made to find out whether there is a difference or not between the result of AHP-TOPSIS DSS and the result of the manual system. In a manual system, the assessment is carried out by the homeroom teacher. The result of the manual system is obtained from SMPN 1 Dumoga. The result of the comparison is shown in Table XIV.

TABLE XIV. COMPARISON BETWEEN MANUAL SYSTEM RESULT AND

AHP-TOPSISDSSRESULT

No. Student's Name

Manual System AHP-TOPSIS DSS Final

Score Rank Final Score (Preference

Value)

Rank

1 Dewi W. 84.54 5 0.32 5 2 Freshylia

L. 87.09 3 0.56 3

3 Jochelin

S. 86.54 4 0.54 4

4 Sevalino

W. 87.36 1 0.821 2

5 Ranti H. 87.27 2 0.823 1 The comparison result shows there is a difference between manual system results and AHP-DSS results in this study. In Table 14, we can see that in the manual system result, Ranti is in second place but in DSS using the AHP- TOPSIS result, Ranti is in first place. Factors that can influence this difference include the lack of objectivity of the committee in making the selection.

IV. CONCLUSION

In this study, AHP was applied to determine the weight of criteria, and TOPSIS was applied to determine the best alternatives. Decision support systems using AHP and TOPSIS can assist the selection committee in selecting high achieving students.

The application of a decision support system using AHP and TOPSIS in this study can make the selection results more objective.

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