Comparison of Weighted Sum Model and Multi Attribute Decision ...

International Journal of Software Engineering and Its Applications Vol. 11, No. 4 (2017), pp. 69-90 http://dx.doi.org/10.14257/ijseia.2017.11.4.06

Comparison of Weighted Sum Model and Multi Attribute Decision Making Weighted Product Methods in Selecting the Best Elementary School in Indonesia Budiharjo1, Agus Perdana Windarto2 and Abulwafa Muhammad3 1

Universitas Prof. Dr. Moestopo (Beragama) Jl. Hang Lekir I No. 8, Senayan, Jakarta 10270 2 STIKOM TunasBangsaPematangsiantar Pematangsiantar, Sumatera Utara, Indonesia 3 Universitas Putra Indonesia "YPTK" Padang Padang, Sumatera Barat, Indonesia [email protected], [email protected], [email protected] Abstract Selection program of the best elementary school in Indonesia aims to spur the development of the growth and improve the quality of the primary school. In this paper, the selection of the best elementary school is implemented based on predefined criteria. To help the selection process, a decision support system is needed. This paper employs Weighted Sum Model (WSM) and Multi Atribute Decesion Making Weighted Product (MADMWP) methods. The results of both methods were tested three times with three periods from the ranked data of schools obtained from Department of Education in Simalungun, North Sumatera, Indonesia. This system can be used to help in solving problems of the best elementary school selection. Keywords: Decision support system; Weighted product; Weighted sum model; Elementary school; Selection.

1. Introduction Presently, high schools are overwhelmed with huge amounts of information regarding student's enrollment, number of courses completed, achievement in each course, performance indicators and other data [1]. This has led to an increasingly complex analysis process of the growing volume of data and to the incapability to take decisions regarding curricula reform and restructuring [2]. Children needs to undergo the school period, therefore schools should be the most favorite place for them to active such as learning, playing and developing creativity [3]. To realize the comfortable and pleasant learning arena, it is necessary to hold the elections of the best school in each region to determine the quality of schools [4]. To determine which one is best school of a particular region, a system that is commonly called a decision support system is needed. Decision Support System is a computer-based system that accumulates a variety of information from various sources, present into organized form, analyze and facilitate the evaluation of the assumptions underlying the usage of certain models [5]. This decision support system usually uses the Weighted Sum Model (WSM) and Multi attribute decesion Making Weighted Product (MADMWP) methods. The processes on WSM methods and MADMWP are not much different. Calculation processes performed by the WSM method are simply to add the multiplication result of an alternative value with weighted criteria [6]. Meanwhile, in the MADMWP method, it is calculated by multiplying the result reappointment criteria values with weighted criteria [7].

ISSN: 1738-9984 IJSEIA Copyright ⓒ 2017 SERSC

International Journal of Software Engineering and Its Applications Vol. 11, No. 4 (2017)

The WSM and MADMWP methods can help in determining the best schools, but in counting only generate the greatest value will be chosen as the best alternative. The calculation will be in accordance with this method, if the alternative is selected to meet the specified criteria [8]. This method was chosen because it can determine the values for each attribute, followed by the selection of the best alternative, in this case the best alternative is the first ranked school based on the criteria that have been determined [9]. This study develops a decision support system that aims to solve the problems in the selection of the best elementary schools in the region Simalungun, North Sumatera, Indonesia using the WSM and MADMWP methods. The developed application system will be addressed to the head of UPT (Technical Implementation Unit) Department of Education of Simalungun in two sub-districts i.e. Dolok Pardemean and Bandar Simalungun, where these two districts are the samples used in this study. Through this system, considering into several factors such as the quality of teachers, the quality of students, facilities and infrastructure of the Department of Education, it is expected to be able to determine the best elementary school (SD) in the region, then the results are published to parents of prospective students so that they know and can select which school is the best for their children. The rest of this paper is organized as follow. Section 2 presents related work on decision support system. Section 3 presents material and method used. Section 4 presents results and following by discussion. Finally, the conclusion of this work is presented in Section 5.

2. Rudimentary 2.1. Decision Support System Decision Support System is a computer-based system that accumulates a variety of information from various sources, present into organized form, analyze and facilitate the evaluation of the assumptions underlying the usage of certain models [5]. A decision can be defined as a choice that has been taken from two or more available alternatives [10]. Each person must make many decisions every day. Potential option of a judgment is formed after learning objective and the alternative minimum [11]. Decision Support System can also be defined as a computer-based information system that combines models and data in an attempt to solve the problem of semi-structured and some unstructured problems with user intervention [12]. Decision Support System can provide an informative analysis to improve the efficiency of decision-making within an organization [13]. Decision Support System, including the decision models, data, and the user interface are very important unity [14]. 2.1.1. Decision Support System Components Decision Support System must have three components that determine technical capabilities of Decision Support Systems [15] i.e.: a. Sub-system Management Database, which is a sub-systems that manage the data by entering a database containing relevant data and managed by software. b. Sub-system Base Management Model, which regulates all issues sub-system integration and data access models of the existing decision in a Decision Support System. c. Sub-system Software Operator Dialogue. This sub-system includes all relations between Decision Support Systems and Users.

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Copyright ⓒ 2017 SERSC


2.1.2. Decision Support System Requirements a. b. c. d. e. f.

According to Bidgoli, the terms of a decision system [16] is given as follow: Requires hardware Requires software Requires people (designers and users) Designed to support a decision Should be able to help decision makers at every level of decision, and Emphasizing the problem of unstructured and semi-structured.

2.1.3. Steps of Decision Making Process The necessary steps in the process of decision making according to [15], are given as follow: a. Intelligence  Forming the perception of the faced situation is to recognize the decisionsituations and defining the main characteristics that exist in these situations  Build a model that represents the situation A model is a vehicle to assist in estimating the likely impact of a decision situation.  Quantitative selection of the size of the fee (disbenefits) and the most appropriate benefits for the faced situation. b. Design The selection of the specific alternatives that are formed by identifying and formulating clear steps can be performed. c. Selection  Evaluate the benefits and costs (disbenefits) of all alternative measures, namely the ratings due to the application of any alternative measures by using measurements of costs and benefits.  Establish criteria to select the best step, namely the adoption of legislation by correlating the results with the aim of making a decision.  Completion of the decision situation i.e taking a step on the basis of acceptable criteria. The steps above can be done repeatedly, either whole or partial steps. It is carried out continuously until the decision situation completely resolved. 2.1.4. Characteristics and Decision Support System Capabilities In respect of the number of the definition put forward regarding the definition and implementation of a Decision Support System, affecting there are many views on the system [17]. Decision Support System has characteristics and abilities [18], namely: a. Supports all activities of the organization b. Supports several decisions that interact can be used repeatedly and constantly c. There are two main components, namely data and models d. Using big external and internal data e. Having the ability what-if analysis and goal seeking analysis f. Using some quantitative models 2.2. Weighted Sum Model (WSM) The WSM is the general model which has been used for different applications such as robotics, processing data, and others [19]. It is a method often used in single dimension issues [20]. If there are alternatives m and n criteria, then according to [21] the best alternative can be formulated as follows:


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n

AiWSMScore   w j aij , for i  1,2,3,, m j 1

(1) where i  1,2,3,, m is the value of the best alternative, n is the number of criteria, an alternative value i the criteria j, are value criteria j and max used to sort the alternativedecision where alternatives have the greatest value will be placed on top [21]. The difficulty in this method is when the criteria used is not a single or multi-dimensional criteria dimensions. In these problems, then the existing criteria should be lumped into the same dimensions [21]. The following examples will be given to further clarify. There is a problem in choosing the best alternative among A1, A2, A3, A4 and A5. While the criteria that determine the selection process is K1, K2 and K3. The values of criteria and criterion value of each alternative are shown in Table 1. Table 1. Sample of Value Criteria Criteria Alternative A1 A2 A3 A4 A5

K1 0.3 15 20 30 20 15

K2 0.4 10 10 15 25 15

K3 0.3 10 15 10 15 10

Based on Table 1, are known value that is given to the criteria K1 is 0.3 or 30%, the criterion K2 is 0.4 or 40% and the criterion K3 is 0.3 or 30%. Then to calculate the value of each alternative used WSM formula in equation (1). Based on the formula in equation (1), A4 is selected as the best choice, because the value of A4 is the highest value of all the available alternatives. The result can be seen in the Table 2 as follow: Table 2. Ranking Results of WSM Alternative A4 A3 A2 A5 A1

WSM values 23.5 18 14.5 13.5 11.5

2.3. Multi Atribute Decision Making Weighted Product (MADMWP) The MADMWP is similar to WSM and also referred to as Multiplicative Exsponent Weighting (MEW). This is another model of MADM scoring, the main difference is instead of adding the usual in mathematical operations, but now it is multiplication. The MADMWP is a finite set of alternative decisions described in terms of some criteria for decision [22]. Preference for alternative Si is given as follows:

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n

S i   xijwi

(2)

j 1

where S xij wi n i j

= Alternative preference analogous to the vector S = The variable value of the alternatives on each attribute = Value weight criteria = The number of criteria = alternative value = value criteria n

where

w j 1

j

 1.w j is the rank of positive value to attribute profits, and negative values

to attribute costs. Relative preference of each alternative, given as: n

Vi 

x

wi ij

j 1 n

x

(3) * j

j 1

where v x w i j n

: Alternative preference analogous to a vector v : Values Criteria : Weights Criteria / Sub criteria : Alternative : Criteria : The number of criteria

Example of WSM will be used also to explain the formula of this MADMWP as given in Table 3 as follow. Table 3. Sample Weight Value Criteria Criteria

K1

K2

K3

Alternative

0.2

0.4

0.3

A1 A2 A3 A4 A5

15 20 30 20 15

10 10 15 25 15

10 15 10 15 10

The MADMWP value calculation will be done using the formulas in equations (2) and (3). From the above results, it can be seen which one is the best alternative, and the results can be seen in Table 4 as follow:


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Table 4. Results on Ranking MADMWP Alternative A4 A3 A2 A5 A1

MADMWP values 23.3797 16.3506 13.9028 13.2809 11.2925

3. Data and Methods 3.1. Research Steps This research was conducted by applying several methods of research as follows: a. Study of literature At this stage, do reference collection is needed in research. This is done to obtain information and data necessary for the writing of this study. References used may be books, journals, articles, and Internet sites related to this study. b. Data collection At this step, the process of collecting data related to this study as teacher data, student data and inventory data to the data will be processed by the system to be created. c. System planning At this step, system design in accordance with a predetermined plan, which include system design, database, and Graphic User Interface, as a design model for the support system to be built. The design process is based on the limitations of this research problem. d. System implementation At this step, the application of the system design of the system has been designed, well systems, databases and Graphic User Interface. e. Testing Systems At this step, the system will be tested to see whether the system is in conformity with the objectives set in this study. f. documentation System At this step, the creation of documentation system performed as research reports to keep the material in the form of written or in other forms that describe the whole system starting from the initial stage to the testing system. 3.2. Location Research and Case Studies This research was conducted in elementary school (SD) Simalungun in two sub-districts i.e. Dolok Pardemean and Bandar Simalungun as described in Table 5. Table 5. Data Objects Primary School became Rate in 2 Sub-districts No 1 2 3 4 5 6 7 8

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Bandar Simalungun SD 0911635 KERASAAN SDN 091618 PERDAGANGAN SDN 091619 PERDAGANGAN SDN 091620 PERDAGANGAN SDN 091621 PERDAGANGAN SDN 091622 PERDAGANGAN SDN 091623 PERDAGANGAN SDN 091624 PERDAGANGAN

No 1 2 3 4 5 6 7 8

Dolok Pardemean SD 094097 PONGKALAN TONGAH SD 094096 NAGORI SD 094097 SIMP. PONGKALAN ATONGAH SDN 091345 SIMPANG RAJA NIHUTA SD 095173 SIHEMUN SD RIAMA SIBUNTUON SDN 091345 PARLAJANGAN SDN 091396 SIBUNTUON



9 10 11 12 13 14 15 16

SDN 091625 BANDAR SDN 091626 BANDAR MARATUR SDN 091627 BANDAR BUNTU SDN 091628 BANDAR BUNTU SDN 091929 SIMP.DOSIN SDN 091630 PEM.KERASAAN SDN 091631 PEM.KERASAAN SDN 091644 BAHLIAS

9 10 11 12 13 14 15 16

SDN 091397 HUTABAYUPANE SDN 091398 SINAMAN PANE SDN 091400 DOLOK SARIBU SDN 091401 PARIKSABUNAGN SDN 091404 PARBALOKAN SDN 091405 SIPINTUANGIN SDN 094099 SIRUBERUBE SDN 095172 SARAGIHRAS

3.3. Analysis System Analysis of the system aims to identify issues that will arise in the manufacturing system, this is done so that in the process of designing an application error does not occur, which means, so that the system is designed to work well, appropriate and robustness of the system will be more awake and finished exactly at the specified time.This system will calculate the selection of the best elementary school in Simalungun. The system is designed using WSM dan MADMWP metods. 3.4. Problem Analysis Simalungun Regency particularly the sub district of Dolok Pardemean and the sub district of Bandar have an election program of the best elementary school that will be done every year. The selection is done to determine the elementary school which deserves to be the best elementary school in the region to serve as the core elementary school and sequential. In addition, the selection of primary school is also intended to motivate every school principal to be more active and more concerned in improving the quality of primary school he leads. To choose the best schools, the calculations performed involving data and in the process a bit easier there was an error when done manually. With the Decision Support System for the selection of the best primary schools, the calculation process will become easier and accurate [23]. Because the system is only intended to determine the best elementary school in Simalungun, then the system is built is a systembased desktop. To identify the problem, Ishikawa fishbone diagram is used (See Figure 1).

Figure 1. Ishikawa Diagram for Problem Analysis System


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Ishikawa diagram is a graphical tool that is used to explore and display of opinion about the core components of a condition in the organization. This diagram can also browse resources on the cause of a problem [15]. 3.5. System Requirements Analysis System Requirements Analysis includes analysis of the system functional requirements and non-functional requirements analysis system. 3.5.1.

System Functional Requirements

Functional requirement that must be owned by the election decision support system of the best elementary school in simalungun is: a. The system can enter student data, teacher data, inventory data, and weights the criteria. b. The system can determine who deserves to be selected for the best elementary schools using WSM and MADMWP. c. The system can show the calculation results based on WSM and MADMWP. 3.5.2. Non-Functional Requirement System To support the performance of the system, the system should be able to function as follows: a. The system can perform calculations election primary school best with high computing speed. b. The system should be easy to use so it can be operated by users. 3.6. Modelling System modeling performed to obtain a clearer picture of any object that will interact with the system, as well as what things should be done by a system so that the system can function properly in accordance with the purpose and usefulness. This study uses UML (Unified Modeling Language) as a modeling language for designing and planning Election Decision Support System for the Best Elementary School in Simalungun. The UML models are used, among others, use case diagrams, activity diagrams, and charts sequence [24]. 3.7. Use Case Diagram Use Case Diagram is a diagram to represent the interactions that occur between the systems by users [25]. Use case diagrams will explain the function of what is done by the system.

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Figure 2. Use Case Diagram of Decision Support System for the Best Elementary School From Figure 2 above, Staff can choose two actions that add data and perform calculations of the system based on the method of WSM and MADMWP. The process can be added on the data stated in Table 6 as follow: Table 6. Table of Use Case in the Process of Adding Data Name Actor Description Basic Flow Alternate Flow Pre Condition Post Condition

Process to add data staff who have been determined use this case to describe the process of adding the data staff are in charge of running the system and directly enter data staff can add data through a menu of data teacher, student data, and inventory data staff can see a table listing the school staff managed to enter data into the table value criteria schools list

In the process of the calculation method WSM and MADMWP, can be expressed in Table 7 below. Table 7. Table of Use Case in the Process of Calculation of the best Primary School Name Actor Description Basic Flow Alternate Flow Pre Condition Post Condition

Calculation method of WSM and MADMWP Staff who have been determined Use case describes the calculation process in determining the best primary schools using the WSM and WPM staff tasked with selecting the form of calculation and enter the weight of the assessment criteria staff can go back to your school and to add new data staff can see the criteria values of all the available alternatives WSM and the staff know the value of the entire alternative WPM in separate tanle

3.7.1. Activity Diagram


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To add data to the process of decision support systems in determining the best elementary school, the activity diagram can be seen in the Figure 3 as follow:

Figure 3. Activity Diagram for Schools List At the moment the system starts the user can directly enter data values necessary criteria to perform calculation of the best elementary school. For the calculation of decision support systems in determining best elementary school WSM method and MADMWP, activity diagram can be seen in the following Figure.

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Figure 4. Activity Diagram for WSM and MADMWP From Figure 4, in the calculation method of WSM and MADMWP, after the system displays the form of account, users then asked to choose the period of alternative data to be counted. Furthermore, users are required to enter the weight value criteria of each criterion will be counted. If the weights of criteria already equipped, then press calculate button to start the calculation. The results of the calculation will automatically appear in the results table calculations. Users can perform calculations repeatedly. 3.7.2. Sequence Diagram The following will explain sequence diagrams i.e. the process of entering data and calculation process that occurs in the Decision Support System in selecting the best elementary school in Simalungun. In the calculation process of determining the best elementary school with methods WSM and MADMWP, the developed sequence diagrams can be seen in the following figure.


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Figure 5. Sequence Diagram Calculation Process of Determining the best Elementary School From Figure 5, the sequence diagram above shows that users access the form computer. Then the user selects the data period and enters the weight values predefined criteria. Furthermore, the calculation result data entered into the database and displayed in the results table calculation.In the process of entering data Decision Support System Selection of the best elementary school in Simalungun, sequence diagrams can be seen in the following figure.

Figure 6. Sequence Diagram of Add Data Process From Figure 6, sequence diagram above shows that users access the form “Input Data”. Form “Input Data” is an early look at this system. Then the user enters values predefined criteria. Furthermore, the data entered into the database and displayed in the data table value criteria.

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3.7.3. Flowchart Sistem The Figure 7 shows a flowchart of Decision Support System for selection of the best elementary school in Simalungun.

Figure 7. Flowchart of Decision Support System in Determining the Best Elementary School

4. Results and Discussion Implementation is a stage that must be passed in the software development process of a system. This phase is carried out after the first through the stages of analysis and design of systems that have been described in the previous chapter. 4.1. Implementation of WSM Application of WSM Method in the system that has been developed on the calculation process in determining the best elementary school in Simalungun is presented in this section. The elementary school is an alternative decision is not of the whole area Simalungun but only on the two sub-districts i.e. Bandar Simalungun and Dolok Pardemean. To obtain the value of each alternative WSM is multiplication value data weighting criteria with predetermined criteria of all alternatives. Then the result of multiplying the data value criteria with criteria weights are summed to obtain the value of


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each alternative WSM. Here is presented the sample data of elementary school is an alternative in the selection of the best elementary school in Simalungun. Table 8. Data Sample of Elementary Schools from Academic Year 2011/2012 School SD 0911635 Kerasaan SDN 091618 Perdagangan SDN 091619 Perdagangan

Student Discipline Scores 63.37 5.35 60.08 5.06 60.70 5.33

Behaviour 5.53 4.94 5.67

Teacher Eduction 2.78 3.80 3.00

Certification Lab Library 1.00 1.00 1.00

1 0 0

1 1 1

Props 13 4 56

In Table 8 above, there are three samples data of elementary schools as an alternative in the selection of the best elementary schools in Simalungun. The steps to calculate WSM value of the available alternatives is discussed as follow. 4.1.1.

Step 1: Determine the Weight Value Criteria

The weight values set by the Department of Education in Simalungun can be seen in Table 9 as follow: Table 9. Weight Value Criteria Criteria Student scores Discipline Behavior Teacher Education certifications Laboratory Library Props 4.1.2.

Weight (%) 10 10 10 20 20 10 10 10

Step 2: Calculate the value WSM using the formula (1)

First, multiply the value of each alternative criteria with weight value criteria as shown in Table 10 below. Table 10. Multiplication Alternative Value to Weight Criteria Elementary school SD 0911635 Kerasaan SDN 091618 Perdagangan SDN 091619 Perdagangan Elementary school SD 0911635 Kerasaan SDN 091618 Perdagangan SDN 091619 Perdagangan

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Student scores 63.37 × 0.1 60.08 × 0.1 60.70 × 0.1 Teacher certification 1.00 × 0.2 1.00 × 0.2 1.00 × 0.2

Discipline 5.35 × 0.1 5.06 × 0.1 5.33 × 0.1 Laboratory 1 × 0.1 0 × 0.1 0 × 0.1

Behavior 5.53 × 0.1 4.94 × 0.1 5.67 × 0.1 Library 1 × 0.1 1 × 0.1 1 × 0.1

Teacher Education 2.78 × 0.2 3.80 × 0.2 3.00 × 0.2 Props 13 × 0.1 4 × 0.1 56 × 0.1



4.1.3.

Step 3: The Value of Each Alternative WSM Obtained

Then add the result of multiplying the value of the alternative criteria with the weight value criteria for WSM value as shown in Table 11. Table 11. Results of WSM Elementary school WSM value 6.337+0.535+0.553+0.556+0.2+0.1+0.1+1.3= SD 0911635 Kerasaan 9.681 8.468 SDN 091618 Perdagangan 6.008+0.506+0.494+0.76+0.2+0+0.1+0.4= SDN 091619 Perdagangan 6.07+0.533+0.567+0.6+0.2+0+0.1+5.6= 13.67 Based on Table 11 alternatives that have the highest WSM valueis SDN 091619 PERDAGANGAN andthe lowest is SDN 091618 PERDAGANGAN. 4.2. Implementation of MADMWP Implementation of MADMWP method in a system that has been developed on the calculation process in determining the best elementary school in Simalungun is presented in this section. The elementary school is an alternative decision is not of the whole area Simalungun but only on the two sub-districts i.e. Bandar Simalungun and Dolok Pardemean. The MADMWP value of each alternative is obtained from the data value criteria raised to weight criteria which are then multiplied the result reappointment. Value criteria must be at least equal to one because the results of the calculation of this MADMWP method will be zero if there is a value of zero criteria [26]. This happens because this method uses the multiplication operator when a value multiply by zero, the result will be zero. Here is a sample data of elementary school is an alternative in the selection of the best elementary school in Simalungun. Table 12. Data Sample of Elementary Schools from Academic Year 2011/2012 Elementary School SD 0911635 Kerasaan SDN 091618 Perdagangan SDN 091619 Perdagangan

Student scores 63.37 60.08 60.70

discipline 5.35 5.06 5.33

behaviour 5.53 4.94 5.67

Teacher certificat education ion 2.78 1.00 3.80 1.00 3.00 1.00

Lab. 1 0 0

library 1 1 1

In Table 12 above, there are 3 sample data elementary schools that become an alternative in the selection of elementary school (SD) in Simalungun. The steps to calculate the value of the available alternatives of MADMWP method are described as follow. 4.2.1.

Step 1: Determine the Weight Value Criteria

The weight values set out in the selection of the best elementary school can be seen in table 13 below. Table 13. Weight Criteria Value Criteria Student scores Discipline Behaviour Teacher education Certification


Weight (%) 10 10 10 20 20

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Props 13 4 56


Laboratory Library Props 4.2.2.

10 10 10

Step 2: Calculate the Value MADM WP using the formula (2)

Because the data held there is zero then first change the value to 1 and then raise to value of each alternative criteria with weight value criteria as shown in Table 14 below. Table 14. Reappointment Value Alternative to Weight Criteria Elementary school SD 0911635 Kerasaan SDN 091618 Perdagangan SDN 091619 Perdagangan Elementary school SD 0911635 Kerasaan SDN 091618 Perdagangan SDN 091619 Perdagangan

4.2.3.

Student scores 63.37^0.1 60.08^0.1 60.70^0.1 Teacher certification 1.00^0.2 1.00^0.2 1.00^0.2

Discipline 5.35^0.1 5.06^0.1 5.33^0.1

Behavior 5.53^0.1 4.94^0.1 5.67^0.1

Laboratory 1^0.1 1^0.1 1^0.1

Teacher education 2.78^0.2 3.80^0.2 3.00^0.2

Library 1^0.1 1^0.1 1^0.1

Props 13^0.1 4^0.1 56^0.1

Step 3: MADMWP value of each Alternative is Obtained

Then multiplying the alternative result reappointment criterion value with value weighting criteria to gain value of MADMWP as can be seen in Table 15 below. Table 15. Results Value of MADMWP Elementary school SD 0911635 Kerasaan SDN 091618 Perdagangan SDN 091619 Perdagangan

MADMWP value 1.514*1.182*1.186*1.226*1*1*1*1.292 = 3.361 1.506*1.176*1.173*1.306*1*1*1*1.148 = 3.114 1.507*1.182*1.189*1.245*1*1*1*1.495 = 3.942

Based on table 4.8 alternatives that have highest value is SDN 091619 Perdagangan with MADMWP value 3.942 andthe lowest is SDN 091618 Perdagangan. 4.3. Testing Systems System testing is performed to determine how the system performance in the process of calculation in determining of the Best Elementary School uses WSM and MADMWP methods. The results of both methods will be compared with data from the three periods of the best Elementary School there is in Simalungun. 4.3.1. Calculation Process Testing Selection of the best Elementary School from Academic Year 2011/2012 Figure 8 presents the results of calculation of the best elementary school from academic year 2011/2012 using WSM and MADMWP methods. Based on calculations by WSM in Figure 8, SD 091620 Perdangan is the elementary school which achieves the highest score of WSM. Meanwhile, the result of the calculation with MADMWP method, SD 091635 Perdagangan is the elementary school which achieves the highest score.

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Based on data from the elementary school rankings, SD 091 620 Perdangan is an elementary school that achieves the best ranking in academic year 2011/2012.

Figure 8. Calculation Results on Selection of the Best Elementary School in Academic Year 2011/2012 4.3.2.

Calculation Process Testing Selection of the Best Elementary School from Academic Year 2012/2013

Figure 9 below presents the results of calculation of the best elementary school from academic year 2012/2013 using WSM and MADMWP methods.


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Figure 9. Results Calculation Selection of the Best Elementary School in Academic Year 2012/2013 Based on calculations by WSM in Figure 9, SDN 091620 Perdagangan is the elementary School which achieves the highest score. Meanhhile, the results of the calculation with MADMWP method, SDN 091625 Bandar is the elementary school which achieves the highest score. Based on data from the elementary school rankings, SDN 091620 Perdagangan is the elementary school that achieves the best rangking in academic year 2012/2013. 4.3.3.

Calculation Process Testing Selection of the Best Elementary School from Academic Year 2013/2014

Figure 10 below presents the results of calculation of the best elementary school from academic year 2013/2014 using WSM and MADMWP methods.

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Figure 10. Results Calculation Selection of the Best Elementary School in Academic Year 2013/2014 Based on calculations by WSM in Figure 10, SDN 091620 Perdagangan is elementary School who gets the highest score. Meanwhile, the result of the calculation with MADMWP method, SDN 091625 Bandar is also elementary school which achieves the highest score. Based on data from the elementary school rankings in Simalungun, SDN 091620 Perdagangan is an elementary school that had the best ratings in academic year 2013/2014. 4.3.4.

Comparative Testing Results Calculation Method of WSM and MADMWP

After three rounds of tests performed by the system against three ranked data period of elementary school in Simalungun, the test results can be expressed in the Table 16. There is a difference in results between the results of calculations by the method of WSM and MADMWP. The results of calculations by the method of WSM in the three periods showed similar results. Meanwhile, the results of the calculation with MADMWP method change in the third period. From the three periods tested, the method of WSM has higher compatibility than the method of MADMWP with data ratings from elementary schools in Simalungun, Indonesia.

5. Conclusion In this paper, comparison of weighted sum model and multi attribute decision making weighted product methods in selecting the best elementary school in Indonesia has been presented. Based on the results of the implementation and testing of the Decision Support System using WSM and MADMWP in determining the best elementary school in Simalungun, it can be concluded that:


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a. The system can solve the problems of the selection of the best elementary school in Simalungun by implementing the method of WSM and MADMWP on the systems. b. The results obtained from the calculation of the system are only as a reference for users to solve problems in determining of the best elementary school in Simalungun. c. After testing the three periods of data ranked schools which are owned by the department of education in Simalungun, the results from WSM showed higher accuracy than that MADMWP. Thus, in the case of the selection of the best elementary school in Simalungun, suitability of WSM is higher than that MADMWP. By using this system, users will be easier to determine the best elementary school. Table 16. Results of Testing System Data Primary School in Simalungun Academic year

WSM results

MADMWP results

2011/2012

SD 091620 Perdangan = 13.67 SD 091635 Perdagangan = 11.99 SDN 091618 Perdagangan = 11.44 SDN 091619 Perdagangan = 10.50 SDN 091621 Perdagangan = 10.01 SDN091622 Perdagangan = 9.68 SDN091623 Perdagangan = 9.34 SDN091624 Perdagangan = 9.33 SDN091625 Bandar = 9.04 SDN091626 Bandar Marutu = 8.89 SDN 091627 Bandar Buntu = 8.70 SDN 091628 Bandar Buntu = 8.61 SDN 091929 Simp.Dosin = 8.60 SDN 091630 Pem.Kerasaan = 8.58 SDN 091631 Pem.Kerasaan = 8.47 SDN 091644 Bahlias = 8.21

SD 091635 Perdagangan = 3.954 SD 091620 Perdagangan = 3.949 SDN 091618 Perdagangan = 3.708 SDN 091619 Perdagangan = 3.509 SDN 091621 Perdagangan = 3.405 SDN 091622 Perdagangan = 3.378 SDN 091623 Perdagangan = 3.378 SDN 091624 Perdagangan = 3.245 SDN 091625 Bandar = 3.215 SDN 091626 Bandar Marutu = 3.117 SDN 091627 Bandar Buntu = 3.037 SDN 091628 Bandar Buntu = 3.033 SDN 091929 Simp.Dosin = 2.965 SDN 091630 Pem.Kerasaan = 2.724 SDN 091631 Pem.Kerasan = 2.666 SDN 091644 Bahlias = 2.663

2012/2013

SDN 091620 Perdagangan = 13.92 SDN 091625 Bandar = 12.15 SDN 091626 BMaratur = 12.02 SDN 091627 Bandar Buntu = 11.22 SDN 091628 Bandar Buntu = 10.20 SDN 091929 Simp.Dosin = 10.06 SDN 091630 Pem.Kerasaan = 9.93 SDN 091631 Pem.Kerasaan = 9.52 SDN 091618 Perdagangan = 9.36 SDN 091619 Perdagangan = 8.91 SDN 091621 Perdagangan = 8.83 SDN 091622 Perdagangan = 8.79 SDN 091623 Perdagangan = 8.76 SDN 091624 Perdagangan = 8.43 SDN 091635 Perdagangan = 8.11 SDN 091644 Bahlias = 8.09

SDN 091625 Bandar = 3.982 SDN 091626 Bandar Maratur = 3.913 SDN 091627 Bandar Buntu = 3.785 SDN 091628 Bandar Buntu = 3.774 SDN 091929 Simp.Dosin = 3.695 SDN 091630 Pem.Kerasaan = 3.686 SDN 091618 Perdagangan = 3.412 SDN 091619 Perdagangan = 3.260 SDN 091621 Perdagangan = 3.167 SDN091622 Perdagangan = 3.153 SDN 091623 Perdagangan = 3.020 SDN 091624 Perdagangan = 2.991 SDN 091631 Pem.Kerasaan = 2.972 SDN 091620 Perdagangan = 2.725 SDN 091635 Kerasaan = 2.663 SDN 091644 Bahlias = 2.613

88



2013/2014

SDN 091620 Perdagangan = 14.19 SDN 091618 Perdagangan = 12.20 SDN 091619 Perdagangan = 11.93 SDN 091621 Perdagangan = 10.64 SDN 091622 Perdagangan = 10.50 SDN 091623 Perdagangan = 9.90 SDN 091624 Perdagangan = 9.74 SDN 091635 Kerasaan = 9.70 SDN 091625 Bandar = 9.66 SDN 091626 Bandar Maratur = 9.59 SDN 091627 Bandar Buntu = 9.33 SDN 091628 Bandar Buntu = 9.31 SDN 091929 Simp.Dosin = 8.87 SDN 091630 Pem.Kerasaan = 8.77 SDN 091631 Pem.Kerasaan = 8.73 SDN 091644 Bahlias = 8.55

SDN 091620 Perdagangan = 4.461 SDN 091618 Perdagangan = 4.121 SDN 091619 Perdagangan = 3.978 SDN 091621 Perdagangan = 3.859 SDN 091622 Perdagangan = 3.794 SDN 091623 Perdagangan = 3.699 SDN 091624 Perdagangan = 3.57 SDN 091635 Kerasaan = 3.552 SDN 091625 Bandar = 3.336 SDN 091626 Bandar Maratur = 3.296 SDN 091627 Bandar Buntu = 3.265 SDN 091628 Bandar Buntu = 3.198 SDN 091929 Simp.Dosin = 3.132 SDN 091630 Pem.Kerasaan = 2.954 SDN 091631 Pem.Kerasaan = 2.691 SDN 091644 Bahlias = 2.660

Acknowledgement This research is supported by Universitas Prof. Dr. Moestopo (Beragama), Jakarta, Indonesia.

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