IMPROVING EMPLOYEE PROMOTION SELECTION

PROCESS BY USING FUZZY ANALYTICAL

HIERARCHY PROCESS AND TOPSIS METHOD IN

COMPANY XYZ

By

Yoana Belanita Riwang

ID No. 004201200008

A Thesis presented to the Faculty of Engineering President

University in partial fulfillment of the requirements of Bachelor

Degree in Engineering Major in Industrial Engineering

2015

ABSTRACT

Employee promotion is the essential practice to manage the human resources as the

asset for the company or business. Both of employee and the company take the

advantages from employee promotion practice. This research analyzes about the

employee promotion selection process in Company XYZ, a well-known oil and gas

business company in Indonesia. Currently, there is no specific quantitative method to

take the decision making in employee promotion selection process. Therefore,

improve of employee promotion selection process is conducted. It includes improve

the criteria and sub-criteria for assess the employees’ performance, the weighting of

each employee promotion candidates through Fuzzy Analytical Hierarchy Process

(Fuzzy AHP) method and Technique for Order Preference by Similarity to Ideal

Solution (TOPSIS) method. Fuzzy AHP method is used to determine the weight of

criteria to goal, sub-criteria to criteria and employee promotion candidates toward

each sub-criterion. TOPSIS method is used to rank the employee promotion

candidates by calculating the distance. Both of Fuzzy AHP and TOPSIS method are

calculated and analyzed to reduce the fuzziness and to take the decision of promoted

employee accurately. The result of research shows that the best three of proposed

promoted employee have better performance result and as the result of reducing

uncertainty in the employee promotion decision making.

Keywords: employee promotion, decision making, fuzzy AHP method, TOPSIS

method, weight, fuzziness

CHAPTER I

INTRODUCTION

1.1 Problem Background

Human resource is one of the important elements in an organization. Human

resources also give big impact to the successfulness level to its organization or

company. Because of that reason, the human resources must be managed with the

right way to explore the human resources ability in terms of achieving business

objectives.

One of the practices to manage human resources is promote higher position of

employee. Promotion is one of the most essential aspects in career development of an

employee. A good company should have clear procedure and factors that will support

the promotion. Both of employee and company have the benefits of employee

promotion. One of the benefits for the company is decreasing the number of

employee turn-over. By conducting the employee promotion, employee could predict

their career development in that company.

The common problem in employee promotion selection process is the dissatisfaction

of employee promotion result. The dissatisfaction of employee promotion result could

be as subjective perspective, mismatches in pairing employee and position and the

long period of the selection process. Moreover, the accuracy of decision making also

might be caused of the decision maker only focus on first criterion while there are

more criteria that also would be affected in employee promotion decision making.

In Company XYZ which is involving in the business firm of oil and gas, employee

promotion is conducted twice a year in the mid year and in the end of the year.

Employee promotion gives the motivation to the employees for improving their work

performance. It is highlighted planning in Company XYZ especially for Human

Resources Division. HR Division will conduct the meeting to determine the employee

who can get the promotion.

Currently, company XYZ does not use any specific quantitative method to decide the

employee promotion selection process. It makes the decision of employee promotion

is hardly to be decided because the process is only conducted based on discussion

without any specific method or approach. Moreover, it creates the dissatisfaction of

employees because the assessment of the employee promotion selection process could

be subjective. This project suggests the Multi Criteria Decision Making approaches

which are Fuzzy Analytical Hierarchy Process (F-AHP) and TOPSIS method. By

having specific methods, it is easier for the Company Management to take the

decision of employee promotion process.

In this research, the decision of employee promotion in Company XYZ is influenced

by personal characteristics, inter-personal relations, work attitude, work result and

education. Each of factors will be placed as a criteria and it will be divided and

formed into sub – criteria. Each of criteria and sub-criteria is based on combination of

literature study and the employee promotion decision making assessment in Company

XYZ.

Fuzzy Analytical Hierarchy Process (FAHP) and Technique for Order Preference by

Similarity to Ideal Solution (TOPSIS) method are two of the Multi Attribute Decision

Making (MADM) methods to find the optimum solution which is the employees that

should be promoted from a number of alternatives to certain criteria. Fuzzy AHP

method will be used to determine the weight to be assigned to the criteria and sub

criteria and to calculate overall score. After the overall score is came the out, the

score will be ranked by using TOPSIS method so the selected employee that will get

job promotion will be shown as a result.

1.2 Problem Statement

Based on the problem faced by Company XYZ, this project is done to answer these

following questions.

What are the criteria and sub-criteria as the indicator performance for

employee promotion candidates?

How the Fuzzy AHP and TOPSIS method could improve employee promotion

selection process in Company XYZ?

Which employee promotion candidate is as the most priority employee to be

promoted according to the performance indicator?

1.3 Objectives

The main objectives of this project are as follows.

To determine criteria and sub-criteria as the employee performance candidates

performance indicator.

To calculate and analyze the Fuzzy AHP and TOPSIS method could improve

employee promotion selection process in Company XYZ.

To describe and list the employee promotion candidate that will be the most

priority employee to be promoted according to the performance indicator.

1.4 Scope

Due to limited time and resources, there are the following project scopes.

The resources data only could be collected from June 2015 – July 2015.

The data are only from employee promoted candidates from WCI Division.

The data of employees promoted candidates are only based on Human

Resources Division approval.

The data are taken from Manager of Human Resources, Head Department of

Human Resources Method, and Head of Service Organization Development,

Planning and Reporting by filling the questionnaire and interviewing.

1.5 Assumption

Some assumptions have to be made in order to cover some areas.

The determination of performance criteria, sub-criteria and indicators is the

authority of Human Resources Division (HR) /Organization Development,

Planning and Reporting (OPR) Section alone.

All reviews are conducted consistently in the future.

There is no external factor except HR/OPR Division that contaminated the

result of employee promotion decision making process.

1.6 Research Outline

Chapter I Introduction

This chapter consists of problem background, problem statement,

objective, scope, and assumption as the introductory of this project.

Chapter II Literature Study

This chapter delivers the theory of decision making method (Fuzzy

AHP and TOPSIS method) as well as the suggested method to achieve

the objective of this project.

Chapter III Research Methodology

In this chapter, the process of conducting this research is described and

explained step by step to capture the image of the overall process.

Chapter IV Data Analysis

This chapter provides the collected data to support this research and

also the decision making method (Fuzzy AHP and TOPSIS method)

analysis to solve the problems.

Chapter V Conclusion and Recommendation

This chapter concludes the research based on the calculation and

analysis as well as gives the recommendation for future research.

1

CHAPTER II

LITERATURE STUDY

2.1 Job Promotion

Nowadays, employee is not only being a worker, most of companies and

businesses view the employee as human capital to achieve the business objectives.

Without capable employees, the companies will not be able to produce business or

company goals, or give the benefit by financial result to the company. Because of

those reasons, the companies view the employee as the asset of human capital for

their businesses.

Employee turnover is one of the common problems of a company. One of the

causes of employee turnover is the companies do not recognize the employee as

the resources or assets to achieve the business objectives. It may cause the time

wasting for the business and the company has to re-organize its hierarchical

structure so that business plans and goals will be met. The main reason why

employee turnover happened is limited career advancement or career path. Every

employee tends to think about their career development. In a good company, one

of the prevention ways the unwanted turn-over is by promoting the employee to

higher level of job or position.

2.1.1 Definition of Job Promotion

Job promotion is the shifting of employee for a job of higher significance and

higher compensation (Malik, Danish and Munir, 2012). In other words, job

promotion is the movement of an employee as the human capital to the higher

level in the organizational hierarchy that leads to higher responsibility and higher

compensation package.

The impacts of job promotion are increasing the salary, better status and prestige,

higher opportunities and challenges, higher authority and responsibility, and

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higher ability to influence organizational decision making. Moreover, the job

promotion also measured how success of an employee in the company as their

career development. Job promotion gives the employee an opportunity for

actualize their selves through challenging tasks and jobs. It makes the employees

have higher motivation to give the best performance for achieving the result.

2.1.2 Purpose of Job Promotion

There are 2 fundamental purposes of job promotion, which are:

1. It assigns more capable individuals for higher responsibility position or

job.

By conducting the job promotion, the chosen employee who had the

greater performance result and potentiality will have higher position or job

to handle higher responsibility and he/she will take more decision for

achieving the organization goals.

2. It motivates employees’ peer to give their best performance for achieving

business goals.

The promotion process can increase the employee motivation to give their

best performance result. It makes the competitive ambience between each

employee to show their performance to their superior. Automatically, if the

motivation is increasing, the productivity will be increasing too. Job

promotion is also on the process to increase the employee retention to

reduce the number of turnover.

2.1.3 Types of Promotion

Based on Phelan and Lin (2001), some types of promotion are explained below.

1. Absolute Merit – Based Promotion.

In this type of promotion, the employees can be promoted if their

performance result is above the certain criteria and if there is a vacancy in

the upper level. At the monitoring period, the employee will stay in the

organization if his/her performance is in below certain performance

criteria.

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2. Relative Merit – Based Promotion.

In this type of promotion, the employees will be promoted if their

performance is above the performance criteria, and will be fired if their

performance is below the performance criteria.

3. Seniority – Based Promotion.

This type of promotion is conducted by the most experience in the

organization. The employee can be promoted based on longest service

time in the organization among the employee peers at the same level.

4. Random Promotion.

This type of promotion does not have base or fundamental criteria to

promote the employee. This type of promotion selects the employee

randomly from the lower level to the higher level regardless of

performance and seniority.

5. Traditional Promotion.

This type of promotion is also called as top – down promotion process.

The superior has main responsibility for seeking the best candidate and

specifying the qualities a successful candidate. This type of promotions is

stressful and time – consuming for superior and candidates and many good

managers are lost the good candidates.

6. ICR Promotion.

ICR stands for Initiative, Creativity, Results. This process is the opposite

of traditional promotion. This type of promotion is called as down – top

promotion process. The promotion system is based on an intuitive

understanding that companies growing rapidly, or needing to innovate,

have to reward the employees who show the initiative and creativity.

2.1.4 Benefit of Promotion

Promotion gives the benefits for both sides which are for employee and the

organization. Below are the benefits for both sides.

Benefits for the company are:

Develop the certain competencies of jobs.

Having a good standard measurement to assess the employee performance.

4

Reducing the number of turn-over.

Increasing the employee motivations that will impacts to the productivity.

Benefits for the employee are:

Assign the employee in a position where an employee’s skills and

knowledge can be better developed.

Higher responsibility and authority to make the decision making that can

impact to the whole organization.

Increase the salary.

Higher status and prestige in the organizational level.

2.1.5 Factors that Affect Job Promotion Decision Making

Deciding the right choice for promoting the employee is difficult process. Because

of that problem, it is needed certain factors to support the decision making of

promotion process. Some factors are involved to get the standard assessment are

explained below.

1. Task environment.

Promotion decision will effectively take if the task environment is routine.

The routine task environment means there are not many several of tasks

and it is not dispersed environment. The past behavior of an employee will

be seen in routine task environment and past behavior is useful as a guide

for future performance.

2. Individual capability.

One of the main factors to evaluate the employee performance is

individual capability. The company tends to choose promoted employee

with heterogeneous capabilities because he/she will give greater

contribution for the company and business.

3. Organizational structure

Every worker wants to actualize their selves for showing their

performances in the company management. By conducting job promotion,

the employee will have an opportunity to get the position in organizational

structure or hierarchical structure.

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4. Frequency of Monitoring.

The monitoring period refers to the period or time between the last

promotion or the hired employee until the promotion decision. If the

monitoring period is longer, the performance assessment and job

promotion decision will be more accurate.

5. Performance Criteria.

Performance criteria become very important as supported factor in

decision making. Performance criteria show the employee result of work

whether they did the task well or not, on – time or not.

6. Transferability of Knowledge.

The company tends to choose employee in a hierarchical structure with the

transferability of knowledge. It means that employee could transfer or

share his/her knowledge so their peers will have the same knowledge and

give better performance for the company.

2.1.6 Common Problem in Promotion Process

Some problems are occurred when the promotion process such as:

1. Promotion makes some employees are disappointed, it is happened when

the employee’s peer with similar qualifications and experience are

promoted because of subjective perspective and lack of systematic

promotion policy in a company.

2. Some employees ignore the promotion, it is happened when the employee

are promoted to the unwanted place or position, unwanted

responsibilities, and the employee feels that he/she will be quite

incompetent to carry out the job.

2.1.7 Criteria and Sub-criteria in Employee Promotion Selection Process

There are many criteria and sub criteria that should be assessed for employee

promotion selection process. Table 2.1 shows the criteria and sub-criteria to select

the promoted employee.

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Table 2.1 Employee Promotion Criteria

No Criteria Sub-criteria Description

1 Personal

Characteristics

Knowledge

Employee shows that he/she has supported

knowledge to do the assigned job.

Ability to learn

Employee able to comprehend a task and

the solution to solve the task.

Innovation

Employee able to create the creative way

by translating the idea to the work result.

Problem solving

Employee able to achieve the solution by

working through the details problem.

Adaptability

Employee able to transform their selves to

the changed environment.

Decision

making ability

Employee able to select the proper action

for solving the problem.

Emotional

stability

Employee able to maintain the emotional

even faced with the pressure.

2 Inter-personal

Relation

Cooperation

Employee able for acting to work together

to reach the goal.

Teamwork

Employee able to work with other

coordinated people or collaborative with

others to get the same purpose.

Team loyalty

Employee shows the faithful commitment

to the group or a team of a person.

Communication

Employee able to deliver the information

to the others in an efficient and effective

way.

3 Work Attitude

Responsibility

Employee able to complete the assigned

task as a duty and satisfactory obligation.

Motivation

Employee shows encouragement and

desired energy to be continually committed

and completed the job.

Discipline

Employee reflects behavior of more

control their selves and willing to obey the

rules.

Commitment

Employee shows the dedication for time,

energy and self for a job.

4 Work Result

Accuracy

Employee shows their work result of being

true, correct and free of mistake or error.

Efficiency

Employee able to complete the task with

the least consumption of resources (time,

energy, etc).

Rapidity

Employee acts to complete the task on-

time.

Completeness of

assignment

Employee able to finish the task or job

completely.

(Source: Avazpour, Ebrahimi, and Fathi, 2013, pp. 969-976)

7

2.1.8 Method for Employee Promotion Decision Making

Based on Setak et al (2012) in journal of Abbasi and Asgari (2014, pp. 351-371),

there are some methods in terms of decision making which are:

Table 2.2 Method for Decision Making

Method Model Description

Multiple

Attribute

Decision

Making

(MADM)

Analytical Hierarchy Process (AHP)

Involve more than one criterion

that generally going against one

into each other.

Analytic Network Process (ANP)

Technique for Order Preference by

Similarity to Ideal Solution (TOPSIS)

Preference Ranking Organization

Method for Enrichment Evaluations

(PROMETHEE)

Multiple Attribute Utility Theory

(MAUT)

Mathematical

Programming

Linear Programming Use quantitative criteria that

elaborate the constraint and

enable having multiple

objectives.

Multi Objective Linear Programming

(MOLP)

Goal Programming

Fuzzy

Approach

Solve by using linguistic variable

to reduce uncertainty of human

judgment.

Artificial

Intelligence

Case Based Reasoning (CBR) Bases on computer system that

reflects on historical data and

experience. Artificial Neural Network

Combined

Approach

AHP + TOPSIS Ensure the decreasing of

uncertainty AHP + MOLP

MAUT + LP

In this research, the fuzzy approach and combined approach are used to reduce the

uncertainty or fuzziness and increase the accuracy of employee promotion

decision making result. The models that will be used are Fuzzy Analytical

Hierarchy Process (F-AHP) and Technique for Order Preference by Similarity to

Ideal Solution (TOPSIS) model. Multiple Attribute Decision Making (MADM)

method is used to solve the problem in this research because the problem has

several criteria to be considered for the result. The table below shows the

comparison when using one method only and the combination methods.

8

Table 2.3 Comparison among Using Fuzzy AHP. TOPSIS and Fuzzy AHP +

TOPSIS

Aspect Fuzzy

AHP

TOPSIS

only

Fuzzy AHP +

TOPSIS

Joint qualitative into quantitative X X

Compare each criterion in pair X X

Make comprehensive structure X X

Reducing uncertainty X X

Describe criteria and sub-criteria in goal selection X X

Compute efficiently X X

Measure the distance X X

Calculate relative closeness X X

Develop the rank X X

2.2 Fuzzy Analytical Hierarchy Process (AHP) Method

As a decision maker, it is needed the system or method to take the decision

accurately. AHP is designed for situations in which ideas, feelings, and emotions

affecting the decision process are quantified to provide a numeric scale for

prioritizing the alternatives.

AHP was introduced by Saaty in 1977. AHP is can be used to solve complex

decision problems. The Analytical Hierarchy Process is one of the methods in

multi criteria decision making (MCDM) method. There are 4 essential principles

in AHP method which are structuring the model, comparing the judgment of the

criteria and alternatives, synthesis of the priorities and logical consistency. The

comparisons in AHP are used to obtain the weights of importance of the decision

criteria. Below is the example of AHP hierarchy structure.

Figure 2.1 AHP Structure

9

Fuzzy AHP is the collaboration between Analytical Hierarchy Process (AHP)

Method and fuzzy set theory. The first developer of fuzzy AHP is Zadeh in 1965

and the first fuzzy AHP application was developed by Laarhoven and Pedrycz.

The difference of Fuzzy AHP and the standard AHP method is in Fuzzy AHP

vagueness of personal judgment is included, it is based on fuzzy logic approach.

Moreover, the pair-wise comparison of both criteria and alternatives in Fuzzy

AHP are using linguistic variables.

There are many theories and models about Fuzzy Analytical Hierarchy Process

method that developed to solve many problems. The three models are stated in

Saphiro et al (2013) which are Van Laarhoven and Pedrycz (1983) model,

Buckley (1985) model and Chang (1996) model. Table 2.4 shows the detail

description of each Fuzzy AHP model.

Table 2.4 Comparison among Laarhoven and Pedrycz, Buckley and Chang Model of

Fuzzy AHP Method

Laarhoven and Pedrycz Buckley Chang

Using Logarithmic Least

Squares for deriving fuzzy

weight

Using the geometric mean for

deriving fuzzy weight

Using arithmetic mean for

deriving fuzzy weight

The multiplication in TFN

is only approximation

If the reciprocal matrix is not

perfect consistency, the

geometric row procedure can

give different weights

compared to the eigenvector

method. [Csutora and Buckley

(2001)]

The normalization formula

does not take into account

constraints derived from the

AHP method [Enea and Piazza

(2004)]

A change in the priorities

may cause rank reversal

when replicating existing

judgments on a single

comparison. [Zhu (2012)]

The method could lead to a

wrong decision, because it

may assign zero weights to

some items (criteria, sub-

criteria or alternatives),

excluding them from the

decision analysis. [Wang et al.

(2008)]

The methodology used to

normalize the local fuzzy

weights was problematic

[Wang et al (2006)]

Uncertainty of local fuzzy

weights for incomplete

fuzzy comparison matrices

[Wang et al (2006)]

(Source: Saphiro and Koissi, 2013)

10

Based on Table 2.4, it shows that the Buckley method has less limitation in the

Fuzzy AHP model and it can be used in many cases. Moreover, Buckley method

has simple model to analyze and it also has been successfully applied in many

problems. Thus, in this research Buckley Model of Fuzzy AHP will be used for

further analysis.

2.2.1 Fuzzy AHP Steps

The steps of Fuzzy Analytical Hierarchy Process method are as follows.

1. Define the problem and determine the kind of wanted solution.

2. Make the hierarchy structure from highest to the lowest level.

3. Construct a set of pair-wise comparison matrices by using linguistic terms.

4. Normalize the data by find the vector summation of each triangular value

and de-fuzzified by using Centre of area method.

2.2.2 Pair-wise Comparison

After the hierarchy is constructed, then the next step is constructing the pair-wise

comparison. Pair-wise comparisons are used to determine the relative importance

of each alternative in terms of each criterion (Triantaphyllou and Mann, 1995). In

this step, the decision maker will express the value of each single pair-wise

comparison. The scale of relative importance is used to express the value. Fuzzy

AHP expresses the value in pair-wise comparison by using triangular fuzzy

number. Below is the table of linguistic terms and the triangular fuzzy number.

Table 2.5 Linguistic Terms and The Corresponding Triangular Fuzzy Number

Intensity of

Importance

Definition Fuzzy Triangular

Scale

1 Equal importance (1, 1, 1)

3 Weak importance of one over another (2, 3, 4)

5 Essential or strong importance (4, 5, 6)

7 Demonstrated importance (6, 7, 8)

9 Absolute importance (9, 9, 9)

2

The intermittent values between two adjacent

scales

(1, 2, 3)

4 (3, 4, 5)

6 (5, 6, 7)

8 (7, 8, 9)

(Source: Ayhan, 2013)

11

After comparison is gained by the scale of priorities, the matrices is constructed.

Below is the example of pair-wise comparison matrices.

m

[ n

n

n

n

]

i m n

(2-1)

The scale of pair-wise comparison is gained based on questionnaire or interview.

When the decision is made by more than one person, the preference of each

decision maker is averaged.

∑

(2-2)

The k is the total number of respondent and is the preference value of each

decision maker.

2.2.3 Synthesis

Synthesis is the process to calculate the pair-wise comparison for taking the

decision from all aspects. Synthesis is used by weighing to show the priority of

each element. There are 3 steps to do the synthesis process, which are:

Calculate the geometric mean of each criterion. Below is the formula of

geometric mean.

(∏

)

(2-3)

Where expresses the triangular value.

Find the vector summation of each .

Replace the fuzzy triangular number by finding the power of summation

vector.

Multiply each of with the reverse vector to find the fuzzy weight of

criterion i ( ). The formula is below.

12

(2-4)

De-fuzified by using Centre of area method, the formula is below.

(2-5)

Normalized the value of by using the formula.

∑

(2-6)

The highest value of will be the suggestion for the decision maker to be

selected.

2.2.4 Consistency Calculation

The consistency of pair-wise comparison is evaluated by calculating Consistency

Ratio (CR). If the CR ≤ 0. it means that the calculation and pair-wise

comparison are consistent. First, calculate consistency index (CI) with the

equation:

CI n

n

(2-7)

Another consistency analysis that might be calculated is consistency ratio (CR). In

general, if

CR

(2-8)

max is gained by summing up the multiplication result between pair-wise

comparison and the priority eigen vector and divide it with the total element. The

Random Index (RI) is described with the table below.

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Table 2.6 Consistency Index for Pair-wise Comparison

Matrix

Measurement (n)

Random Index (RI)

1, 2 0.0

3 0.58

4 0.9

5 1.12

6 1.24

7 1.32

8 1.41

9 1.45

10 1.49

11 1.51

12 1.48

2.2.5 The Advantages of AHP Method

There are some advantages of Analytical Hierarchy Process (AHP) method, which

AHP makes some problem into flexible model and easy to understand.

AHP solves the complex problem by approaching the system and

deductive integration.

AHP handles the dependency elements in a system.

AHP uses hierarchy structure to represent the elements into different level.

AHP provides the scale of measurement and method to get the scale of

priority.

AHP considers the logic consistency to determine the scale of priority.

2.3 TOPSIS Method

TOPSIS stands for Technique of Order Preference by Similarity to Ideal Solution.

Based on Ahmadi, Taghipourian, and Yousef (2009), TOPSIS Method was

developed by Hwang and Yoon in 1981. There are three types of attributes or

criteria of TOPSIS method which are:

Qualitative benefit attribute or criteria.

Quantitative benefit attribute or criteria.

Cost attribute or criteria.

TOPSIS method selects the best alternative that has closest value to the positive

ideal solution and furthest from negative ideal solution. The positive ideal solution

will increases the benefit criteria and decreases the cost criteria. In other hand, the

14

negative ideal solution will increases the cost criteria and decreases the benefit

criteria.

2.3.1 TOPSIS Method Steps

Below are the steps of TOPSIS Method.

1. Normalized the decision matrix by using the formula below.

√∑

; i 3 n

(2-9)

2. Weighted the normalized decision matrix by using formula below.

(2-10)

3. Determine the positive ideal solution and negative ideal solution.

{ }

(2-11)

{ }

(2-12)

4. Calculate the distance of each alternative positive ideal solution (PIS) and

negative ideal solution (NIS) by using formula below.

√∑

, j J

(2-13)

√∑

, i J

(2-14)

5. Calculate the closeness coefficient of each alternative by using formula

below.

(2-15)

6. Rank the value of from the highest to the lowest so the alternative’s

rank is determined.

15

In solving a problem, TOPSIS get the input from another adopting model. Figure

4.2 will shows the flow process of TOPSIS Method briefly. Fuzzy AHP Method

will compares each criteria by using pair-wise comparison matrix then, the weight

will be determined and the number will be de-fuzzified to be calculated its

consistency. Consistency is calculated to measure whether the pair-wise

comparison matrix is consistent or not criteria’s weight is able as an input for

TOPSIS Method as the method to rank the employee promotion candidates.

Start

Decision

Matrix

Normalization

Weight

Determination

Defining

Positive Ideal

Solution (PIS)

and Negative

Ideal Solution

(NIS)

Distance

Calculation

Relative

Closeness

Alternative

Ranking

Finish

Figure 2.2 Flow Process of TOPSIS Method

1

CHAPTER III

RESEARCH METHODOLOGY

3.1 Research Flowchart

The following diagram illustrates the research methodology of this research.

Figure 3.1 Research Flowchart

Initial

Observati

on

• Observe the Employee Promotion System and Process in Company

XYZ.

• Identify the main problem.

Problem

Identificat

ion

• Identify the background and problem mapping.

• Determine the research's objective, scope and assumption.

Literature

Study

• Theoretical groundings on employee promotion.

• The indicator of employee promotion performance.

• The Fuzzy AHP and TOPSIS method to improve decision of employee promotion.

Data

Collection

• Take the data (employee promoted candidates) from HR division.

• Discuss with HR Manager and team to define the criteria and sub-criteria.

Data

Analysis

• Current situation analysis.

• Employee promotion indicator classification.

• Employee performance assessment.

• Employee promotion decision analysis.

• Result and improvement of the employee promoted selection.

Conclusio

n &

Recomme

ndation

• Conclusion based on calculation and analysis for the research.

• Give recommendation for further research.

2

3.1.1 Initial Observation

The observation is conducted in Company XYZ specifically in HR (Human

Resources) division. The decision making of promoted employee is based on the

discussion from its superior or hierarchy and the management. Each of division

will give the employee promoted candidates to HR division and HR division will

select only some candidates based on discussion with HR team. The employee

promoted candidates with HR approval will be the final candidates and the status

of promotion will be decided based on discussion with the management.

3.1.2 Problem Identification

Problems are identified based on the finding problem on decision making of

employee promotion selection process. The decision making of employee

promotion process is determined by many factors such as personnel

characteristics, education, etc. The status of employee promotion in Company

XYZ is determined through the management meeting discussion and it does not

use specific quantitative method or calculation to decide the promoted employee.

Interviewing the related people in Human Resources Division is done to know

more about the problem. Next, the objective, scope and assumption of the project

are set.

3.1.3 Literature Study

Literature study is done as a theoretical base from problem solving to related issue

faced by the company. Literature study is also as the basic of this project

execution. The literature study is collected from books, journals, and other sources

to analyze the problem and find the solution to answer the questions. The

explanation of literature study includes:

Theoretical groundings on employee promotion.

The indicator of employee promotion performance.

The Fuzzy AHP and TOPSIS method to improve decision of employee

promotion.

3

3.1.4 Data Collection

To analyze and improve the decision making of employee promotion, the data

should be collected. The data is collected through:

Discussion, interview and spreading questionnaire to some people who

directly conduct and manage employee promotion process such as:

1. Manager of Human Resources.

2. Head Department of Human Resources Method.

3. Head Service of Organization Development, Planning and Reporting.

The data of employee promoted candidates in the mid of 2015 based on

HR approval. The data includes the performance assessment of employee,

the factors as the criteria that affect the decision of employee promotion

which are competencies criteria, personnel criteria, future career criteria

and education criteria.

3.1.5 Data Analysis

After the data is gathered, the data could be analyzed. This chapter includes:

Current situation analysis.

Based on the current data, it is found that there is no specific quantitative

method or calculation to determine the promoted employee. Currently, the

decision result of employee promotion is based on meeting discussion with

management. It may causes the dissatisfaction of employee promotion’s

result because the decision could be subjective and only focus on one

criterion.

Employee promotion indicator classification.

From the literature study, the promotion indicator is found based on

Avazpour, Ebrahimi, and Fathi (2013). Company XYZ also had the

promotion indicators for the employee promoted candidates. After

discussing and interviewing some people who directly conduct the

employee promotion, the employee promotion indicator is developed. The

employee promotion indicator in this research is the result of combination

between the promotion indicator from literature study and promotion

indicator from Company XYZ. The result is also based on the discussion

4

from the representative of Company XYZ. The criteria that has been

decided, it is derived into sub-criteria. The detail description is explained

in this sub-chapter.

Employee performance assessment.

This sub-chapter explains the assessment of preference comparison from

criteria, sub-criteria and employee promoted candidate. The data is based

on the result of questionnaires from Manager of Human Resources, Head

Department of Human Resources Method and Head Service of

Organization Development, Planning and Reporting. During the interview

and questionnaire session, the data of employee performance assessment is

prepared. The data of employee performance assessment is quantified by

Human Resources Department. Thus, the data will be the guide for the

respondent to answer the questions in the questionnaire. The data is

analyzed and described in a matrix.

Employee promotion decision analysis.

This sub-chapter explains the weight of each criterion towards goal, each

sub-criterion towards criterion and employee promoted candidates toward

each sub-criterion. Those are the steps of AHP method. After the weighing

process, the ranking process is conducted by using TOPSIS Method.

Result and improvement of the employee promoted selection.

The difference between current employee promoted and proposed

employee promoted will be analyzed and the reason of proposed employee

promoted is also explained in this part.

3.1.6 Conclusion and Recommendation

This chapter will answer the problem statements as the research question and to

fulfill the objective of this research. The result of this chapter is based on Chapter

4 which is employee that has highest value should be promoted. The

recommendation is given for further research to implement the better

improvement of employee promotion selection in company XYZ.

5

3.2 Research Framework

The framework is begun from studying and observing the employee promotion

selection process and its method. The method to select the promoted employee is

also done. Then, the analysis by Fuzzy AHP and TOPSIS method has been

developed.

Figure 3.2 Research Framework

StartIdentify the

problem

Employee promotion

selection learning

Observe the

current situation

Sorting the

employee

promoted

candidates data

Determination of

criteria and sub-

criteria by qualitative

analysis

Fuzzy Analytical

Hierarchy Process

(FAHP) method is

started

Making

questionnaire to

determine the

weight

Weight

Determination

De-fuzzy the

fuzzy number

Comparison between

Current & Proposed

promoted employee

Conclusion and

recommendation

Finish

Normalized the

decision matrix

Distance

Calculation of PIS

and NIS

Relative

Closeness

Measurement

Rank the

promoted

employee

candidates

Confirmation

to HR/OPR?

No

Yes

Pairwise

Comparison

Consistency

Calculation

CR ≤ 0.10 ?

Yes

TOPSIS Method

is started

No

1

CHAPTER IV

DATA COLLECTION AND ANALYSIS

4.1 Current Situation Analysis

Company XYZ has the business field in oil and gas. As the top company,

Company XYZ prioritizes their employees as the human capital to develop the

business and achieve the business goals. One of the practices to develop their

human capital by promoting their employees to higher level.

Information regarding employee promotion selection process and the actual

implementation is collected through the discussion, interview and questionnaire

with Human Resources Department, especially Organization Development,

Planning and Reporting (OPR) section. In order to analyze and give improvement

to the employee promotion system, the current system is studied.

The first sub-process in employee promotion selection process is internal

preparation. In this phase, each of division in Company XYZ will give the

employee promotion candidates to HR Department. HR Department will collect

the data information of employee promotion candidates including their

performance appraisal. The second step is socialization. In this step, HR

department will makes the timeline of employee promotion selection process and

make the guideline of employee promotion process.

The third phase is Proposal Preparation. This phase focuses on the approval from

the Head of Entity of each employee promotion candidate. Head of Entity will

give the notes or justification for employee promotion candidate. Moreover, in

this phase, Head of Entity will give the decision whether the employee promotion

candidates from his/her division are allowed to join employee promotion selection

process or not. The decision is based on some criteria and considerations for

employee promotion process. The next phase is pre-exercise. This phase will be

conducted as a meeting for Head of Entity from each employee promotion

2

candidates and HR representative as the facilitator. The input of this process is the

information data of employee promotion candidates which have approved by their

Head of Entity. The output of this process is the final data for final meeting with

President Director.

The last step is the final meeting. This meeting will be conducted with President

Director, Head of Entity and HR representative as the facilitator. President

Director as the decision maker will decide whether the employee promotion

candidate will be promoted or not. The decision of President Director is based on

final data from Pre-Exercise phase. Figure 4.1 shows the employee promotion

selection process in a brief way.

Figure 4.1 Employee Promotion Selection Process

In the last phase, Final Meeting, it is found that there is a problem to determine the

status of employee promotion candidates, whether he/she should be promoted or

not. The problem arises because there is no weight of each criteria and sub criteria

Internal Preparation :

Each division gives

the employee

promotion candidates

to HR

Socialization :

Make the timeline

Proposal Preparation :

Proposal justification

by Head of Entity

assisted by HR

Pre – Exercise :

Conduct a meeting

with Head of Entity

and HR

Final Meeting :

Conduct a final meeting

with President Director,

Head of Entity and HR

Approved by

President Director?

PromotedNot Promoted

Finish

Start

YesNo

3

to assess the employee performance. The decision is taken based on discussion

and management meeting without specific quantitative method and calculation.

Furthermore, it may causes the subjective assessment and makes the decision

maker only focuses on one criteria. It leads to the dissatisfaction of employee

promotion result.

Another problem is there is no limitation grade or value to determine the status of

employee promotion selection, whether the employee should be promoted or not.

It is caused of most of the informational data is qualitative data and the current

system does not use specific method or calculation. The decision is made based on

the discussion between President Director, Head o Entity and HR Representative

as the facilitator.

4.2 Employee Promotion Indicator Classification

An interview and discussion is done by asking some questions to Manager of

Human Resources, Head Department of Human Resources Method, and Head

Service of Organization Development, Planning, and Reporting. From the

literature study, it is known that there are some considerations as the criteria and

sub criteria for employee promotion selection process. The literature study

explains there are 4 main criteria to determine the employee promotion which are

personal characteristics, inter-personal relations, work attitude and work result.

During the interview and discussion session, Manager of Human Resources, Head

Department of Human Resources Method, and Head Service of Organization

Development, Planning, and Reporting are asked some questions such as the

method to select the promoted employee, negative impact when chose the wrong

promoted employee, the factors as the consideration that affect employee

promotion decision, persons who take the responsibility of employee promotion

selection process. For the detail, Appendix 1 will show the complete questions of

interview.

4

The result of interview and discussion shows that there are 4 criterions that affect

employee promotion decision. Table 4.1 shows the current criteria and sub-criteria

of employee promotion selection in Company XYZ.

Table 4.1 Current Criteria and Sub-criteria of Employee Promotion Selection

No Criteria Sub Criteria Description

1 Competencies

Technical

knowledge

Employee has knowledge that associated

with related job/assignment.

Non technical

knowledge

Employee has knowledge that associated

with the soft skills.

2 Personnel

Criteria

Hierarchy

Observation

Employee has the good judgment from its

hierarchy of an employee.

Performance Rating

Employee has good rating or value of

employee performance result.

PP Matrix

Employee has good value of PP Matrix that

shows the balance of employee potential and

performance result.

Service Year

How many years the employee works in the

company that shows the loyalty.

Age of Employee How old the employee.

Position Year

How many years the employee stays or

works in the same position.

Attendance

Employee has good attendance rating of

employee for working.

3 Future Career Potentiality

Employee has good potential the employee

to hold the next and higher position.

4 Education

Last Educational

Background

Employee has supported educational

background.

Last GPA

Employee has supported and good GPA in

last academic year.

Number of training

Employee has followed related trainings for

next position.

By comparing the criteria and sub criteria from literature study and the current

criteria and sub criteria of employee promotion selection in Company XYZ, it will

be combined into criteria and sub-criteria that will be used in this research. The

combination of criteria and sub-criteria from literature study and current criteria

and sub-criteria of employee promotion selection in Company XYZ is done by

discussing with Manager of Human Resources and OPR Section. Table 4.2 shows

the criteria and sub criteria that will be used in this research for employee

promotion selection process.

5

Table 4.2 Criteria and Sub criteria for Employee Promotion Selection

No Criteria Sub criteria Description

1 Personal

Characteristics

Technical

knowledge

Employee has knowledge that associated

with related job/assignment.

Non technical

knowledge

Employee has knowledge that associated

with the soft skills.

Ability to learn Employee able to comprehend a task and the

solution to solve the task.

Innovation Employee able to create the creative way by

translating the idea to the work result.

Problem solving Employee able to achieve the solution by

working through the details problem.

Adaptability Employee able to transform their selves to

the changed environment.

Decision making

ability

Employee able to select the proper action for

solving the problem.

Age of Employee How old the employee.

Hierarchy

Observation

Employee has the good judgment from its

hierarchy of an employee.

Service Year How many years the employee works in the

company that shows the loyalty.

Position Year How many years the employee stays or

works in the same position.

Emotional stability Employee able to maintain the emotional

even faced with the pressure.

2 Inter-personal

Relation

Cooperation Employee able for acting to work together to

reach the goal.

Teamwork

Employee able to work with other

coordinated people or collaborative with

others to get the same purpose.

Team loyalty Employee shows the faithful commitment to

the group or a team of a person.

Communication Employee able to deliver the information to

the others in an efficient and effective way.

3 Work Attitude

Responsibility Employee able to complete the assigned task

as a duty and satisfactory obligation.

Motivation

Employee shows encouragement and desired

energy to be continually committed and

completed the job.

Discipline Employee reflects behavior of more control

their selves and willing to obey the rules.

Attendance Employee has good attendance rating of

employee for working.

Commitment Employee shows the dedication for time,

energy and self for a job.

6

Table 4.2 Criteria and Sub criteria for Employee Promotion Selection (continued)

No Criteria Sub criteria Description

4 Work Result

Accuracy

Employee shows their work result of being

true, correct and free of mistake or error.

Efficiency

Employee able to complete the task with the

least consumption of resources (time, energy,

etc).

Rapidity Employee acts to complete the task on-time.

Performance Rating

Employee has good rating or value of

employee performance result.

PP Matrix

Employee has good value of PP Matrix that

shows the balance of employee potential and

performance result.

Completeness of

assignment

Employee able to finish the task or job

completely.

5 Education

Last Educational

Background

Employee has supported educational

background.

Last GPA

Employee has supported and good GPA in

last academic year.

Number of training

Employee has followed related trainings for

next position.

4.2.1 Analysis of Criteria and Sub-criteria

Table 4.2 shows the criteria and sub-criteria that will be used in this research.

Below is the explanation for each criteria and sub criteria that will be used for

improving employee promotion selection system.

4.2.1.1 Criterion of Personnel Characteristics

Personnel characteristics are the important criteria to decide the employee

promotion selection. The personnel characteristics criteria also reflects the

employee self quality and shows whether the employee deserves for a promotion

or not. The employee self quality reflects on the working experience (service year

criteria and position year criteria), knowledge and other characteristics that

indicate the personnel perspective. Moreover, this criterion shows the employee

value that reflects another criterion in employee promotion selection process.

The criteria of personnel characteristics is derived into some sub-criterion such as

technical knowledge, non technical knowledge, ability to learn, innovation,

problem solving, adaptability, decision making ability, age of employee, hierarchy

7

observation, service year, position year, and emotional stability. Those kinds of

sub-criteria are shown as the indicator of personnel characteristics criteria.

4.2.1.2 Criterion of Inter-personal Relations

Criteria of Inter-personal relations show the relation between employee promotion

candidates and hierarchy, relation between employee promotion candidate and

peer, and relation between employee promotion candidate and subordinate. This

criterion shows whether the employee has the politeness and could build the

cooperation and discussion with other people from different backgrounds.

This criterion is derived into some sub-criteria such as cooperation, teamwork,

team loyalty, and communication. This criteria and sub criteria focuses on

relationship of employee promotion candidates with others that shows open and

professional communication flow to perform and accomplish the job and goal.

4.2.1.3 Criterion of Work Attitude

This criterion shows the manner of employee to complete the job and their feeling

towards the assigned tasks or jobs. There are three aspects that are influenced by

work attitude which are job satisfaction, job involvement and work engagement.

In order of job satisfaction, if the employee shows the good work attitude, the job

satisfaction from employee perspective and company perspective is also

increasing. Moreover, work attitude also influences the job involvement which

measures what level of employee shows the enthusiasm to the job for doing it.

The work engagement is also affected by work attitude, it shows what degree of

employee engages to the all aspects of company and helps the company to

develop and achieve its goals.

Responsibility, motivation, discipline, attendance, and commitment are the factors

as the sub-criteria to support the criteria of work attitude. Those sub criteria show

what should the employee has to support the performance result. They also reflect

the working environment. Mostly, if the working environment is fit and

8

comfortable to work, the employee work attitude will also be good to give his/her

best performance.

4.2.1.4 Criterion of Work Result

Work result is the essential measurement criterion for employee promotion

selection. It determines whether the employee succeed to do the job or not. There

are some aspects that should be considered on employee work result such as

accuracy, efficiency, rapidity, performance rating, PP matrix, and completeness of

assignment. Those aspects will be the sub criteria for the criteria of work result.

Most of employee promotion selection decision maker only prioritizes and looks

on this criteria because this criteria tends to be easier to be calculated and

measured.

4.2.1.5 Criterion of Education

Nowadays, company prioritizes the employee that has the good and supported

educational background. The educational background is considered in all aspects

of a business, it starts from the job applicants apply the job vacancy in the

company until the employee promotion process. Company tends to look the

promoted employee from high educational background. For example, employee A

and B are employee promotion candidates. Both of them show the good working

performance, good work attitude, suitable personnel characteristics for next job

and have good inter-personal relations. But, A is only bachelor degree while B is a

master degree. Company decides to promote B to the higher job because B has

more supported educational background. There are 3 sub criteria in this criterion

which are last educational background, last GPA, and number of training.

Figure 4.2 shows the hierarchy design for employee promotion selection process

in Company XYZ. It is based on combination of Table 2.1 and the list of criteria

and sub-criteria that are already in Company XYZ for employee promotion

selection process. There are some of criteria and sub-criteria that are deleted or

added in the hierarchy design of criteria and sub-criteria for this research. The

“Knowledge” sub-criterion in Table 2.1 is divided into two sub-criteria which are

9

Technical Knowledge and Non technical knowledge. Hierarchy Observation sub-

criterion, Service Year sub- criterion, Age of Employee sub-criterion and Position

Year sub-criterion are added in Personnel Characteristics criterion. Attendance

sub-criterion is added in Work Attitude sub-criterion. Furthermore, Performance

Rating sub- criterion and PP Matrix sub-criterion are added in Work Result

criterion. The Future Career criterion is deleted from the list of criteria for this

research. The last criterion is Education criterion which is added in the

hierarchical design of criteria and sub-criteria for this research.

Figure 4.2 Hierarchy Design of Employee Promotion Selection

Employee

Promotion Selection

Personal

Characteristics

Inter-personal

relationsWork Attitude Work Result Education

Technical

Knowledge

Non technical

Knowledge

Ability to learn

Innovation

Problem Solving

Adaptability

Decision making

ability

Age of Employee

Hierarchy

Observation

Service Year

Position Year

Emotional Stability

Cooperation

Teamwork

Team Loyalty

Communication

Responsibility

Motivation

Discipline

Attendance

Commitment

Accuracy

Efficiency

Rapidity

Performance Rating

PP Matrix

Completeness of

Assignment

Last academic

Last GPA

Number of training

10

4.3 Employee Performance Assessment

The questionnaire is given to fulfill the data for determining the weight of criteria,

sub criteria and the employee promoted candidates. The data are collected from

three respondents and all the data will be developed together into one absolute

data. Appendix 2 shows the questionnaire which is spread to 3 respondents. The

respondents are representative from Human Resources Department which

conducts the Employee Promotion Process. Those 3 respondents are directly

manage and involved in employee promotion process. Table 4.3 below shows the

respondents’ data as the HR representative.

Table 4.3 Respondents Data

Respondent Position in Company

Respondent 1 Manager of Human Resources

Respondent 2 Head Department of Human Resources Method

Respondent 3 Head Service of Organization Development, Planning and Reporting

Manager of Human Resources has highest responsibility of conducting

employee promotion process. Manager of Human Resources is the person who

has highest authority of Human Resources Division.

Head Department of Human Resources Method has the duty to supervise

the employee promotion process. Furthermore, the employee promotion

indicator and the system of employee promotion are also the duties of Head

Department of Human Resources Method.

Head Service of Organization Development, Planning and Reporting is

directly arrange and collect the data of employee promoted candidates. The

another duty is to arrange the schedule to conduct final meeting with President

Director.

During the questionnaire session, the data of employee performance assessment is

prepared as a guide for the respondent to fill the questionnaire. The data of

employee performance assessment is quantified by Human Resources

Department. The data are assessed by superior of each employee promoted

candidate. The data of employee performance assessment is from the human’s

judgment as the linguistic variable. The superior’s judgment is the confidential

11

data and it could not be shown in this research. The example of the employee

performance assessment is explained as follows.

Sub-criterion of ability to learn is one of the intangible sub-criteria in employee

performance assessment for the decision making of employee promotion selection

process in Company XYZ. The ability to learn sub-criterion is assessed by each of

superior to their subordinates. This sub-criterion is indicated by the ability of

employee to comprehend a task and the solution to solve the task. The assessment

value is categorized by a certain scale from 1 until 10. The scale 1 represents the

lowest ability of employee to solve the task, problem or project. While, the scale

10 represents the highest ability of employee to solve the task, problem or project.

The rest of employee performance assessment is same as the example above.

The questionnaire consists of the preference of importance comparison for two

aspects which are what aspect is more necessary and what level of necessary is.

The level of necessary is symbolized by number that has already explained in

Chapter 2. Then, the data are developed into a matrix. The matrix is developed for

criteria comparison, sub-criteria comparison and employee promoted candidates

comparison. When two same aspects are met each other in a matrix, the value will

be 1 which means they are equally importance and necessary.

Table 4.4 Preference Comparison of Criteria in Matrix

Criteria Personal

Characteristics

Inter-

personal

Relation

Work

Attitude

Work

Result Education

First Person

Personal

Characteristics 1 5 3 1/3 6

Inter-personal

Relation 1/5 1 1/3 1/6 2

Work Attitude 1/3 3 1 1/4 5

Work Result 3 6 4 1 7

Education 1/6 ½ 1/5 1/7 1

Second Person

Personal

Characteristics 1 4 3 1/3 5

Inter-personal

Relation 1/4 1 1/3 1/5 2

12

Table 4.4 Preference Comparison of Criteria in Matrix (continued)

Second Person

Work Attitude 1/3 3 1 1/4 4

Work Result 3 5 4 1 6

Education 1/5 ½ 1/4 1/6 1

Third Person

Personal

Characteristics 1 5 4 1/2 6

Inter-personal

Relation 1/5 1 1/3 1/5 3

Work Attitude ¼ 3 1 1/4 5

Work Result 2 5 4 1 7

Education 1/6 1/3 1/5 1/7 1

Table 4.4 presents the pair-wise comparison of criteria in employee promotion

decision making. One criterion is compared with another criterion with certain

scale. Since there are 5 criteria, the matrix also follows the number of criteria

which is 5 x 5 matrix scale. For the next step, there are some abbreviations that

will be used. The description of abbreviation is explained in the table below.

Before, the pair-wise is converted into triangular fuzzy number, the consistency of

matrix should be calculated.

Table 4.5 Abbreviation Explanation

Abbre-

viation Explanation

Abbre-

viation Explanation

PC1 Personal Characteristics - Technical

knowledge IR4

Inter-personal Relation –

Communication

PC2 Personal Characteristics - Non

technical knowledge WA1

Work Attitude - Responsibility

PC3 Personal Characteristics - Ability to

learn WA2

Work Attitude - Motivation

PC4 Personal Characteristics –

Innovation WA3

Work Attitude - Discipline

PC5 Personal Characteristics - Problem

solving WA4

Work Attitude – Attendance

PC6 Personal Characteristics –

Adaptability WA5

Work Attitude - Commitment

PC7 Personal Characteristics - Decision

making ability WR1

Work Result – Accuracy

PC8 Personal Characteristics - Age of

Employee WR2

Work Result – Efficiency

PC9 Personal Characteristics - Hierarchy

Observation WR3

Work Result – Rapidity

PC10 Personal Characteristics - Service

Year WR4

Work Result - Performance

Rating

13

Table 4.5 Abbreviation Explanation (continued)

Abbre-

viation Explanation

Abbre-

viation Explanation

PC11 Personal Characteristics - Position

Year WR5

Work Result - PP Matrix

PC12 Personal Characteristics -

Emotional stability WR6

Work Result - Completeness of

assignment

IR1 Inter-personal Relation –

Cooperation E1

Education - Last Educational

Background

IR2 Inter-personal Relation –

Teamwork E2

Education - Last GPA

IR3 Inter-personal Relation - Team

loyalty E3

Education - Total number of

followed training

Then, criteria are derived into the sub criteria. The personal characteristics

criterion has more total number of sub criteria than the other criteria which has 12

sub criteria. The education criterion has least total number of sub criteria than the

other criteria which has 3 sub criteria. The comparison for each sub criterion is

done based on one criterion. Since there are five criteria, so there will be five

comparison tables. This chapter only shows the Work Result sub criteria. The rest

can be seen in the Appendices.

Table 4.6 Preference Comparison of Sub-Criteria in Matrix

Sub-

criteria WR1 WR2 WR3 WR4 WR5 WR6

First Person

WR1 1 1/2 3 1/4 1/3 2

WR2 2 1 4 1/3 1/2 3

WR3 1/3 1/4 1 1/6 1/4 1/2

WR4 4 3 6 1 2 5

WR5 3 2 4 1/2 1 3

WR6 1/2 1/3 2 1/5 1/3 1

Second Person

WR1 1 1/2 3 1/4 1/4 3

WR2 2 1 4 1/3 1/3 4

WR3 1/3 1/4 1 1/5 1/5 1/2

WR4 4 3 5 1 3 2

WR5 4 3 5 1/3 1 4

WR6 1/3 1/4 2 1/2 1/4 1

Third Person

WR1 1 1/3 3 1/5 1/3 2

WR2 3 1 5 1/3 1/2 4

WR3 1/3 1/5 1 1/6 1/4 1/3

14

Table 4.6 Preference Comparison of Sub-Criteria in Matrix (continued)

Third Person

WR4 5 3 6 1 2 5

WR5 3 2 4 1/2 1 4

WR6 1/2 ¼ 3 1/5 1/4 1

The comparison is also done for among employee promotion candidates towards

sub criterion. The matrix of preference comparison matrix for among employee

promotion candidates towards sub-criteria can be seen in the Appendix 4.

4.4 Employee Promotion Decision Analysis

After collecting all data by doing the observation, the decision for employee

promotion candidates that mostly meets the performance indicator is taken. There

are two combination methods to analyze the data which are Fuzzy Analytical

Hierarchy Process (F-AHP) and Technique for Order Preference by Similarity to

Ideal Solution (TOPSIS) method. The purpose of using Fuzzy AHP is to

determine the weight. The weight as the result of Fuzzy AHP will be used as the

input for TOPSIS method. The final result is the rank of employee promotion

candidates based on the calculation of the biggest distance.

4.4.1 Consistency Determination

In this sub-chapter, the consistency of preference comparison matrix is calculated

before analyzing the data by using Fuzzy AHP. If the consistency ratio is more

than 10%, it means that the preference comparison matrix can not be used for the

further step. The data should be re-taken to get the consistency in less than 10%.

Basically, calculating the consistency ratio follows to do the AHP method steps.

First, the geometric mean is calculated to calculate the aggregate value from 3

respondents.

Table 4.7 shows the final matrix including the geometric mean from 3

respondents. After that, the eigen value and eigen vector are calculated. Eigen

vector is as the weight for AHP Method an eigen value is calculated to

determining the consistency. The consistency value can be seen on column

“Consistency Ratio”.

15

Table 4.7 Criteria Weighting and Consistency Calculation

Criteria Personal

Characteristics

Inter-

personal

Relation

Work

Attitude

Work

Result Education

Eigen

Vector

Personal

Characteristics 1 4.642 3.302 0.382 5.646 0.28

Inter-personal Relation 0.215 1 0.333 0.188 2.289 0.073

Work Attitude 0.303 3 1 0.25 4.642 0.15

Work Result 2.621 5.313 4 1 6.649 0.453

Education 0.177 0.437 0.215 0.15 1 0.044

Sum 4.316 14.39 8.851 1.97 20.23 1

Eigen Value 5.374

CI 0.093

CR 0.083

Calculation 1:

Row: Personal Characteristics – Column: Inter-personal Relation

√

Calculation 2:

Row: Sum – Column: Personal Characteristics

Calculation 3:

Row: Personal Characteristics – Column: Eigen Vector

(

)

Calculation 4:

Row: Eigen Value (λmax) – Column: Eigen Vector

( ) ( ) ( ) ( )

( )

Calculation 5:

Row: Consistency Index (CI) – Column: Eigen Vector

16

Calculation 6:

Row: Consistency Ratio (CR) – Column: Eigen Vector

Based on table 4.7, it shows that the consistency ratio (CR) of matrix is 0.083449.

The value of CR is less than 0.1, it means that the consistency of the matrix is

consistent. Then, because of the matrix is consistent, the value of pair-wise

comparison could be converted to fuzzy triangular number. Table 4.8 shows the

summary of consistency calculation for each sub criterion and among employee

promotion candidates towards each sub-criterion.

Table 4.8 Summary Table of Consistency Calculation between Each Sub-Criterion

towards Criterion

Sub-

Criteria

Consistency Ratio

(CR)

Sub-

Criteria

Consistency Ratio

(CR)

PC1

0.093957523

IR4 0.00457389

PC2 WA1

0.040143205

PC3 WA2

PC4 WA3

PC5 WA4

PC6 WA5

PC7 WR1

0.011214312

PC8 WR2

PC9 WR3

PC10 WR4

PC11 WR5

PC12 WR6

IR1

0.00457389

E1

0.083479993 IR2 E2

IR3 E3

The detail consistency calculation of each sub criterion towards one criterion is in

Appendix 5. Based on Table 4.8, it is shown that all of the consistency ratios

between the sub criteria are less than 10%. The smallest number of consistency

ratio is from Inter-personal Relations sub criteria which is 0.457389% and the

largest number of consistency ratio is from Personal Characteristics sub criteria

which is 9.3957523%. Next, the consistency calculation is also constructed for

17

employee promotion candidates towards the sub-criterion. Table 4.9 shows the

consistency ratio for each matrix of employee promotion candidates towards each

of sub-criterion.

Table 4.9 Summary Table of Consistency Calculation between Employee Promotion

Candidates towards Each Sub-Criterion

Sub-Criteria

Consistency Ratio

(CR) Sub-Criteria

Consistency Ratio

(CR)

PC1 1.25% IR4 5.25%

PC2 3% WA1 5.41%

PC3 0.76% WA2 6.92%

PC4 0.87% WA3 2.15%

PC5 7.34% WA4 7.37%

PC6 4.14% WA5 9.08%

PC7 7.96% WR1 1.89%

PC8 4.57% WR2 1.34%

PC9 3.42% WR3 3.38%

PC10 9.79% WR4 0.52%

PC11 7.13% WR5 0.20%

PC12 5.49% WR6 3.36%

IR1 4.29% E1 7.15%

IR2 9.78% E2 9.70%

IR3 4.13% E3 3.18%

Based on Table 4.9, it is shown that all of the preference comparison matrices

between employee promotion candidates and each sub-criterion are consistent

matrix. It is supported by the all of the consistency calculations are less than 10%

or 0.1. The highest consistency ratio is 9.79% which is between service year sub-

criterion and 14 employee promotion candidates. The smallest consistency ratio is

0.2% which is between PP Matrix sub-criterion and 14 employee promotion

candidates. The rest of detail consistency calculation for among employee

promotion candidates toward sub-criteria is in Appendix 6.

4.4.2 Weight Determination

After the consistency ratio is calculated, the next step is determining the weight.

In this part, Fuzzy AHP Method will be used to determine the weight. First, the

preference comparison matrix will be transformed into Triangular Fuzzy Number

(TFN). TFN will transform the linguistic variable to be calculated by fuzzy

18

approach. In this part, the weight calculation is done for determining the criteria’s

weight. The rest of detail weight calculation can be seen in Appendix 7 for sub-

criteria weighting and Appendix 8 for employee promotion candidate weighting

toward each of sub-criterion. Table 4.10 shows the triangular fuzzy number of

each decision maker’s preferences.

Table 4.10 Triangular Fuzzy Number of Each Decision Maker’s Preferences

Criteria Personal

Characteristics

Inter-

personal

Relation

Work

Attitude

Work

Result Education

First Person

Personal

Characteristics (1,1,1) (4,5,6) (2,3,4) (1/4,1/3,1/2) (5,6,7)

Inter-personal

Relation (1/6,1/5,1/4) (1,1,1) (1/4,1/3,1/2) 1/7,1/6,1/5) (1,2,3)

Work Attitude (1/4,1/3,1/2) (2,3,4) (1,1,1) (1/5,1/4,1/3) (4,5,6)

Work Result (2,3,4) (5,6,7) (3,4,5) (1,1,1) (6,7,8)

Education (1/7,1/6,1/5) (1/3,1/2,1/1) (1/6,1/5,1/4) (1/8,1/7,1/6) (1,1,1)

Second Person

Personal

Characteristics (1,1,1) (3,4,5) (2,3,4) (1/4,1/3,1/2) (4,5,6)

Inter-personal

Relation (1/5,1/4,1/3) (1,1,1) (1/4,1/3,1/2) (1/6,1/5,1/4) (1,2,3)

Work Attitude (1/4,1/3,1/2) (2,3,4) (1,1,1) (1/5,1/4,1/3) (3,4,5)

Work Result (2,3,4) (4,5,6) (3,4,5) (1,1,1) (5,6,7)

Education (1/6,1/5,1/4) (1/3,1/2,1/1) (1/5,1/4,1/3) 1/7,1/6,1/5) (1,1,1)

Third Person

Personal

Characteristics (1,1,1) (4,5,6) (3,4,5) (1/3,1/2,1/1) (5,6,7)

Inter-personal

Relation (1/6,1/5,1/4) (1,1,1) (1/4,1/3,1/2) (1/6,1/5,1/4) (2,3,4)

Work Attitude (1/5,1/4,1/3) (2,3,4) (1,1,1) (1/5,1/4,1/3) (4,5,6)

Work Result (1,2,3) (4,5,6) (3,4,5) (1,1,1) (6,7,8)

Education (1/7,1/6,1/5) (1/4,1/3,1/2) (1/6,1/5,1/4) (1/8,1/7,1/6) (1,1,1)

The second step, calculate the average of each decision maker’s preferences as the

aggregate value of decision maker’s preferences based on Equation 2-2.

19

Table 4.11 Aggregate Value of Decision Maker’s Preferences

Criteria Personal

Characteristics

Inter-personal

Relation

Work

Attitude

Work

Result Education

Personal

Characteristics (1,1,1)

(3.67;4.67;

5.67)

(2.33;3.33;

4.33)

(0.28;0.39;

0.67)

(4.67;5.67;

6.67)

Inter-personal

Relation

(0.18;0.22;

0.28) (1,1,1)

(0.25;0.33;

0.5)

(0.16;0.19;

0.23)

(1.33;2.33;

3.33)

Work Attitude (0.23;0.31;

0.44) (2,3,4) (1,1,1)

(1/5,1/4,

1/3)

(3.67;4.67;

5.67)

Work Result (1.67;2.67;

3.67)

(4.33;5.33;

6.33) (3,4,5) (1,1,1)

(5.67;6.67;

7.67)

Education (0.15;0.18;

0.22)

(0.31;0.44;

0.73)

(0.18;0.22;

0.28)

(0.13;0.15;

0.18) (1,1,1)

Calculation 7:

[(

)] [(

)] [(

)] ( )

After the average of decision maker’s preference is calculated, the geometric

mean of each criterion is calculated to determine the fuzzy comparison values by

using Equation 2-3. Table 4.18 presents the geometric means of fuzzy comparison

values.

Table 4.12 Geometric Means of Fuzzy Comparison Values

Criteria Personal Characteristics 2.218216728 3.213770777 4.712915198

Inter-personal Relation 0.21567051 0.321606803 0.478629028

Work Attitude 0.698859357 1.027529139 1.481873699

Work Result 4.894066484 7.099209909 9.406879851

Education 0.105220584 0.140504072 0.204031915

Total 8.132033663 11.8026207 16.28432969

Reverse 0.12297047 0.084726945 0.06140873

Increasing Order 0.06140873 0.084726945 0.12297047

Calculation 8:

( )

Calculation 9:

( )

Calculation 10:

( )

20

Calculation 11:

Calculation 12:

Table 4.12 also shows the total and reverse of geometric means of fuzzy

comparison scale for criteria. In the last row, the increasing order of fuzzy

triangular number is presented. The next step after calculate the geometric means

is calculating the fuzzy weight of each criteria. Equation 2-4 is used to determine

the fuzzy weight. Table 4.13 shows the relative fuzzy weight for each criterion.

Table 4.13 Relative Fuzzy Weight for Each Criterion

Criteria Personal Characteristics 0.136217871 0.272292981 0.579549396

Inter-personal Relation 0.013244052 0.027248762 0.058857236

Work Attitude 0.042916065 0.087059405 0.182226705

Work Result 0.300538406 0.601494371 1.156768435

Education 0.006461462 0.011904481 0.0250899

Calculation 13:

Calculation 14:

Calculation 15:

Next, the number is de-fuzzified by calculating , it is the average value of

relative fuzzy weight. Then, the matrix should be normalized by calculating .

Table 4.14 shows the value of and .

21

Table 4.14 Average Value of Relative Fuzzy Weight and Normalized Value

Criteria Personal Characteristics 0.329353416 0.282152216

Inter-personal Relation 0.033116684 0.028370575

Work Attitude 0.104067392 0.089153

Work Result 0.68626707 0.587914882

Education 0.014485281 0.012409327

Total 1.167289843 1

Calculation 16:

( )

Calculation 17:

After all of the criteria are calculated by using Fuzzy AHP, the next step is to

calculate the sub-criteria’s weight by doing the same steps above. The detail

calculations and tables are in Appendix 5. Table shows the summary table of

relative fuzzy weight, average relative fuzzy weight and the normalized value

between each of sub-criterion towards one criterion.

Table 4.15 Summary Table of , Mi , and Ni Between Each of Sub-Criterion

Towards One Criterion

Sub-

Criteria Relative Fuzzy Weight

Average Relative Fuzzy

Weight

Normalized

Value

PC1 0.281195 0.715225 1.268685 0.755034746 0.650378222

PC2 0.05251 0.179464 0.882296 0.371423098 0.214661331

PC3 0.017766 0.066243 0.370443 0.151484235 0.083152795

PC4 0.001753 0.005029 0.026514 0.01109863 0.006490346

PC5 0.006597 0.025124 0.155777 0.062499499 0.033251986

PC6 0.000053 0.000194 0.00124 0.000495717 0.000263663

PC7 0.000152 0.000533 0.002912 0.00119897 0.000668954

PC8 8.03 10-7

1.84 10-6

8.42 10-6

3.68737 10-6

2.36786 10-6

PC9 1.1 10-5

5.43 10-5

0.000346 0.00013717 6.99944 10-5

PC10 4.38 10-6

1.48 10-5

8.3 10-5

3.40772 10-5

1.89935 10-5

PC11 1.58 10-6

4.68 10-6

2.6 10-5

1.07683 10-5

6.16001 10-6

PC12 0.00211 0.008114 0.052923 0.021048693 0.011035187

IR1 1.95 10-7

3.6 10-6

0.000128 0.687371951 0.589622318

IR2 1.92 10-8

2.73 10-7

9.18 10-6

0.268878524 0.230641908

IR3 7.23 10-8

1.36 10-6

5.39 10-5

0.064568627 0.055386466

22

Table 4.15 Summary Table of , Mi , and Ni Between Each of Sub-Criterion

Towards One Criterion (continued)

Sub-

Criteria Relative Fuzzy Weight

Average Relative Fuzzy

Weight

Normalized

Value

IR4 5.81 10-10

1.05 10-8

4.29 10-7

0.144964367 0.124349308

WA1 0.268162 0.597488 1.262011 0.709220156 0.574618584

WA2 0.014675 0.035549 0.094787 0.048337093 0.039163286

WA3 0.034022 0.083612 0.211915 0.10984966 0.089001498

WA4 0.007719 0.015621 0.038998 0.020779185 0.016835542

WA5 0.117837 0.267731 0.652609 0.346058977 0.280381089

WR1 0.008438 0.037659 0.128153 0.058083166 0.000284278

WR2 0.037476 0.109767 0.363447 0.170229859 0.000833161

WR3 1.940534 1.789892 1.845594 1.858673524 0.009096959

WR4 142.2947 152.1644 126.7383 140.3991229 0.687159478

WR5 52.98213 60.61907 59.76171 57.78763667 0.282831697

WR6 3.868925 4.041339 4.222815 4.044359616 0.019794426

E1 0.422727 0.639074 0.924979 0.662260294 0.62715149

E2 0.162573 0.254997 0.400064 0.272544607 0.258096036

E3 0.080347 0.105928 0.177254 0.121176476 0.114752474

Based on Table 4.15, it shows that the column “Relative Fuzzy Weight” are

divided into 3 columns which represents the . There are 3 numbers

of relative fuzzy weights because of the fuzzy approach uses triangular fuzzy

number. The highest average relative fuzzy weight is 140.3991229 which belong

to Performance Rating sub-criterion’s weight. The smallest average relative fuzzy

weight is 3.68737 10-6

which belong to Age of Employee sub-criterion’s weight.

In the sixth column, it is described the normalized value which can be used for

TOPSIS method. The biggest number of normalized value is 0.687159478 which

belong to Performance Rating sub-criterion and the smallest number of

normalized value is 2.36786 10-6

which belong to Age of Employee sub-

criterion. Next, the employee promotion candidates’ weights are calculated

towards each of sub-criterion. The detail calculation of weight determination can

be seen in Appendix 6. Table 4.16 shows the summary of normalized weight

between employee promotion candidates toward sub-criterion.

23

Table 4.16 Summary Table of Ni between Employee Promotion Candidates toward

Sub-criterion

Sub-

Criteria

Employee Promotion Candidates

1 2 3 4 5

PC1 0.10313392 0.011337752 0.000244989 0.009532027 0.095613451

PC2 0.294190637 0.011316026 0.000774836 0.000834734 0.063702638

PC3 0.291740198 0.045766981 0.000458313 0.005120107 0.046596967

PC4 0.189221005 0.032070436 0.002991185 0.031819189 0.178302004

PC5 0.289116166 0.004931139 5.14927 10-5

0.005065827 0.072189514

PC6 0.117657095 0.022882551 7.48754 10-5

0.019573778 0.113432436

PC7 0.247961252 0.029545384 0.000560524 0.003842928 0.026090909

PC8 0.000555309 0.000522215 0.000481227 0.000411664 0.011099014

PC9 0.101089877 0.016565804 8.01903 10-5

0.017170921 0.120106563

PC10 0.000713638 0.0004857 0.001496091 0.000557209 5.72929 10-5

PC11 0.073518012 0.439812424 0.000526941 0.005110247 0.000526941

PC12 0.295572898 0.010609337 5.94515 10-5

0.010417699 0.09577658

IR1 0.068822868 0.012293746 0.000185182 0.012149272 0.066944674

IR2 0.101598063 0.019424871 0.000271627 0.001536715 0.10474884

IR3 0.217297352 0.046263385 8.03615 10-5

0.042778027 0.213920205

IR4 0.052029652 0.052029652 0.000743951 0.009699159 0.051165599

WA1 0.148404124 0.022378362 7.46819 10-5

0.003723637 0.022777416

WA2 0.285148915 0.006444073 0.000698176 0.006950461 0.068504192

WA3 0.301536354 0.009147588 0.00012357 0.005995816 0.073270981

WA4 0.149505094 0.004358964 6.58753 10-5

0.004454127 0.029567778

WA5 0.064837355 0.005561627 0.000121836 0.008662154 0.085149897

WR1 0.27565301 0.050755364 0.000123769 0.010034823 0.050755364

WR2 0.214551199 0.039268568 0.002766894 0.039268568 0.214811328

WR3 0.105569558 0.027653149 6.16526 10-5

0.003977779 0.12087333

WR4 0.006298051 0.00296794 0.00296794 0.00296794 0.00296794

WR5 0.000437584 0.006848365 0.056120881 0.006848365 0.000790548

WR6 0.070245885 0.016113389 3.53778 10-5

0.00153487 0.078193779

E1 0.074702511 0.018301108 0.000232785 0.002022651 0.075962574

E2 0.282546563 0.010637112 0.000117115 0.009675414 0.07134267

E3 0.067735968 0.012143926 0.000182626 0.012143926 0.067735968

Table 4.16 Summary Table of Ni between Employee Promotion Candidates toward

Sub-criterion (continued)

Sub-

Criteria

Employee Promotion Candidates

6 7 8 9 10

PC1 0.011337752 1.59721 10-5

0.10313392 0.0017012 0.0017012

PC2 0.000923466 4.38 10-5

0.263970561 0.000834734 0.001143988

PC3 0.00488571 4.60948 10-5

0.271324647 0.005120107 0.000492184

PC4 0.032070436 0.000197173 0.170794541 0.00262663 0.002534653

24

Table 4.16 Summary Table of Ni between Employee Promotion Candidates toward

Sub-criterion (continued)

Sub-

Criteria

Employee Promotion Candidates

6 7 8 9 10

PC5 0.004857097 3.67957 10-5

0.2844191 0.004857097 0.000934384

PC6 0.002850343 0.000926243 0.111174698 0.00318327 0.000361482

PC7 0.004012929 8.02555 10-6

0.65366836 0.003842928 0.000560524

PC8 0.019278906 0.674633209 0.133732481 0.009101557 0.126759071

PC9 0.00330647 6.13846 10-6

0.219625063 0.000371895 0.000382123

PC10 7.29454 10-5

0.064642971 0.368376673 0.426825992 0.064642971

PC11 0.005084447 0.387474903 0.005110247 0.005110247 5.91348 10-5

PC12 0.002346173 0.287539357 5.41825 10-6

0.000270385 0.0003044

IR1 0.001873528 1.97616 10-5

0.383509068 0.000188479 0.000165174

IR2 0.001578697 2.0121 10-5

0.10558045 0.001536715 0.001536715

IR3 0.008404922 1.25667 10-5

0.213920205 0.000697774 0.000697774

IR4 0.008330053 1.20308 10-5

0.409126386 0.000644901 0.000644901

WA1 0.003872948 9.67297 10-6

0.143858417 0.000588691 6.82301 10-5

WA2 0.006444073 6.26909 10-5

0.280004499 0.000673674 0.000673674

WA3 0.006931726 2.00242 10-5

0.296844229 0.001182534 0.001182534

WA4 0.0005115 7.42349 10-6

0.14719481 0.000454818 0.000544422

WA5 0.008658383 1.59757 10-5

0.377874022 0.0014591 0.000113378

WR1 0.000397131 1.30024 10-5

0.271380207 0.000862236 0.000397131

WR2 0.003149491 3.38283 10-5

0.214811328 0.002915755 0.002766894

WR3 0.000393749 3.74602 10-6

0.104137991 0.000365466 0.000373481

WR4 0.005658257 6.85532 10-5

0.003054006 0.003054006 0.004710247

WR5 0.006848365 0.00038148 0.000358856 0.056120881 0.057649269

WR6 0.001469674 5.48504 10-6

0.377743958 0.001469674 0.000308986

E1 0.002022651 5.16042 10-6

0.401835871 0.000242156 0.000242156

E2 0.001632635 1.93766 10-5

0.282546563 0.000117115 0.000117115

E3 0.001916221 2.01735 10-5

0.389639232 0.000169709 0.00023153

Table 4.16 Summary Table of Ni between Employee Promotion Candidates toward

Sub-criterion (continued)

Sub-

Criteria

Employee Promotion Candidates

11 12 13 14

PC1 0.650723 1.6 10-5

0.011493 1.6 10-5

PC2 0.294191 4.68 10-5

0.06798 4.68 10-5

PC3 0.281348 0.000458 0.046597 4.56 10-5

PC4 0.182386 0.00021 0.174574 0.000203

PC5 0.269423 4.97 10-5

0.064027 4.09 10-5

PC6 0.59811 8.01 10-6

0.009757 8.88 10-6

PC7 0.001327 7.75 10-5

0.028493 8.39 10-6

PC8 0.000356 0.010127 0.000315 0.012627

PC9 0.505306 7.05 10-6

0.015975 6.64 10-6

25

Table 4.16 Summary Table of Ni between Employee Promotion Candidates toward

Sub-criterion (continued)

Sub-

Criteria

Employee Promotion Candidates

11 12 13 14

PC10 0.070823 0.000451 0.000411 0.000444

PC11 0.000546 0.071949 0.000546 0.004626

PC12 0.287037 4.79 10-6

0.010051 4.65 10-6

IR1 0.400204 1.79 10-5

0.053609 1.67 10-5

IR2 0.641521 1.87 10-5

0.020609 1.89 10-5

IR3 0.21392 7.44 10-5

0.041862 7.11 10-5

IR4 0.415421 0.000128 1.21 10-5

1.25 10-5

WA1 0.632253 7.37 10-6

0.021977 6.15 10-6

WA2 0.280004 7.91 10-5

0.064256 5.64 10-5

WA3 0.296844 0.000125 0.006782 1.32 10-5

WA4 0.634248 3.43 10-5

0.029038 1.48 10-5

WA5 0.377874 0.000114 0.069543 1.57 10-5

WR1 0.288731 0.000128 0.050755 1.37 10-5

WR2 0.226737 0.000456 0.038432 3.12 10-5

WR3 0.614033 7.64 10-5

0.022472 8.77 10-6

WR4 0.957066 0.002933 0.002715 0.002572

WR5 0.05922 0.056121 0.006848 0.685407

WR6 0.383675 3.54 10-5

0.069161 7.46 10-6

E1 0.349673 4.82 10-5

0.074703 6.35 10-6

E2 0.273823 0.000126 0.06728 1.91 10-5

E3 0.377624 1.84 10-5

0.070415 2.38 10-5

The weight of criteria to goal, sub-criteria to criteria and employee promotion

candidates to sub-criteria has been determined. The weight will be used for

determining the employee that will be promoted. Moreover, the weight is as the

input for the next method which is TOPSIS Method. The summary of normalized

weights is shown in the previous table.

4.4.3 Distance Development

The normalized weight of criteria to goal, sub-criteria to criteria and employee

promotion candidates to sub-criteria has been determined by using Fuzzy AHP

Method. In this sub-chapter, TOPSIS Method is started to use. The objective of

this part is to determine the distance of both positive ideal solution (PIS) and

negative ideal solution (NIS).

26

First, the weight of one employee promotion candidates can be obtained by

calculating the average of one row that is assigned for one employee based on

table 4.16. Table 4.17 shows the average value for one employee promotion

candidates.

Table 4.17 Average Weight of Employee Promotion Candidates

Employee Promotion Candidates Weight

1 0.149713

2 0.032948

3 0.002426

4 0.009796

5 0.074099

6 0.005371

7 0.04721

8 0.232959

9 0.017886

10 0.009077

11 0.352148

12 0.004798

13 0.038023

14 0.023546

Total 1

Calculation 18:

Employee Promotion Candidates 1:

(0.10313392034935 + 0.294190637404948 + 0.291740198211053 +

0.189221005303481 + 0.289116165940721 + 0.117657094783005 +

0.247961252374469 + 0.000555308793799226 + 0.101089877478117 +

0.000713638285370311 + 0.0735180121967943 + 0.295572898121002 +

0.068822867626202 + 0.101598063064651 + 0.217297351825441 +

0.0520296516145768 + 0.148404123736236 + 0.285148914820449 +

0.301536353892129 + 0.14950509368928 + 0.0648373546169248 +

0.275653009575227 + 0.214551199073963 + 0.105569558066732 +

0.00629805103799796 + 0.000437584200741271 + 0.0702458845316356 +

0.0747025108941181 + 0.282546563307626 + 0.0677359682122615) / 30 =

0.149713

27

Second, the normalization of the decision matrix is calculated by multiplying the

average weight of employee promotion candidates and the normalized weight of

each employee promotion candidates toward sub-criteria. The value of average

weight of employee promotion candidates are shown in Table 4.17. The value of

normalized weight of each employee promotion candidates toward sub-criteria is

shown in Table 4.16. Table 4.18 shows the result of normalization of decision

matrix.

Table 4.18 Normalization of Decision Matrix

Sub-

Criteria

Employee Promotion Candidates

1 2 3 4 5 6 7

PC1 0.01544 0.000374 5.94 10-7

9.34 10-5

0.007085 6.09 10-5

7.54 10-7

PC2 0.044044 0.000373 1.88 10-6

8.18 10-6

0.00472 4.96 10-6

2.07 10-6

PC3 0.043677 0.001508 1.11 10-6

5.02 10-5

0.003453 2.62 10-5

2.18 10-6

PC4 0.028329 0.001057 7.26 10-6

0.000312 0.013212 0.000172 9.31 10-6

PC5 0.043284 0.000162 1.25 10-7

4.96 10-5

0.005349 2.61 10-5

1.74 10-6

PC6 0.017615 0.000754 1.82 10-7

0.000192 0.008405 1.53 10-5

4.37 10-5

PC7 0.037123 0.000973 1.36 10-6

3.76 10-5

0.001933 2.16 10-5

3.79 10-7

PC8 8.31 10-5

1.72 10-5

1.17 10-6

4.03 10-6

0.000822 0.000104 0.031849

PC9 0.015134 0.000546 1.95 10-7

0.000168 0.0089 1.78 10-5

2.9 10-7

PC10 0.000107 1.6 10-5

3.63 10-6

5.46 10-6

4.25 10-6

3.92 10-7

0.003052

PC11 0.011007 0.014491 1.28 10-6

5.01 10-5

3.9 10-5

2.73 10-5

0.018293

PC12 0.044251 0.00035 1.44 10-7

0.000102 0.007097 1.26 10-5

0.013575

IR1 0.010304 0.000405 4.49 10-7

0.000119 0.004961 1.01 10-5

9.33 10-7

IR2 0.015211 0.00064 6.59 10-7

1.51 10-5

0.007762 8.48 10-6

9.5 10-7

IR3 0.032532 0.001524 1.95 10-7

0.000419 0.015851 4.51 10-5

5.93 10-7

IR4 0.00779 0.001714 1.8 10-6

9.5 10-5

0.003791 4.47 10-5

5.68 10-7

WA1 0.022218 0.000737 1.81 10-7

3.65 10-5

0.001688 2.08 10-5

4.57 10-7

WA2 0.042691 0.000212 1.69 10-6

6.81 10-5

0.005076 3.46 10-5

2.96 10-6

WA3 0.045144 0.000301 3 10-7

5.87 10-5

0.005429 3.72 10-5

9.45 10-7

WA4 0.022383 0.000144 1.6 10-7

4.36 10-5

0.002191 2.75 10-6

3.5 10-7

WA5 0.009707 0.000183 2.96 10-7

8.49 10-5

0.00631 4.65 10-5

7.54 10-7

WR1 0.041269 0.001672 3 10-7

9.83 10-5

0.003761 2.13 10-6

6.14 10-7

WR2 0.032121 0.001294 6.71 10-6

0.000385 0.015917 1.69 10-5

1.6 10-6

WR3 0.015805 0.000911 1.5 10-7

3.9 10-5

0.008957 2.11 10-6

1.77 10-7

WR4 0.000943 9.78 10-5

7.2 10-6

2.91 10-5

0.00022 3.04 10-5

3.24 10-6

WR5 6.55 10-5

0.000226 0.000136 6.71 10-5

5.86 10-5

3.68 10-5

1.8 10-5

WR6 0.010517 0.000531 8.58 10-8

1.5 10-5

0.005794 7.89 10-6

2.59 10-7

E1 0.011184 0.000603 5.65 10-7

1.98 10-5

0.005629 1.09 10-5

2.44 10-7

E2 0.042301 0.00035 2.84 10-7

9.48 10-5

0.005286 8.77 10-6

9.15 10-7

28

Table 4.18 Normalization of Decision Matrix (continued)

Sub-

Criteria

Employee Promotion Candidates

1 2 3 4 5 6 7

E3 0.010141 0.0004 4.43 10-7

0.000119 0.005019 1.03 10-5

9.52 10-7

Table 4.18 Normalization of Decision Matrix (continued)

Sub-

Criteria

Employee Promotion Candidates

1 2 3 4 5 6 7

PC1 0.024026 3.04 10-5

1.54 10-5

0.229151 7.66 10-8

0.000437 3.76 10-7

PC2 0.061494 1.49×10-5

1.04×10-5

0.103599 2.25×10-7

0.002585 1.1×10-6

PC3 0.063207 9.16×10-5

4.47×10-6

0.099076 2.2×10-6

0.001772 1.07×10-6

PC4 0.039788 4.7×10-5 2.3×10-5

0.064227 1.01×10-6

0.006638 4.78×10-6

PC5 0.066258 8.69×10-5

8.48×10-6

0.094877 2.39×10-7

0.002435 9.62×10-7

PC6 0.025899 5.69×10-5

3.28×10-6

0.210623 3.84×10-8

0.000371 2.09×10-7

PC7 0.152278 6.87 10-5

5.09 10-6

0.000467 3.72 10-7

0.001083 1.97 10-7

PC8 0.031154 0.000163 0.001151 0.000125 4.86 10-5

1.2 10-5

0.000297

PC9 0.051164 6.65 10-6

3.47 10-6

0.177943 3.38 10-8

0.000607 1.56 10-7

PC10 0.085816 0.007634 0.000587 0.02494 2.16 10-6

1.56 10-5

1.04 10-5

PC11 0.00119 9.14 10-5

5.37 10-7

0.000192 0.000345 2.07 10-5

0.000109

PC12 1.26 10-6

4.84 10-6

2.76 10-6

0.10108 2.3 10-8

0.000382 1.09 10-7

IR1 0.089342 3.37 10-6

1.5 10-6

0.140931 8.6 10-8

0.002038 3.93 10-7

IR2 0.024596 2.75 10-5

1.39 10-5

0.22591 8.98 10-8

0.000784 4.44 10-7

IR3 0.049835 1.25 10-5

6.33 10-6

0.075332 3.57 10-7

0.001592 1.67 10-6

IR4 0.095309 1.15 10-5

5.85 10-6

0.14629 6.13 10-7

4.6 10-7

2.94 10-7

WA1 0.033513 1.05 10-5

6.19 10-7

0.222647 3.54 10-8

0.000836 1.45 10-7

WA2 0.065229 1.2 10-5

6.11 10-6

0.098603 3.79 10-7

0.002443 1.33 10-6

WA3 0.069152 2.12 10-5

1.07 10-5

0.104533 6 10-7

0.000258 3.1 10-7

WA4 0.03429 8.14 10-6

4.94 10-6

0.223349 1.65 10-7

0.001104 3.48 10-7

WA5 0.088029 2.61 10-5

1.03 10-6

0.133068 5.45 10-7

0.002644 3.71 10-7

WR1 0.06322 1.54 10-5

3.6 10-6

0.101676 6.16 10-7

0.00193 3.23 10-7

WR2 0.050042 5.22 10-5

2.51 10-5

0.079845 2.19 10-6

0.001461 7.34 10-7

WR3 0.02426 6.54 10-6

3.39 10-6

0.216231 3.67 10-7

0.000854 2.06 10-7

WR4 0.000711 5.46 10-5

4.28 10-5

0.337029 1.41 10-5

0.000103 6.06 10-5

WR5 8.36 10-5

0.001004 0.000523 0.020854 0.000269 0.00026 0.016139

WR6 0.087999 2.63 10-5

2.8 10-6

0.135111 1.7 10-7

0.00263 1.76 10-7

E1 0.093611 4.33 10-6

2.2 10-6

0.123137 2.31 10-7

0.00284 1.5 10-7

E2 0.065822 2.09 10-6

1.06 10-6

0.096426 6.05 10-7

0.002558 4.5 10-7

E3 0.09077 3.04 10-6

2.1 10-6

0.132979 8.84 10-8

0.002677 5.59 10-7

Calculation 19:

Employee Promotion Candidates 1 – PC1 =

29

After the normalization decision matrix is calculated, the positive ideal solution

(PIS) and the negative ideal solution (NIS) value can be determined. The

difference between PIS and NIS is located on finding maximum value for positive

ideal solution while finding minimum value for negative ideal solution. Table

below shows the calculation of PIS value.

Table 4.19 Calculation of Positive Ideal Solution

Sub-

Criteria MAX

Employee Promotion Candidates

1 2 3 4 5 6 7

PC1 0.229151 0.045672 0.052339 0.05251 0.052467 0.049313 0.052482 0.05251

PC2 0.103599 0.003547 0.010656 0.010732 0.010731 0.009777 0.010732 0.010732

PC3 0.099076 0.003069 0.00952 0.009816 0.009806 0.009144 0.009811 0.009816

PC4 0.064227 0.001289 0.00399 0.004124 0.004085 0.002603 0.004103 0.004124

PC5 0.094877 0.002662 0.008971 0.009002 0.008992 0.008015 0.008997 0.009001

PC6 0.210623 0.037252 0.044045 0.044362 0.044281 0.040892 0.044356 0.044344

PC7 0.152278 0.013261 0.022893 0.023188 0.023177 0.022603 0.023182 0.023188

PC8 0.031849 0.001009 0.001013 0.001014 0.001014 0.000963 0.001008 0

PC9 0.177943 0.026507 0.03147 0.031664 0.031604 0.028575 0.031657 0.031663

PC10 0.085816 0.007346 0.007362 0.007364 0.007364 0.007364 0.007364 0.00685

PC11 0.018293 5.31 10-5

1.45 10-5

0.000335 0.000333 0.000333 0.000334 0

PC12 0.10108 0.003229 0.010147 0.010217 0.010196 0.008833 0.010215 0.007657

IR1 0.140931 0.017064 0.019748 0.019861 0.019828 0.018488 0.019859 0.019861

IR2 0.22591 0.044394 0.050747 0.051035 0.051029 0.047589 0.051032 0.051035

IR3 0.075332 0.001832 0.005448 0.005675 0.005612 0.003538 0.005668 0.005675

IR4 0.14629 0.019182 0.020902 0.0214 0.021373 0.020306 0.021388 0.021401

WA1 0.222647 0.040172 0.049244 0.049572 0.049555 0.048823 0.049562 0.049571

WA2 0.098603 0.003126 0.009681 0.009722 0.009709 0.008747 0.009716 0.009722

WA3 0.104533 0.003527 0.010864 0.010927 0.010915 0.009822 0.010919 0.010927

WA4 0.223349 0.040388 0.049821 0.049885 0.049865 0.048911 0.049884 0.049885

WA5 0.133068 0.015218 0.017658 0.017707 0.017684 0.016068 0.017695 0.017707

WR1 0.101676 0.003649 0.010001 0.010338 0.010318 0.009587 0.010338 0.010338

WR2 0.079845 0.002278 0.00617 0.006374 0.006314 0.004087 0.006373 0.006375

WR3 0.216231 0.04017 0.046362 0.046756 0.046739 0.042963 0.046755 0.046756

WR4 0.337029 0.112954 0.113523 0.113584 0.113569 0.11344 0.113568 0.113586

WR5 0.020854 0.000432 0.000426 0.000429 0.000432 0.000432 0.000433 0.000434

WR6 0.135111 0.015524 0.018112 0.018255 0.018251 0.016723 0.018253 0.018255

E1 0.123137 0.012533 0.015015 0.015163 0.015158 0.013808 0.01516 0.015163

E2 0.096426 0.00293 0.009231 0.009298 0.00928 0.008306 0.009296 0.009298

E3 0.132979 0.015089 0.017577 0.017683 0.017652 0.016374 0.017681 0.017683

SUM 0.535357 0.672947 0.677991 0.677334 0.636427 0.677818 0.673557

S+ 0.731681 0.820334 0.823402 0.823003 0.797764 0.823297 0.820705

30

Table 4.19 Calculation of Positive Ideal Solution (continued)

Sub-

Criteria MAX

Employee Promotion Candidates

8 9 10 11 12 13 14

PC1 0.229151 0.042076 0.052496 0.052503 0 0.05251 0.05231 0.05251

PC2 0.103599 0.001773 0.01073 0.010731 0 0.010733 0.010204 0.010732

PC3 0.099076 0.001287 0.009798 0.009815 0 0.009816 0.009468 0.009816

PC4 0.064227 0.000597 0.004119 0.004122 0 0.004125 0.003317 0.004124

PC5 0.094877 0.000819 0.008985 0.009 0 0.009002 0.008546 0.009001

PC6 0.210623 0.034123 0.044338 0.044361 0 0.044362 0.044206 0.044362

PC7 0.001083 0 0.023168 0.023187 0.023046 0.023188 0.02286 0.023188

PC8 0.000297 4.84 10-7

0.001004 0.000942 0.001006 0.001011 0.001014 0.000996

PC9 0.177943 0.016073 0.031661 0.031662 0 0.031664 0.031448 0.031664

PC10 0.02494 0 0.006112 0.007264 0.003706 0.007364 0.007362 0.007363

PC11 0.000345 0.000292 0.000331 0.000335 0.000328 0.000322 0.000334 0.000331

PC12 0.10108 0.010217 0.010216 0.010217 0 0.010217 0.01014 0.010217

IR1 0.140931 0.002661 0.019861 0.019861 0 0.019862 0.019291 0.019862

IR2 0.22591 0.040528 0.051023 0.051029 0 0.051035 0.050682 0.051035

IR3 0.075332 0.00065 0.005673 0.005674 0 0.005675 0.005438 0.005675

IR4 0.14629 0.002599 0.021397 0.021399 0 0.021401 0.021401 0.021401

WA1 0.222647 0.035772 0.049567 0.049571 0 0.049572 0.0492 0.049572

WA2 0.098603 0.001114 0.00972 0.009721 0 0.009722 0.009247 0.009722

WA3 0.104533 0.001252 0.010923 0.010925 0 0.010927 0.010873 0.010927

WA4 0.223349 0.035743 0.049881 0.049883 0 0.049885 0.049393 0.049885

WA5 0.133068 0.002028 0.0177 0.017707 0 0.017707 0.01701 0.017707

WR1 0.101676 0.001479 0.010335 0.010337 0 0.010338 0.009949 0.010338

WR2 0.079845 0.000888 0.006367 0.006371 0 0.006375 0.006144 0.006375

WR3 0.216231 0.036853 0.046753 0.046754 0 0.046756 0.046387 0.046756

WR4 0.337029 0.11311 0.113552 0.11356 0 0.113579 0.113519 0.113548

WR5 0.020854 0.000431 0.000394 0.000413 0 0.000424 0.000424 2.22E-05

WR6 0.135111 0.00222 0.018248 0.018254 0 0.018255 0.017551 0.018255

E1 0.123137 0.000872 0.015162 0.015162 0 0.015163 0.014471 0.015163

E2 0.096426 0.000937 0.009298 0.009298 0 0.009298 0.008811 0.009298

E3 0.132979 0.001782 0.017683 0.017683 0 0.017684 0.016979 0.017683

SUM 0.388175 0.676494 0.677742 0.028086 0.677969 0.667978 0.677527

S+ 0.623037 0.822493 0.823251 0.16759 0.823389 0.817299 0.82312

Calculation 20:

Employee Promotion Candidates 1 – PC1 = ( )

31

Calculation 21:

S+ – Employee Promotion Candidates 1 =

√

= 0.731681

There are no differences for the formula to find the distance between positive

ideal solution and negative ideal solution. The positive ideal solution is based on

the maximum value normalization decision matrix for each sub-criterion whereas

negative ideal solution is based on the minimum value normalization decision

matrix for each sub-criterion.

Table 4.20 Calculation of Negative Ideal Solution

Sub-

Criteria MIN

Employee Promotion Candidates

1 2 3 4 5

PC1 7.66372 10-8

0.000238 1.39 10-7

2.68 10-13

8.7 10-9

5.02 10-5

PC2 2.24525 10-7

0.00194 1.39 10-7

2.74 10-12

6.32 10-11

2.23 10-5

PC3 1.07319 10-6

0.001908 2.27 10-6

1.49 10-15

2.41 10-9

1.19 10-5

PC4 1.00818 10-6

0.000802 1.11 10-6

3.9 10-11

9.65 10-8

0.000175

PC5 1.24912 10-7

0.001874 2.64 10-8

0 2.45 10-9

2.86 10-5

PC6 3.84491 10-8

0.00031 5.68 10-7

2.05 10-14

3.68 10-8

7.06 10-5

PC7 1.97469 10-7

0.001378 9.47 10-7

1.35 10-12

1.4 10-9

3.74 10-6

PC8 1.16737 10-6

6.72 10-9

2.57 10-10

0 8.21 10-12

6.74 10-7

PC9 3.38245 10-8

0.000229 2.98 10-7

2.58 10-14

2.83 10-8

7.92 10-5

PC10 3.91767 10-7

1.13 10-8

2.44 10-10

1.05 10-11

2.57 10-11

1.49 10-11

PC11 5.36746 10-7

0.000121 0.00021 5.5 10-13

2.45 10-9

1.48 10-9

PC12 2.3007 10-8

0.001958 1.22 10-7

1.47 10-14

1.04 10-8

5.04 10-5

IR1 8.6029 10-8

0.000106 1.64 10-7

1.32 10-13

1.41 10-8

2.46 10-5

IR2 8.98023 10-8

0.000231 4.09 10-7

3.24 10-13

2.24 10-10

6.02 10-5

IR3 1.94942 10-7

0.001058 2.32 10-6

0 1.75 10-7

0.000251

IR4 2.9433 10-7

6.07 10-5

2.94 10-6

2.28 10-12

8.97 10-9

1.44 10-5

WA1 3.53838 10-8

0.000494 5.44 10-7

2.13 10-14

1.33 10-9

2.85 10-6

WA2 3.79407 10-7

0.001822 4.49 10-8

1.73 10-12

4.58 10-9

2.58 10-5

WA3 2.99759 10-7

0.002038 9.07 10-8

0 3.41 10-9

2.95 10-5

WA4 1.59801 10-7

0.000501 2.06 10-8

0 1.89 10-9

4.8 10-6

WA5 2.95553 10-7

9.42 10-5

3.35 10-8

0 7.15 10-9

3.98 10-5

32

Table 4.20 Calculation of Negative Ideal Solution (continued)

Sub-

Criteria MIN

Employee Promotion Candidates

1 2 3 4 5

WR1 3.00241 10-7

0.001703 2.8 10-6

0 9.6 10-9

1.41 10-5

WR2 7.34117 10-7

0.001032 1.67 10-6

3.57 10-11

1.47 10-7

0.000253

WR3 1.49558 10-7

0.00025 8.3 10-7

0 1.51 10-9

8.02 10-5

WR4 3.2364 10-6

8.83 10-7

8.94 10-9

1.57 10-11

6.68 10-10

4.7 10-8

WR5 1.80097 10-5

2.26 10-9

4.31 10-8

1.4 10-8

2.41 10-9

1.65 10-9

WR6 8.582 10-8

0.000111 2.82 10-7

0 2.23 10-10

3.36 10-5

E1 1.49588 10-7

0.000125 3.63 10-7

1.72 10-13

3.87 10-10

3.17 10-5

E2 2.84099 10-7

0.001789 1.23 10-7

0 8.93 10-9

2.79 10-5

E3 8.83767 10-8

0.000103 1.6 10-7

1.26 10-13

1.41 10-8

2.52 10-5

SUM 0.022278 0.000228 1.41 10-8

5.92 10-7

0.001411

S- 0.149257 0.015114 0.000119 0.000769 0.03757

Table 4.20 Calculation of Negative Ideal Solution (continued)

Sub-

Criteria MIN

Employee Promotion Candidates

6 7 8 9 10

PC1 7.66372 10-8

3.7 10-9

4.59 10-13

0.000577 9.21 10-10

2.36 10-10

PC2 2.24525 10-7

2.24 10-11

3.4 10-12

0.003782 2.16 10-10

1.03 10-10

PC3 1.07319 10-6

6.33 10-10

1.22 10-12

0.003995 8.19 10-9

1.15 10-11

PC4 1.00818 10-6

2.93 10-8

6.89 10-11

0.001583 2.11 10-9

4.84 10-10

PC5 1.24912 10-7

6.74 10-10

2.6 10-12

0.00439 7.53 10-9

6.98 10-11

PC6 3.84491 10-8

2.33 10-10

1.91 10-9

0.000671 3.24 10-9

1.05 10-11

PC7 1.97469 10-7

4.56 10-10

3.29 10-14

0.023188 4.7 10-9

2.39 10-11

PC8 1.16737 10-6

1.05 10-8

0.001014 0.000971 2.61 10-8

1.32 10-6

PC9 3.38245 10-8

3.14 10-10

6.55 10-14

0.002618 4.38 10-11

1.18 10-11

PC10 3.91767 10-7

0 9.31 10-6

0.007364 5.83 10-5

3.44 10-7

PC11 5.36746 10-7

7.17 10-10

0.000335 1.42 10-6

8.26 10-9

0

PC12 2.3007 10-8

1.58 10-10

0.000184 1.54 10-12

2.32 10-11

7.51 10-12

IR1 8.6029 10-8

9.95 10-11

7.17 10-13

0.007982 1.08 10-11

2 10-12

IR2 8.98023 10-8

7.04 10-11

7.4 10-13

0.000605 7.51 10-10

1.92 10-10

IR3 1.94942 10-7

2.02 10-9

1.59 10-13

0.002483 1.51 10-10

3.77 10-11

IR4 2.9433 10-8

1.98 10-9

7.49 10-14

0.009084 1.26 10-10

3.09 10-11

WA1 3.53838 10-8

4.31 10-10

1.77 10-13

0.001123 1.1 10-10

3.41 10-13

WA2 3.79407 10-7

1.17 10-9

6.66 10-12

0.004255 1.36 10-10

3.29 10-11

WA3 2.99759 10-7

1.36 10-9

4.17 10-13

0.004782 4.35 10-10

1.09 10-10

WA4 1.59801 10-7

6.69 10-12

3.64 10-14

0.001176 6.36 10-11

2.29 10-11

WA5 2.95553 10-7

2.13 10-9

2.1 10-13

0.007749 6.66 10-10

5.38 10-13

WR1 3.00241 10-7

3.36 10-12

9.83 10-14

0.003997 2.29 10-10

1.09 10-11

WR2 7.34117 10-7

2.62 10-10

7.45 10-13

0.002504 2.64 10-9

5.94 10-10

WR3 1.49558 10-7

3.86 10-12

7.45 10-16

0.000589 4.08 10-11

1.05 10-11

WR4 3.2364 10-6

7.37 10-10

0 5.02 10-7

2.64 10-9

1.56 10-9

33

Table 4.20 Calculation of Negative Ideal Solution (continued)

Sub-

Criteria MIN

Employee Promotion Candidates

6 7 8 9 10

WR5 1.80097 10-5

3.52 10-10

0 4.3 10-9

9.72 10-7

2.55 10-7

WR6 8.582 10-8

6.1 10-11

3 10-14

0.007744 6.87 10-10

7.39 10-12

E1 1.49588 10-7

1.15 10-10

8.84 10-15

0.008763 1.75 10-11

4.2 10-12

E2 2.84099 10-7

7.2 10-11

3.98 10-13

0.004332 3.28 10-12

6.07 10-13

E3 8.83767 10-8

1.04 10-10

7.47 10-13

0.008239 8.69 10-12

4.05 10-12

SUM 5.77 10-8

0.001543 0.124547 5.93 10-5

1.92 10-16

S- 0.00024 0.039275 0.352913 0.007702 0.001387

Table 4.20 Calculation of Negative Ideal Solution (continued)

Sub-

Criteria MIN

Employee Promotion Candidates

11 12 13 14

PC1 7.66372 10-8

0.05251 0 1.91 10-7

8.97 10-14

PC2 2.24525 10-7

0.010733 0 6.68 10-6

7.7 10-13

PC3 1.07319 10-6

0.009816 1.27 10-12

3.14 10-6

0

PC4 1.00818 10-6

0.004125 0 4.4 10-5

1.42 10-11

PC5 1.24912 10-7

0.009002 1.3 10-14

5.93 10-6

7.01 10-13

PC6 3.84491 10-8

0.044362 0 1.38 10-7

2.92 10-14

PC7 1.97469 10-7

2.18 10-7

3.05 10-14

1.17 10-6

0

PC8 1.16737 10-6

1.54 10-8

2.25 10-9

1.17 10-10

8.77 10-8

PC9 3.38245 10-8

0.031664 0 3.69 10-7

1.5 10-14

PC10 3.91767 10-7

0.000622 3.14 10-12

2.32 10-10

1.01 10-10

PC11 5.36746 10-7

3.68 10-8

1.19 10-7

4.08 10-10

1.17 10-8

PC12 2.3007 10-8

0.010217 0 1.46 10-7

7.47 10-15

IR1 8.6029 10-8

0.019862 0 4.15 10-6

9.44 10-14

IR2 8.98023 10-8

0.051035 0 6.14 10-7

1.26 10-13

IR3 1.94942 10-7

0.005675 2.63 10-14

2.53 10-6

2.19 10-12

IR4 2.9433 10-8

0.021401 1.01 10-13

2.73 10-14

0

WA1 3.53838 10-8

0.049572 0 6.98 10-7

1.2 10-14

WA2 3.79407 10-7

0.009722 0 5.97 10-6

8.98 10-13

WA3 2.99759 10-7

0.010927 8.99 10-14

6.63 10-8

9.88 10-17

WA4 1.59801 10-7

0.049885 2.34 10-17

1.22 10-6

3.56 10-14

WA5 2.95553 10-7

0.017707 6.23 10-14

6.99 10-6

5.67 10-15

WR1 3.00241 10-7

0.010338 9.94 10-14

3.72 10-6

5.37 10-16

WR2 7.34117 10-7

0.006375 2.11 10-12

2.13 10-6

0

WR3 1.49558 10-7

0.046756 4.72 10-14

7.3 10-7

3.23 10-15

WR4 3.2364 10-6

0.113586 1.17 10-10

1 10-8

3.29 10-9

WR5 1.80097 10-5

0.000434 6.31 10-8

5.88 10-8

0.00026

WR6 8.582 10-8

0.018255 7.04 10-15

6.91 10-6

8.08 10-15

E1 1.49588 10-7

0.015163 6.65 10-15

8.07 10-6

0

E2 2.84099 10-7

0.009298 1.03 10-13

6.54 10-6

2.74 10-14

34

Table 4.20 Calculation of Negative Ideal Solution (continued)

Sub-

Criteria MIN

Employee Promotion Candidates

11 12 13 14

E3 8.83767 10-8

0.017684 0 7.17 10-6

2.22 10-13

SUM 0.646724 1.84 10-7

0.000119 0.00026

S- 0.804192 0.000429 0.010927 0.016124

4.4.4 Employee Promotion Candidates Rank

After the positive ideal solution and negative ideal solution are gained, the relative

closeness coefficient should be calculated to rank the employee promotion

candidates. The relative closeness coefficient shows the distance between PIS

value and NIS value. The employee promotion candidate who has the largest

distance is the most priority employee that should be promoted.

Table 4.21 Relative Closeness Coefficient Calculation

Employee

Promotion

Candidates

S+ S

-

1 0.731681 0.149257 0.1694299

2 0.820334 0.015114 0.0180912

3 0.823402 0.000119 0.000144

4 0.823003 0.000769 0.0009339

5 0.797764 0.03757 0.0449756

6 0.823297 0.00024 0.0002917

7 0.820705 0.039275 0.0456694

8 0.623037 0.352913 0.3616095

9 0.822493 0.007702 0.0092772

10 0.823251 0.001387 0.0016819

11 0.16759 0.804192 0.8275437

12 0.823389 0.000429

13 0.817299 0.010927

14 0.82312 0.016124

Calculation 22:

Employee Promotion Candidates 1 =

= 0.1694299

After the relative closeness coefficient as the distance has been defined, the goal

of this research which is determining the rank of employee promotion candidates

35

comes closer. Next, the employee promotion candidates are arranged from the

largest distance until the smallest distance. Based on table 4.22, the employee 11

has the largest distance which means employee 11 is the most priority that should

be promoted while employee 3 has the smallest distance which means employee 3

is the least priority that should be promoted.

Table 4.22 Employee Promotion Candidates Rank

Rank

Employee

Promotion

Candidates

1 11 0.827544

2 8 0.361609

3 1 0.16943

4 7 0.045669

5 5 0.044976

6 14 0.019213

7 2 0.018091

8 13 0.013193

9 9 0.009277

10 10 0.001682

11 4 0.000934

12 12 0.000521

13 6 0.000292

14 3

4.5 Comparison for Best Three Current Promoted Employee and Proposed

Promoted Employee

The problem of this research is based on the employee promotion selection

process system. There is no specific method that will be used during the employee

promotion selection process. It causes the subjective assessment and it may cause

the dissatisfaction from other employee promotion candidates. In this sub chapter,

only the best three of current promoted employee and the best three of proposed

promoted employee will be discussed and analyzed further.

4.5.1 Comparison to Distance

After the analysis and calculation has been done, the best three of proposed

promoted employees are coming up. The best three of proposed promoted

employee are Employee 11, Employee 8 and Employee 1. Whereas, the best three

36

of current promoted employees are Employee 8, Employee 1 and Employee 5.

Compared to the current promoted employees, the proposed promoted employees

have higher point in priority criteria. Figure 4.3 shows the comparison of distance

through Fuzzy AHP and TOPSIS Method from current and proposed promoted

employees which are as the final analysis of the research.

Figure 4.3 shows the big different distance numbers between current and proposed

promoted employees which are between Employee 8, Employee 1, Employee 5

and Employee 11, Employee 8, Employee 1. Based on the theory, the best

promoted employee is chosen by looking the biggest distance number that

employee made.

As can be seen in Figure 4.3, the best three of current and proposed promoted

employee are different. Moreover, those three pairs have big differences in terms

of distance value. Based on that reason, it can be said that the best three of

proposed promoted employees are more suitable to be promoted than the best

three of current promoted employees. In this case, the suitability means the

indicator of employee promotion candidates that the company has been made

previously.

Figure 4.3 Comparisons between Current and Proposed Promoted Employee toward

Distance

Current Promoted

Employee:

Employee 8 : 0.361609

Employee 1 : 0.16943

Employee 5 : 0.044976

Proposed Promoted

Employee:

Employee 11 : 0.827544

Employee 8 : 0.361609

Employee 1 : 0.16943

37

4.5.2 Comparison to Sub-criteria

There are five criteria that assessed along the observation of this research such as

personnel characteristics, inter-personal relation, work attitude, work result and

education. Sub-criteria has also determined regarding to the criteria. There are 12

sub-criteria based on personnel characteristics criteria, 4 sub-criteria based on

inter-personal relation criteria, 5 sub-criteria based on work attitude criteria, 6

sub-criteria based on work result criteria and 3 sub-criteria based on education

criteria.

The blue line represents Employee 8 as the first priority of current promoted

employee and the red line represents Employee 1 as the first priority of proposed

promoted employee. The number in the left side of graphs shows the weight of

each employee promoted based on sub-criteria that show in below part of the

graph. Generally, the graph can be looked and analyzed separately from one

employee to another. But, there are some points that are close enough such as in

PC4 (Innovation sub-criteria), PC5 (Problem Solving sub-criteria), etc.

WR4 (Performance Rating sub-criteria) as the sub-criteria which has the largest

weight sub-criteria shows a huge difference between Employee 8 and Employee

11. Based on the figure 4.4, it shows that Employee 11 has larger weight value

than Employee 8. It means that the performance rating of proposed promoted

employee is better than the performance rating of current promoted employee.

Next, PC1 (Technical Knowledge sub-criteria) also shows a huge difference

between Employee 8 and Employee 11. Employee 11 has bigger weight in

technical knowledge sub-criteria than Employee 8. That condition also happened

in other sub-criteria such as PC 6 (Adaptability sub-criteria), PC 9 (Hierarchy

Observation sub-criteria), IR 2 (Teamwork sub-criteria), IR 4 (Communication

sub-criteria), WA 1 (Responsibility sub-criteria), and WA 4 (Attendance sub-

criteria).

Because of the reasons above, Employee 11 is better choice to be promoted than

Employee 8. As the explanation and analysis before, Employee 11 wins 19 sub-

38

criteria among all of the 30 sub-criteria. In addition, based on the weight of

criteria to goal, the work result criteria contributes 58.79% from 100%, it is more

than half from the total percentage. The graphic shows that Employee 11 is totally

win over Employee 8 in Work Result criteria. In conclusion, Employee 11 places

higher than Employee 8 in the Work Result criteria.

Figure 4.4 Comparisons between Employee 8 (Current) and Employee 11

(Proposed) as the First Priority Promoted Employee

The second comparison is between Employee 1 (Current) and Employee 8

(Proposed) as the second priority to be promoted. The blue line represents

Employee 1 as the current promoted employee and the red line represents

Employee 8 as the proposed promoted employee. Based on the figure 4.5, it can

be seen that the graph is easy to identify because the points that represent on both

employees are found rarely near into each other.

Based on Figure 4.5, it shows that the points between PC 1 until PC 6 have little

range and it means there is no significant difference between Employee 1 and

Employee 8. But, PC 7 (Decision Making Ability sub-criteria) shows huge

difference, it is clearly shown that Employee 8 wins over Employee 1. It is also

happened in PC 9 (Hierarchy Observation sub-criteria), PC 10 (Service Year sub-

criteria), IR 1 (Cooperation sub-criteria), IR 4 (Communication sub-criteria), WA

5 (Commitment sub-criteria), WR 6 (Completeness of Assignment sub-criteria),

and E1 (Last Educational Background sub-criteria).

0

0.2

0.4

0.6

0.8

1

1.2

PC

1

PC

2

PC

3

PC

4

PC

5

PC

6

PC

7

PC

8

PC

9

PC

10

PC

11

PC

12

IR1

IR2

IR3

IR4

WA

1

WA

2

WA

3

WA

4

WA

5

WR

1

WR

2

WR

3

WR

4

WR

5

WR

6

E1

E2

E3

8

11

39

Because of the reasons above, Employee 8 is better choice to be promoted than

Employee 1 as the second priority to be promoted. As the explanation and analysis

before, Employee 8 wins 17 sub-criteria among all of the 30 sub-criteria. In

addition, based on the weight of criteria to goal, the work result criteria

contributes 58.79% from 100%, it is more than half from the total percentage. The

graphic shows that Employee 8 is totally win over Employee 1 in Work Result

criteria. In conclusion, Employee 8 places higher than Employee 1 in the Work

Result criteria.

Figure 4.5 Comparisons between Employee 1 (Current) and Employee 8 (Proposed)

as the Second Priority Promoted Employee

The third comparison is between Employee 5 (Current) and Employee 1

(Proposed) as the third priority to be promoted. The blue line represents Employee

5 as the current promoted employee and the red line represents Employee 1 as the

proposed promoted employee. Based on the figure 4.6, it can be seen that the

graph is easy to identify because the points that represent on both employees are

found rarely near into each other.

Based on Figure 4.6, it shows that the points between PC 8 (Age of Employee

sub-criteria), PC9 (Hierarchy Observation sub-criteria), PC 10 (Service Year sub-

criteria), IR1 (Cooperation sub-criteria), IR 2 (Teamwork sub-criteria), IR 3(Team

Loyalty sub-criteria), IR 4 (Communication sub-criteria),WR2 (Efficiency sub-

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

PC

1

PC

2

PC

3

PC

4

PC

5

PC

6

PC

7

PC

8

PC

9

PC

10

PC

11

PC

12

IR1

IR2

IR3

IR4

WA

1

WA

2

WA

3

WA

4

WA

5

WR

1

WR

2

WR

3

WR

4

WR

5

WR

6

E1

E2

E3

1

8

40

criteria), WR 3 (Rapidity sub-criteria), WR 4 (Performance Rating), WR 5 (PP

Matrix sub-criteria), WR 6 (Completeness of Assignment sub-criteria),E1 (Last

Educational Background sub-criteria) and E3 (Total number of followed training

sub-criteria) have little range and it means there is no significant difference

between Employee 5 and Employee 1. But, PC 1 (Technical Knowledge sub-

criteria) until PC 7 (Decision Making Ability sub-criteria), PC 11 (Position Year

sub-criteria), PC 12 (Emotional Stability sub-criteria), WA 1 (Responsibility sub-

criteria) until WR 1 (Accuracy sub-criteria) and E2 (Last GPA sub-criteria) shows

huge difference, it is clearly shown that Employee 5 wins over Employee 1.

Because of the reasons above, Employee 1 is better choice to be promoted than

Employee 5 as the third priority to be promoted. As the explanation and analysis

before, Employee 1 has higher weight value in 21 sub-criteria among all of the 30

sub-criteria. In addition, based on the weight of criteria to goal, the work result

criteria contributes 58.79% from 100%, it is more than half from the total

percentage. The graphic shows that Employee 1 has totally higher result of weight

value over Employee 5 in Work Result criteria. In conclusion, Employee 1 places

higher than Employee 5 in the Work Result criteria.

Figure 4.6 Comparisons between Employee 5 (Current) and Employee 1 (Proposed)

as the Third Priority Promoted Employee

4.5.3 Comparison to Criteria

In this section, the best three of current promoted employees and the best three of

proposed promoted employees are compared toward each of criterion. Figure 4.7

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

PC

1

PC

2

PC

3

PC

4

PC

5

PC

6

PC

7

PC

8

PC

9

PC

10

PC

11

PC

12

IR1

IR2

IR3

IR4

WA

1

WA

2

WA

3

WA

4

WA

5

WR

1

WR

2

WR

3

WR

4

WR

5

WR

6

E1

E2

E3

5

1

41

shows the comparison between Employee 8 (current) and Employee 11 (proposed)

as the first priority employee to be promoted toward the criteria. The graph is

based on the calculation of Fuzzy AHP method in terms of determining

normalized weight. In the personnel characteristics criteria, inter-personal relation

criteria, work attitude criteria and work result criteria, Employee 11 wins over

Employee 8. But there is slightly difference in Education criteria. As mentioned

earlier, work result criteria takes more than half of total weight. Then, Figure 4.7

shows Employee 11 gives much higher value than Employee 8. Therefore,

Employee 8 is totally defeated by Employee 11 according to the performance of

criteria. In conclusion, Employee 11 is used as the first priority employee to be

promoted.

Figure 4.7 Comparison between Employee 8 (Current) and Employee 11 (Proposed)

as the First Priority toward Criteria

Second, Employee 1 (current) and Employee 8 (proposed) are compared as the

second priority employee to be promoted. Based on Figure 4.8, it shows that

Employee 8 wins all the criteria result. Employee 1 is totally lost compared with

Employee 8. In conclusion, Employee 8 is used as the second priority employee to

be promoted.

0

0.5

1

1.5

2

2.5

3

3.5

Personnel

Characteristics

Inter-personal

Relation

Work Attitude Work Result Education

Employee 8

Employee 11

42

Figure 4.8 Comparison between Employee 1 (Current) and Employee 8 (Proposed)

as the Second Priority toward Criteria

Third, Employee 5 (current) and Employee 1 (proposed) are compared as the third

priority employee to be promoted. Based on Figure 4.9, it shows that Employee 1

wins all the criteria result. Employee 5 is totally lost compared with Employee 1.

In conclusion, Employee 1 is used as the third priority employee to be promoted.

Figure 4.9 Comparison between Employee 5 (Current) and Employee 1 (Proposed)

as the Third Priority toward Criteria

0

0.5

1

1.5

2

2.5

3

Personnel

Characteristics

Inter-personal

Relation

Work Attitude Work Result Education

Employee 1

Employee 8

0

0.5

1

1.5

2

2.5

Personnel

Characteristics

Inter-personal

Relation

Work Attitude Work Result Education

Employee 5

Employee 1

1

CHAPTER V

CONCLUSION AND RECOMMENDATION

5.1 Conclusion

The objectives of this research in Company XYZ are successfully achieved. The

conclusion of this research is sentenced as the following below.

a. Company XYZ has developed the criteria and sub-criteria to assess the

employee promotion candidates’ performance result. They are Personnel

Characteristics criteria (Technical Knowledge, Non-technical Knowledge,

Ability to Learn, Innovation, Problem Solving, Adaptability, Decision

Making Ability, Age of Employee, Hierarchy Observation, Service Year,

Position Year and Emotional Stability), Inter-Personal Relation criteria

(Cooperation, Teamwork, Team Loyalty and Communication), Work

Attitude criteria (Responsibility, Motivation, Discipline, Attendance and

Commitment), Work Result criteria (Accuracy, Efficiency, Rapidity,

Performance Rating, PP Matrix and Completeness of Assignment) and

Education criteria (Last Educational Background, Last HPA and Total

number of followed training).

b. This research use Fuzzy Analytical Hierarchy (Fuzzy AHP) and Technique

for Order Preference by Similarity to Ideal Solution (TOPSIS) method.

Fuzzy AHP Method is used to determine the weight of each criteria

towards the goal, sub-criteria towards the criteria and employee promotion

candidate towards each of sub-criterion. Then, the weight result is used as

the input for TOPSIS Method. TOPSIS Method will rank and list the

employee promotion candidates by calculating the distance. These two

methods will decrease the subjective perspective and increase the accuracy

to decide which one of the employee that should be the most prioritized

employee to be promoted.

c. After implementing the Fuzzy AHP method and TOPSIS method, the

result is came up. The result shows that the best three of employee

promotion candidates are Employee 11, Employee 8 and Employee 1 for

2

Company XYZ regarding to the company indicator towards the employee

promotion candidates.

5.2 Recommendation

For further improvement in the next research, the recommendation is made, which

is:

To assure the observation’s result, the other methods such as Fuzzy ANP,

ELECTRE or PROMOTHEE can be applied to solve the research problem

and the results can be compared.

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