.
DEVELOPMENT OF FUZZY DECISION MODEL FOR ETHIOPIAN
CONSTRUCTION CONTRACTORS SELECTION
By
SIFEREW BISHAW
A Thesis Submitted as a partial Fulfillment for the Degree of Master of Science in Civil
Engineering (Construction Technology and Management)
to
DEPARTMENT OF CIVIL ENGINEERING
ADDIS ABABA SCIENCE AND TECHNOLOGY UNIVERSITY
OCTOBER, 2019
i
.
Certification
This is to certify that the thesis prepared by Mr. Siferew Bishaw entitled “DEVELOPMENT OF
FUZY
DECISION
MODEL
FOR
ETHIOPIAN
CONSTRUCTION
CONTRACTORS
SELECTION” and submitted as a partial fulfillment for the Degree of Master of Science
complies with the regulations of the University and meets the accepted standards with respect to
originality, content, and quality.
Date of Defence:
Principal Advisor
Wubishet Jekale (Dr. Ing) ____________________
__________________
Signature
Date
Members of Examining board
1. Dr. Bahiru Bewket ____________________
External examiner:
__________________
Signature
2. Dr. Belachew Asteray ____________________
Internal examiner:
Date
__________________
Signature
3. Dr. Melaku Sisay ____________________
ERA PG Coordinator
Date
_________________
Signature
4. Alemayehu Feyisa____________________
Dep’t Head of Civil Eng.
5. Dr. Brook Abate____________________
Dean, College
Signature
Date
__________________
Signature
Date
__________________
Date
ii
.
Declaration
I hereby declare that this thesis entitled “DEVELOPMENT OF FUZY DECISION MODEL FOR
ETHIOPIAN CONSTRUCTION CONTRACTORS SELECTION” was prepared by me, with the
guidance of my advisor. The work contained herein is my own except where explicitly stated
otherwise in the text, and that this work has not been submitted, in whole or in part, for any other
degree or professional qualification.
Author: Signature Date
Siferew Bishaw ………………………………………………………………….
Witnessed by:
Student Advisor:Signature
Date
Wubishet Jekale (Dr. Ing.) ………………………………………………………
Student Co-advisor:Signature
Date
_______________________________________________________________
iii
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Table of Contents
Certification .................................................................................................................................ii
Declaration ..................................................................................................................................iii
Table of Contents ........................................................................................................................ iv
List of Acronyms and Abbreviations ......................................................................................... vii
List of Tables .............................................................................................................................. ix
List of Figures .............................................................................................................................. x
Abstract ....................................................................................................................................... xi
ACKNOWLEDGMENTS ......................................................................................................... xii
CHAPTER ONE
INTRODUCTION
1.1. Background of the study ....................................................................................................... 1
1.2.
Statement of the Problem.................................................................................................. 3
1.3. Objective of the Study .......................................................................................................... 4
1.3.1. General Objective ........................................................................................................................ 4
1.3.2. Specific Objectives ...................................................................................................................... 4
1.4. Research Questions ............................................................................................................... 4
1.5. Scope of the Study ................................................................................................................ 4
1.6. Significance of the study ...................................................................................................... 4
CHAPTER TWO
LETERATURE REVIEW
2.1. Introduction ......................................................................................................................... 5
2.2. Theoretical Review.............................................................................................................. 7
2.2.1 Analytical Hierarchy Process (AHP) .............................................................................. 7
2.2.2 Fuzzy Set Theory (FST) ................................................................................................. 8
2.2.3 Fuzzy Analytical Hierarchy Process (FAHP) ................................................................. 8
2.3. Empirical Review ................................................................................................................ 9
2.3.1 Analytical Hierarchy Process (AHP) .............................................................................. 9
2.3.2 Fuzzy Numbers, Fuzzy Set, and Fuzzy Logic .............................................................. 12
2.3.2.1 Fuzzy Logic System ............................................................................................. 12
2.3.2.2 Fuzzification ........................................................................................................ 13
2.3.2.3 Fuzzy Rules .......................................................................................................... 13
iv
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2.3.2.4 Rule Base Reduction Methods ............................................................................. 14
2.3.2.5 Membership Function .......................................................................................... 15
2.3.2.5.1 Triangular Membership Function ............................................................ 15
2.3.2.5.2 Gaussian Membership Function .............................................................. 16
2.3.2.5.3 Trapezoidal Membership Function .......................................................... 16
2.3.2.6 Defuzzification..................................................................................................... 17
2.3.2.6.1 Centre of Gravity (CoG) Method/Weighted Average Method ................ 17
2.3.2.6.2 Mean of Maximum (MoM) Method ........................................................ 18
2.3.2.7 Conceptual Model .............................................................................................. 18
2.3.3 Fuzzy Analytic Hierarchy Process (FAHP) .................................................................. 20
2.3.3.1 Fuzzy AHP (Synthetic Extent Method) ............................................................... 24
2.3.3.2 Selection Criteria ................................................................................................. 26
2.3.3.2.1 Selection Criteria Overview ..................................................................... 26
2.3.3.2.2 Selection Criteria and Evaluation Methodology in Ethiopia ................... 28
2.4. Summary of the Literature Review ..................................................................................... 32
CHAPTER THREE
RESEARCH METHODOLOGY
3.1 Introduction ......................................................................................................................... 33
3.2 Research Design ................................................................................................................. 34
3.3 Sampling (Data Collection) ................................................................................................ 34
3.4 Methods .............................................................................................................................. 34
3.5 Data Analysis ...................................................................................................................... 35
CHAPTER FOUR
RESULTS AND DISCUSSION
4.1 Identifying Criteria & Developing a hierarchical structure ............................................................. 36
4.2 Modeling in Fuzzy AHP .................................................................................................................. 37
4.2.1 Determining Relative Importance ............................................................................................ 37
4.2.2 Model Formulation .................................................................................................................. 44
4.3 Ranking Contractors ........................................................................................................................ 45
4.3.1 Determining Linguistic terms for Contractors rating ................................................................ 45
4.3.2 Developing Codes (IF-THEN rule) in MATLAB Software ...................................................... 46
4.4 MODEL VALIDATION (Case Study) ............................................................................................ 47
4.4.1 Introduction ............................................................................................................................... 47
v
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4.4.2 Contractors rating for each criterion ......................................................................................... 47
4.4.2.1 Contractors Selection based on the current practice ......................................................... 47
4.4.3 Contractors Selection Based on the New Model ....................................................................... 50
4.4.3.1 Contractors Ranking (without software) ......................................................................... 51
4.4.3.2 Ranking supported by software (MATLAB) ................................................................... 52
4.4.3.2.1 Variable Creation & Assigning Values ................................................................ 52
4.4.3.2.2 Running the Software and data interpretation ...................................................... 53
4.4.4 Discussion and Interpretations .................................................................................................. 56
4.4.4.1 Based on the current practice ............................................................................................ 56
4.4.4.2 Scores based on the new model......................................................................................... 56
CHAPTER FIVE
CONCLUSION AND RECOMMENDATIONS
5.1 Conclusions .................................................................................................................................. 58
5.2 Recommendation .......................................................................................................................... 59
References ................................................................................................................................ 60
Appendices ............................................................................................................................... 63
vi
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List of Acronyms and Abbreviations
AHP
Analytical Hierarchy Process
ANP
Analytic Network Process
BV
Bid Value
CC
Closeness Coefficient
COA
Center of Area
COG
Center of Gravity
CBR
Case-Based Reasoning
DEA
Data Envelopment Analysis
EBV
Estimated Bid Value
FAHP
Fuzzy Analytical Hierarchy Process
FEAHP
Fuzzy Extent Analytic Hierarchy Process
FLC
Fuzzy Logic Control
FNR
Fuzzy Number Recognition
FNWC
Fuzzy Number Weight Center
FPPA
Federal Procurement and Property Administration
FS
Financial Soundness
GA
Genetic Algorithm
GS
General Suitability
HSE
Health Safety and Environment
NIS
Negative Ideal Solution
LBV
Lowest Bid Value
vii
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MA
Management Ability
MCDM
Multi-Criteria Decision Model
MoM
Mean of Maximum
PIS
Positive Ideal Solution
R
Reputability
RS
Resource
SC
Score
SCM
Supply Chain Management
SMART
Simple Multi-Attribute Rating Technique
TC
Technical Capability
TSK
Takagi - Sugeno - Kang
TOPSIS
Technique for Order Preference by Similarity to Ideal Solution
VAT
Value Added Tax
viii
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List of Tables
Table No.
Description
Page No.
Table 2.1
Calculated Random indices
12
Table 2.2
Triangular Fuzzy Membership
25
Table 2.3
Main and sub-criteria
27
Table 2.4
Technical Evaluation
30
Table 4.1
Linguistic terms
38
Table 4.2
Fuzzified Pair-wise Comparison Matrix
40
Table 4.3
Fuzzy Geometric Mean
41
Table 4.4
Fuzzy weight
42
Table 4.5
Fuzzified and defuzzified crisp value
43
Table 4.6
Normalized Weight
43
Table 4.7
Linguistic Variables with fuzzy values
45
Table 4.8
Score and Rank of contractors
49
Table 4.9
Bid Evaluators Linguistic Rating
50
Table 4.10
Crisp Values
50
Table 4.11
Score and Rank of Contractors Manually Calculated
51
Table 4.12
Score and Rank of Contractors Supported by software
55
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List of Figures
Figure No.
Description
Page No.
Figure2.1
Fuzzy Logic System
13
Figure 2.2
Triangular Membership Function
15
Figure 2.3
Gaussian Membership Function
16
Figure 2.4
Fuzzy Inference System
17
Figure 2.5
Fuzzy Decision System
19
Figure 2.6
Most important criteria
28
Figure 4.1
Major and Sub Criteria
37
Figure4.2
Fuzzy Scale of Relative Importance
39
Figure4.3
Linguistic Terms with Fuzzy Variables
45
Figure 4.4
Variables and the corresponding Values
52
Figure 4.5
Codes fed into MATLAB
53
Figure 4.6
MATLAB output in Weighted Product Model
54
Figure 4.7
MATLAB output in Weighted Sum Model
55
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Abstract
Choosing the right contractor to deliver a project in time, within budget and with better quality is
the most significant decision-making process to ensure the successful completion of construction
projects. As we are observing from day to day, many contractors failed to accomplish projects
due to different reasons like labor problems, financial problems, poor performance, social and
political problems, lack of safety considerations at worksite, management capability, etc. All
these cases have led to the impression that the current scenario of awarding the contracts is
inefficient in selecting the contractor capable of meeting the demands and challenges of present
times and hence needs to be reviewed accordingly.
The construction contractors’ selection under practice currently in Ethiopia screen out and makes
out of competition those capable contractors at the time of technical evaluation which is not fair
to lose the chance of competing for financial evaluation due to missing insignificant scores at the
time of technical evaluation.
The objectives of this research were to determine the most important criteria in construction
contractor selection and develop decision support model using fuzzy analytical hierarchy process
(FAHP)
This study presenteda contractor selection model using fuzzy Analytical Hierarchy Process
(FAHP). About 32 selection criteria were identified and grouped into 8 major criteria. The major
criteria were weighted and a decision support model was developed and the validity of the
developed model was tested in a real project (Case Study) supported by MATLAB software.
Keywords- Multi-criteria decision-making (MCDM), Fuzzy Analytical Hierarchy Process
(FAHP), MATLAB.
xi
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ACKNOWLEDGMENTS
First of all, I would like to express my special gratitude to my advisor, Dr. Ing. Wubishet Jekale,
for his supervision and excellent advice, and also for spending his precious time to improve the
quality of this research.
I would like to express my appreciation to all organizations and individuals who contributed
directly or indirectly to this thesis and provided the necessary materials and support forthe
realization of this thesis. Especial thanks are forwarded to EMH Consulting Architects and
Engineers for providing necessary data for my case study.
I would like to thank all experts who played the most important role during my study by
providing
necessary
information
and
giving
xii
much
time
for
the
interview .
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CHAPTER ONE
INTRODUCTION
1.1. Background of the study
Selection of a contractor for a construction project has been primarily based on bid price alone.
The selection of the lowest bidder is one of the major reasons for project delivery problem.
When contractor faced with a shortage of work, desperately quoted a low bid price simply to
remain in business with the expectation to be offset through claims. So, the selection of the
contractor for construction projects should be based on a set of multiple decision criteria both
price and non-price related (Kolekar P. B 2014). Choosing the right contractor increases the
chances of reaching the goals of the project which, first of all, are keeping the schedule of the
cost, time and quality(Edyta Plebankiewicz 2009)
There are lots of proposed models for contractor selection and evaluation. MCDM approaches
extensively proposed for contractor selection such as the analytic network process (ANP), fuzzy
set theory, analytic hierarchy process (AHP), data envelopment analysis (DEA), mathematical
programming, case-based reasoning (CBR), genetic algorithm (GA) and simple multi-attribute
rating technique (SMART)(Ho et al, 2010). Finding the best way to evaluate and select
contractors is difficult and employer companies use different ways facing this problem. Then the
most important issue in contractor selection is to develop a method to choose the right one and it
is essential to use a systematical and effective procedure or method to select the most appropriate
contractor(Ho et al, 2010). Some innovative approaches, based on artificial intelligence
techniques such as Fuzzy Logic match very well with decision-making situations where
contractor’s evaluation is also perceptive, decision-makers’ express heterogeneous judgments,
many decision rules are implied and unstructured, precise and accurate data are not available.
The nature of contractor selection decision-making problems is generally complicated and
unstructured and many quantitative and qualitative criteria must be considered to identify the
appropriate contractor.Most of the contractors' selection proposed models is according to simple
decision-making process.It doesn't seem most of this method pays attention to the unstructured
and complicated nature of current Contractor selection in MCDM context.Contractors evaluation
1
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and selection is especially an MCDM problem consists of multi-criteria factors and the factors
can be both qualitative and quantitative.
The analytic hierarchy process (AHP) first introduced by Thomas L. Saaty(Saaty 1980),is
described by Nydick and Hill (1992)as a methodology to rank alternative courses of action based
on the decision makers’ judgement concerning the importance of the criteria and the extent to
which they are met by each alternative (cited in Patrick Sik et al., 1999). AHP is an effective
decision-making
technique
based
on
multi-criteria
decision-making
methodology
(MCDM).(Prof. Rajiv. B Bhatt (Ph.D. Cont.) 2011)
The analytic hierarchy process (AHP) is widely used for tacklingmulti-attribute decision-making
problems in real situations but this method is often criticized for using a discrete scale of one to
nine and to its inability to adequately handle the inherent uncertainty and imprecision associated
with decision maker`s perception. However, in many practical cases, the human preference
model is uncertain and decision-makers might be reluctant or unable to assign exact
numerical values to the comparison judgments.
AHP, in spite of its popularity and simplicity in concept, is not sufficient to take into account the
uncertainty associated with the mapping of one’s perception to a number. It feels more confident
to give interval judgments than fixed value judgments. To improve the AHP method,fuzzy
numbers are used to decide the priority of one decision variable over another and this is fuzzy
extended of AHP (FEAHP) approach to represent decision-makers' comparison judgments to
decide the final priority of different decision criteria(Prof.Rahmatollah et al, 2014)
In this paper one of the multi-criteria decision model, Fuzzy AHP is dealt and developed for
Ethiopian contractors’ selection decision-making process.
2
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1.2. Statement of the Problem
The Ethiopian Federal Government procurement and property administration proclamation no
649/2009 article 33 (1) states to use open bidding as the preferred procedure of procurement
except as otherwise provided in the proclamation to use other options (article 33(2). The
proclamation describes the major qualification criteria for National Competitive Bidding. a)
average annual volume of work over the past specified yearsb)Experience as a prime contractor
in the construction of similar contract c)Proposal of the timely acquisition of equipment(own,
lease, hire, etc.) d)Personnel with specific qualification and experience e) Liquid assets and/or
credit facilities net of other contractual commitments and exclusive of any advance payments
which may be made under the Contract.
Even though the proclamation listed some qualification criteria, these criteria are not enough to
evaluate contractors.In Ethiopiancurrent practice, the employerreviews the contractors' resources
and capabilities concerning the stated specific project requirement indicated in the
bidding/prequalification process. There are two approaches of contractors’ evaluation in Ethiopia
to be followed after the legal qualification of contractors is checked. In the first approach, there
is no discrimination or ranking of contractors. A qualified contractor who is near the upper
boundary of the qualification criteria is not distinguished from another contractor who is near the
lower limit of the qualification criteria. The second approach, two-staged evaluations and scoring
method (FPPA, version 1 August 2011), which is comparatively advanced and aimed in
determining the lowest evaluated bid offering the best economic advantage but still it doesn't
solve the vagueness of the decision-making process.
The construction contractors’ selection under practice currently in Ethiopia screen out and makes
out of competition those capable contractors at the time of technical evaluation which is not fair
to lose the chance of competing for financial evaluation due to missing insignificant scores at the
time of technical evaluation.
This study focuses to make advancement in contractors’ selection process, by assisting the
evaluators/decision-makers to be supported by multi-criteria decision-making models to weigh
and rank participating contractors as the decision-making process is a group work and it is also
full of uncertainties.
3
.
1.3. Objective of the Study
1.3.1. General Objective
The general objective of this study is todevelop a multi-criteria decision-making model for
Ethiopian construction contractors’ selection by using Fuzzy Analytical Hierarchy Process
(FAHP).
1.3.2. Specific Objectives
The specific objectives of this study are;
To determine selection criteria in addition to those criteria which are being under practice
currently in Ethiopia.
To develop MCDM (multi-criteria decision-making model) by using Fuzzy Analytical
Hierarchy Process supported by MATLAB software.
1.4. Research Questions
This study tried to answer the following questions:
Are the qualification criteria for contractors’ selection currently under practice in
Ethiopia enough?
How can we develop a Multi-criteria decision model by using Fuzzy Analytical
Hierarchy Process for contractors’ selection?
How could the decision-makers be supported by software during Contractor Selection
Process?
1.5. Scope of the Study
This study is limited to the determining of contractors’ selection criteria and development of
fuzzy decision making model in Ethiopia.
1.6. Significanceof the study
The findings of this research can:
Assist decision-makers/evaluators by easily ranking participating contractors in such a
multi-criteria decision process which is full of uncertainties.
Identify additional qualification criteria for the sake of creating a better competition field
for contractors and also for creating a better chance of getting the right contractor for
employers.
4
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CHAPTER TWO
LITERATURE REVIEW
2.1. Introduction
Traditionally, one of the most frequently used procedures for selecting contractors has been open
tendering where the lowest bidder is awarded the contract. However, the lowest bidder is not
always the most economical choice in the long term as the client runs the risk of poor
performance by that contractor during the project life. Therefore, choosing the right contractor
involves much more than visualizing a series of price list, and choices will depend on a wide
range of factors which involve both quantitative and qualitative. Contractor selection and
evaluation is especially an MCDM problem consists of multi-criteria factors and the factors can
be both qualitative and quantitative(Ana Nieto-Morote et al 2012).
There are lots of proposed models for contractor selection and evaluation. MCDM approaches
extensively proposed for contractor selection such as the analytic network process (ANP), fuzzy
set theory, analytic hierarchy process (AHP), data envelopment analysis (DEA), mathematical
programming, case-based reasoning (CBR), genetic algorithm (GA) and simple multi-attribute
rating technique (SMART)(Ho et al, 2010). Finding the best way to evaluate and select
contractors is difficult and employer companies use different ways facing this problem. Then the
most important issue in contractor selection is to develop a method to choose the right one and it
is essential to use a systematical and effective procedure or method to select the most appropriate
contractor(Ho et al, 2010). Some innovative approaches, based on artificial intelligence
techniques such as Fuzzy Logic match very well with decision-making situations where
contractor’s evaluation is also perceptive, decision-makers’ express heterogeneous judgments,
many decision rules are implied and unstructured, precise and accurate data are not available.
In recent decade there were some researches about a contractor or supplier evaluation and
selection that use AHP, fuzzy set theory, and integration of these two methods to deal with
supplier selection problems. (Chang B. et al, 2011)developed a web-based AHP system to
evaluate the casting suppliers for 18 criteria. (Kumar J. 2011)applied AHP to evaluate and select
suppliers.(Kaur Prabjot et al, 2009)also used a fuzzy AHP for supplier selection. (Kumar J. et al,
2011)) proposed a rule-based model with the application of AHP to aid the decision-makers in
5
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vendor evaluation and selection taking the power transmission industry. (Jiang W et al.,
2011)proposed a methodology with the application of fuzzy set theory (FST), based on twenty
criteria to deal with supplier evaluation and selection problem.
Decision-makers can use linguistic variables both for the criteria and for the degree of satisfying
them by contractors. Li (2015) proposed a fuzzy framework to solve construction contractor
prequalification problems that takes full advantage of the experts' knowledge, experiences, and
make the decision-maker feels comfortable to give judgment on the prequalification issue.
The framework includes decision criteria analysis, weights assessment, and ranking orders
determination of contractors. Relative importance of criteria and evaluation of criteria assigned
by decision makers are expressed in linguistic variables and then a fuzzy arithmetical operation
is employed to aggregate the fuzzy numbers into the final decisions. Once final fuzzy assessment
of contractors has been obtained, four approaches, i.e., fuzzy number recognition (FNR) method,
fuzzy TOPSIS (FT) method, fuzzy number weight center (FNWC) method and simple
defuzzification method are applied to rank contractors(Ana Nieto-Morote et al 2012).
Fuzzy analytical hierarchy decision-making model (FAHP) is preferred from other analytical
hierarchy (AHP) models for this paper considering its recentness and also relatively more precise
for such kind of group decision work in case of high uncertainty.
6
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2.2. Theoretical Review
2.2.1 Analytical Hierarchy Process (AHP)
The Analytical Hierarchy Process (AHP) is a decision aiding tools based on multi-criteria
decision making for dealing with complex and multi-attribute decision(Prof. Rajiv. Et al, 2011).
It aims at quantifying relative priorities for a given set of alternative on a ratio scale, based on the
judgment of the decision-maker and stresses the importance of the intuitive judgment of a
decision-maker as well as the consistently of the comparison of the alternative in the decisionmaking process. The application of Analytic Hierarchy Process can be found in such diverse
fields as portfolio selection model solve by using AHP methodology include project procurement
system (Mohammed I.A, Khalil 2000, cited in (Prof. Rajiv et al, 2011)),
Since some of the evaluation criteria involve a high degree of subjective judgment and individual
preferences, it is very difficult for the decision-maker to express their preferences in exact
numerical values and to provide exact pairwise comparison judgments so AHP, in spite of its
popularity and simplicity in concept, is not sufficient to take into account the uncertainty
associated with the mapping of one's perception to a number. The linguistic assessment of human
feelings and judgments are vague and it is not reasonable to represent it in terms of precise
numbers. It feels more confident to give interval judgments than fixed value.
The analytic hierarchy process (AHP) is widely used for tackling multi-attribute decision-making
problems in real situations but this method is often criticized for using a discrete scale of one to
nine and to its inability to adequately handle the inherent uncertainty and imprecision associated
with decision maker`s perception. However, in many practical cases, the human preference
model is uncertain and decision-makers might be reluctant or unable to assign exactnumerical
values to the comparison judgments.
To improve the AHP method, triangular fuzzy numbers are used to decide the priority of one
decision variable over another and this is fuzzy extended of AHP (FEAHP) approach to represent
decision-makers' comparison judgments to decide the final priority of different decision
criteria(Rahmatollah et al, 2014)
7
.
2.2.2 Fuzzy Set Theory (FST)
The Fuzzy Set Theory introduced by Zadeh is suitable for dealing with imprecision and
uncertainty associated with data in decision problems. Most real-world prequalification problems
involve uncertainty and imprecision in the estimates of performance ratings and criteria weights
due to the own nature of construction projects and subjectivity of decision-makers' judgments. In
this decision environment, it is too complex to reasonably describe the problem by conventional
quantitative expressions; therefore, it is more adequate to express decision-makers' judgments in
qualitative form than quantitative one. Fuzzy Set Theory is an adequate tool to deal with vague,
imprecise and uncertain problems by using the concept of linguistic variable, which is a variable
whose values are words or sentences in a natural language instead of numerical values. In a
universal set of discourse X, a fuzzy subset A of X is defined by a membership function μA (x),
which maps each element x in X to a real number in the interval [0, 1]. The function value of μA
(x) signifies the grade of membership of x in A. When μA (x) is large, its grade of membership
of x in A is strong.
2.2.3 Fuzzy Analytical Hierarchy Process (FAHP)
Fuzzy set theory has the advantage of mathematically represent uncertainty and vagueness and
provide formalized tools for dealing with the imprecision intrinsic to many problems. Like other
artificial intelligence method, it has some advantages within uncertain, imprecise and vague
contexts than AHP and other MCDM method, in resembles human judgments.In this approach,
triangular fuzzy numbers are used in the preferences of one criterion over another (Chan et al.,
2014).
Analytical Hierarchy Process (AHP) is one of the best ways for deciding among the complex
criteria structure at different levels. Fuzzy AHP is a synthetic extension of the classical AHP
method when the fuzziness of the decision-maker is considered(ÖZDAĞOĞLU 2007).This
technique is a combination of two different techniques, the analytical hierarchy process and
fuzzy set theory (Ahmad Zaki Mohamed Noor et al., 2018).
When using Fuzzy logic, the importance of each criterion gets influenced by the level of
decomposition in the hierarchical model. Fuzzy logic cannot measure the level of consistency in
the judgments provided by a decision-maker. On the other hand, Analytic Hierarchy Process
(AHP) cannot capture subjectivity (or fuzziness) of human judgments as the verbal assessments
are converted into crisp values. Fuzzy Analytic Hierarchy Process (FAHP) is a merger of the two
8
.
methods, Fuzzy logic and the Analytic Hierarchy Process (AHP), which inherits the advantages
of both and, therefore, addresses the above-mentioned problems. The FAHP method is useful in
identifying a suitable supplier and to evaluate its performance(Ishizaka 2014).
2.3. Empirical Review
This Section will provide empirical related review on the extension of this classical Analytical
Hierarchy Method to a Fuzzy Analytical Hierarchy Process method. In the first section, the
traditional analytical hierarchy process, which is the basis for the AHP is dealt. In the next
section, fuzzy set, Fuzzy logic, and fuzzy numbers are reviewed since it is necessary to have a
background of fuzzy system to deal with problems of decision which are full of uncertainties and
vagueness. Lastly, the Fuzzy Analytical Hierarchy process which is the combination of the two
techniques is reviewed.
2.3.1 Analytical Hierarchy Process (AHP)
AHP is a method for ranking decision alternatives and selecting the best one when the decisionmaker has multiple criteria (Taylor, 2004, cited in (ÖZDAĞOĞLU 2007) ). It answers the
question, "Which one?". With AHP, the decision-maker selects the alternative that best meets his
or her decision criteria developing a numerical score to rank each decision alternative based on
how well each alternative meets them. In AHP, preferences between alternatives are determined
by making pairwise comparisons. In a pairwise comparison, the decision-maker examines two
alternatives by considering one criterion and indicates a preference. These comparisons are made
using a preference scale, which assigns numerical values to different levels of preference.
The standard preference scale used forAHP is 1-9 scale which lies between “equal importance”
to “extreme importance” where sometimes different evaluation scales can be used such as 1 to 5.
In thepairwise comparison matrix, the value 9 indicates that one factor is extremely
moreimportant than the other, and the value 1/9 indicates that one factor is extremely
lessimportant than the other, and the value 1 indicates equal importance. Therefore, if the
importance of one factor with respect to a second is given, then the importance of the second
factor with respect to the first is the reciprocal. Ratio scale and the use of verbal comparisons are
used for weighting ofquantifiable and non-quantifiable elements (Pohekar ve Ramachandran,
2004 cited in (ÖZDAĞOĞLU 2007)).
9
.
The application of the AHP to the complex problem usually involves four major steps (Cheng, et
al, 1999):
1. Break down the complex problem into several small constituent elements and then structure
the elements in a hierarchical form.
2. Make a series of pairwise comparisons among the elements according to a ratio scale.
3. Use the eigenvalue method to estimate the relative weights of the elements.
4. Aggregate these relative weights and synthesize them for the final measurement of given
decision alternatives.
The AHP is a powerful and flexible multi-criteria decision-making tool for dealing with complex
problems where both qualitative and quantitative aspects need to be considered. The AHP helps
analysts to organize the critical aspects of a problem into a hierarchy rather like a family tree
(Bevilacqua et al, 2004, cited in (ÖZDAĞOĞLU 2007)).
The essence of the process is the decomposition of a complex problem into a hierarchy with goal
(criterion) at the top of the hierarchy, criteria and sub-criteria at levels and sub-levels of the
hierarchy, and decision alternatives at the bottom of the hierarchy. Elements at given hierarchy
levels are compared in pairs to assess their relative
preference with respect to each of the elements at the next higher level. Themethod computes
and aggregates their eigenvectors until the composite final vector of weight coefficients for
alternatives is obtained. The entries of final weight coefficients vector reflect the relative
importance (value) of each alternative with respect to the goal stated at the top of the hierarchy
(Pohekar ve Ramachandran, 2004). A decision-maker may use this vector according to his
particular needs and interests. To elicit pairwise comparisons performed at a given level, a matrix
A is created in turn by putting the result of pairwise comparison of element i with element j into
the position aji as below(ÖZDAĞOĞLU 2007).
10
.
Where n = criteria number to be evaluated
Ci = i. criteria
Aij = importance of i. criteria according to jth criteria
The weights and performances (local priorities) are derived from this matrix A by using the
Eigenvector method (Saaty, T.L., 1980 cited in(Ishizaka 2014):
If CR, the ratio of CI and RI (an average CI of 500 randomly filled matrices of the same
dimension), is less than 10%, then the evaluations of the decision-maker can be considered as
having an acceptable consistency.
CR = CI/RI,
where CR is the consistency ratio
RI is the random index
11
.
Table2.1: Calculated RandomIndices, RI (Saaty, 1977)
n
3
4
5
6
7
8
9
10
RI
0.58
0.9
1.12
1.24
1.32
1.41
1.45
1.49
2.3.2 Fuzzy Numbers, Fuzzy Set, and Fuzzy Logic
Among the various types of fuzzy sets of special significance are fuzzy numbers defined as A
={x, μA (x)} where x takes its number on the real line ú and membership function μA: ú6 [0, 1],
which have the following characteristics : (i) Constant on (-∞, a] and [d, ∞): μA (x)=0 œ x 0 (-∞,
a] U [d, ∞); (ii) Strictly increasing on [a, b] and strictly decreasing on [c, d]; and (iii) Constant on
[b, c]: μA (x)=1 œ x 0 [ b, c], where a, b, c, d are real numbers and eventually a = - ∞, or b = c,
or a = b, or c = d or d = ∞. For convenience, LμA is named as left membership function of a
fuzzy number A, defining LμA(x) = μA (x), œ x 0 [a,b]; RμA is named as right membership
function of a fuzzy number A, defining RμA(x) = μA (x), œ x Є [c, d]. A trapezoidal fuzzy
number A is a fuzzy number denoted as A=(a, b, c, d) which membership function is defined as:
where a, b, c, d are real numbers and a < b < c < d. If b=c, it is defined as a triangular fuzzy
number.
2.3.2.1 Fuzzy Logic System
Fuzzy logic consists of mathematical ideologies for knowledge illustration founded on degrees of
membership and is logic with many values; its reasoning is dealt as an approximate rather than
cast stone and exact. Fuzzy logic has four main components: Fuzzifier, determining rules, engine
for inferencing and defuzzifier. The Fuzzy logic system is shown below.
12
.
Figure 2.1: Fuzzy logic system,(Chai et al., 2015)
The process of Fuzzy logic consists of finding a crispset of input data that are collected and
transformed intointo a fuzzy set by the fuzzy linguistic variables, linguistic fuzzy terms and
membership functions, this is the Fuzzification step. Based on a set of rules an inference is made
and the resultant fuzzy yield is changed to a crisp output by the membership functions, during
the defuzzification stage.
2.3.2.2 Fuzzification
Variables of linguistic nature can be the input or output parameters of the fuzzy system where
values are natural language words or expressions as opposed to numerical values. Fuzzification
practices the theory of fuzzy set operations. This step is used to map the crisp values attained
from the inputs into ranks of the membership functions of linguistic relations of fuzzy sets
(Zadeh, 1965). For example, the Fuzzification of a four feet woman in height might fit into two
sets of fuzzy “Average” and “tall”. The membership functions µAand µBare the symbols used to
portray the two fuzzy sets “Average” and “tall” respectively. The woman’s height, 5.5 feet, goes
with rank of 0.70 on the fuzzy set “average” and a rank of 0.30 to the fuzzy set “tall”. In the
Fuzzification step, we transform the input rate (5.5 feet) into the score of membership (0.70 for
“average” and 0.30 for “tall”) (Gathaiya, 2007)
2.3.2.3 Fuzzy Rules
Rules compare ideas and contrast one event to another one based on if-then statements in
computing. In fuzzy instrument, we use the fuzzy sets and the rules for verdict and as the way of
selecting decision and are traded with fuzzy rules which maneuver using sets of if-then
statements. For Example, if C then X, if D then Y, where C and D are all sets of X and Y i.e. IF
variable IS set THEN action. The count of rules generated is given by the count of the linguistic
13
.
variable used. Boolean logic operators AND, OR, and NOT are used in fuzzy logic, typically
demarcated as the minima, maxima, and complement.
2.3.2.4 Rule Base Reduction Methods
Rules count lessening is an essential issue in fuzzy system creation, particularly for actual time
Fuzzy logic control (FLC) Plan. The count of rules in a complex fuzzy control system can grow
exponentially depending on the count of the input variable. For that reason, reducing the rules is
a very vital concern in such designs. Several ways of reducing the number of rules have been
discovered.
I.
Fuzzy clustering is thought as one of the central techniques using numerical example for
Creation of fuzzy rules. The algorithm plots data plugs into asset of number clusters (). In
the fuzzy system, the number of rules depends on the number of Cluster centers.
Controlling the number of cluster centers aids in controlling the count of rules. However,
a challenge with control applications is often that there is no enough datato mine a whole
rule base for the controller (Gathaiya, Decision Support system for supplier selection
2007)
II.
We can use the sliding mode control and fuzzy logic control to decrease the ranting
bySliding mode control and enrich vigor in the fuzzy logic control. This
amalgamationyields rules size reduction. However, this tactic is disadvantageous since
the constraints for the switch utility need to be nominated by an expert or planned over
conventional control theory (Manoj et al, 2015).
III.
The minimization way of membership functions is not combined but are changed by a
New membership function with minimum and maximum values of the first and the last
Membership function, the departing point of the two is the peak of the created
Membership function this technique is appropriate if the data available is not enough to
Train the model (Matthews, 2013).
IV.
Ledeneva, (2006) proposed a fuzzy control structure in a hierarchy where the first-level
Rules are those connected to the most central variables and are collected to form the first
level of hierarchy. The next second most variable, with the outputs of the first-level, are
then selected as inputs to the second level hierarchy.
The set of rules are built
hierarchically; the input variables of the fuzzy controller are distributed according to
14
.
various levels of reasoning and are not treated in parallel anymore. The control difficult is
thus resolved serially. The first level of hierarchy has the rules associated with key
variables and assembled to form the hierarchy. The following key variables, alongside the
output of first level, are then treated as inputs to the second level of hierarchy and so on
(Metaxiotis et al,2012).
2.3.2.5 Membership Function
Membership functions are applied during the fuzzificationand defuzzification stages of a fuzzy
Logic system, to convert the input values that are not fuzzy to be in fuzzy linguistic term and
vice versa. Membershipfunction is used to quantify a linguistic term. There are various shapes of
membership functions formed using straight lines as discussed below.
2.3.2.5.1 Triangular Membership Function
Figure 2 depicts the membership function of triangle nature coordinates a, b, and c represents the
three vertices x of the fuzzy set A i.e. µA (x). the lower boundary of set A with degree
membership zero is expressed by coordinate a coordinate c is the upper boundary with degree
membership of zero. Lastly, coordinate b with the degree of membership of one is the third apex
of the triangle. The triangle membership function is well thought to be ample for netting the
vagueness of these linguistic valuations (Mehrdad and abbas, 2011).
Fig.2.2:Triangular Membership function (Chai et al,2015)
15
.
Equation below symbolized the scientific used to compute the degree of membership for
component x in a set of fuzzy A:
f (x, a, b, c)
=
0,
x≤a
(1)
(x-a)/(b-a), a ≤ x ≤ b
(c-x)/(c-b), b ≤ x ≤ c
0,c≤x
2.3.2.5.2 Gaussian Membership Function
Gaussian membership function is represented in formula 2 below
µ(x)=[x-b/δ)²]
x is the input variable, b the membership function center while σ is the constant for the width of
the membership function. Gaussian fuzzy membership utilities are among the most used in fuzzy
logic systems (foundations of fuzzy logic, 2014). figure below depicts a characteristics Gaussian
membership function.
Fig.2.3: Gaussian Membership Function (Chai et al, 2015)
2.3.2.5.3 Trapezoidal Membership Function
Equation (3) below shows a membership functions for trapezoidal with four parameters {a, b, c,
d} as shown in:
trapezoidal (x; a, b, c, d) =max (min(x-ab/-a,1,d-xd/-c),0)
The four corners of the typical trapezoidal membership function are determined by coordinates
{a, b, c, d} in x axis such that a<b=c<d.
16
.
Because of their modest formulas and easy computational, triangular membership functions and
trapezoidal membership functions have been applied extensively in real-time scenarios.
However, they are not even at the curve points identified by the perimeter (Mehrdad & Abbas,
2011).
Fig.2.4: Fuzzy Inference System (Gathaiya, Decision Support System for Supplier Selection
2007)
2.3.2.6 Defuzzification
On inference, a fuzzy value will be the typical result. This result needs to be defuzzzified to
achieve a crisp output. The work of the defuzzifier component of a Fuzzy Logic System is to do
that. Defuzzification is accomplished depending on the membership function of the output
variable (Fuzzy Logic Fundamentals, 2011). Several defuzzification methods are existing for this
setup, some are discussed below.
2.3.2.6.1 Centre of Gravity (CoG) Method/Weighted Average Method
This is the methodology for calculating a crisp value (µ) from the central-point of the output
fuzzy set by a rated average of the membership grades. With an existing fuzzy set µ (xi) having a
17
.
discrete universe, and the membership value being in the membership function. We can represent
the rated average of the elements in the support set as below (Foundations of Fuzzy Logic,
2014).
2.3.2.6.2 Mean of Maximum (MoM) Method
The Mean of Maximum method is used to discover the medium z where the membership of the
fuzzy set is at a maximum. Could be the maximum points occur severally and as such the
common training is to take the mean of all maximum values. The calculation complexity is
simplified in this method by ignoring the shape of the fuzzy set completely; this yields somewhat
good results (Fuzzy Logic Fundamentals,2011). For a particular setting there occurs a fuzzy set
A in a Z universe. The extension opinion says that if there exists a function f, then the fuzzy set
B is specified by the equation:
B=f (A) =∑ µA (xi)/f (xi)
2.3.2.7 Conceptual Model
Mostly used fuzzy structures are; fuzzy pure systems, Takagi-Sugeno-Kang (TSK) and combined
fuzzy system having the fuzzifying and fuzzifying parts(Li-Xin 2011). We used the combined
fuzzy system in the model we developed because our inputs and outputs are real numbers. This
system comprises a fuzzier part in the inputs for changing intrinsic numbers to fuzzy sets and a
defuzzifier part in the output that does the vice versa. Figure 4 below shows the architecture of
the system developed by composing three main blocks. Fuzzy logic systems and expert systems
are used in handling complex and difficult tasks; however, fuzzy logic's ability to handle
ambiguity gives it an advantage over the expert systems. To effectively handle ambiguities,
linguistic rules are used to emulate human operation and assist make decisions. The ability to
make decisions in fuzzy logic is time-saving and minimizes the need for human engagement.
18
.
Fig.2.5:Fuzzy Decision Support System for supplier selection, (Li-Xin 2011)
The description of the various elements in the above architecture to be adopted in our study is;
A-Fuzzy inference engine: This is the package that scrutinizes the rules and data accumulated in
the database and generates the logical output. We can have a different selection from the fuzzy
interference depending on the aggregation, implication, and operators used for s-norm and tnorms engine(Li-Xin 2011).
B-User Interface: This is the module that assists the users to interact with the system during data
entry and also for viewing the results once generated by the system.
C-Fuzzy rule base: These are qualified statements represented as “IF x is Xi and y is Yi and
THEN o is Oi” where x and y are linguistic input variables used to determine the inputs
interactions and developed from subject matter experts’ inputs. Xi and Yi are likely linguistic
values for x and y respectively.
19
.
2.3.3 Fuzzy Analytic Hierarchy Process (FAHP)
In most of the real-world problems, some of the decision data can be precisely assessed while
others cannot.Humans are unsuccessful in making quantitative predictions, whereas they
arecomparatively efficient in qualitative forecasting(Kulak ve Kahraman, 2005). Essentially, the
uncertainty in the preference judgments gives rise to uncertainty in the ranking of alternatives as
well as difficulty in determining the consistency of preferences.
This approach was introduced by Laarhoven and Pedrycz (1983) cited in(Ishizaka 2014). The
Fuzzy AHP method is identical to the traditional AHP (section 2.3.1) at the exception of the
conversion of the verbal appreciation into the numeric scale. The procedure is based on the
following steps(Ishizaka 2014):
a) Develop a hierarchical structure.This step is identical to the two previous methods
b) Define the Fuzzy judgments
To capture vagueness, imprecision, and uncertainty of the linguistic scale, are converted
into fuzzy numbers.
c) Fuzzy Weights
The criteria have received a linguistic evaluation. This linguistic evaluation is
transformed into a pairwise comparison and inserted into the comparison matrix.
d) Calculation of the fuzzy priorities
Fuzzy priorities are calculated exactly in the same way criteria are calculated. The
linguistic performances are pairwise compared and entered in a comparison matrix for
each criterion. Then, they are separated in four matrices corresponding to low, modallow, modal-upper and upper points of the membership function. The local priorities are
then calculated for each matrix with the eigenvalue method.
e) Overall priorities and defuzzification
f) The local priorities are multiplied by the criteria weights to produce overall fuzzy
priorities. The transformation of the fuzzy priorities into a crisp priority is calculated.
Sensitivity analysis can be performed to test if the results are robust. This exercise is
more intensive than in the normal AHP because more sensitivity analyses corresponding
to the hierarchies may be needed.
(Li 2015)proposed a fuzzy framework to solve construction contractor prequalification problems
that takes full advantage of the experts’ knowledge, experiences, and makes the decision-maker
20
.
feels comfortable to give judgment on prequalification issue. The framework includes decision
criteria analysis, weights assessment, and ranking orders determination of contractors. Relative
importance of criteria and evaluation of criteria assigned by decision-makers are expressed in
linguistic variables and then a fuzzy arithmetical operation is employed to aggregate the fuzzy
numbers into the final decisions.
To calculate the local weight of each criterion, experts are required to provide their comparative
judgment on the relative importance of one criterion on other, belonging both to the same level
and group in the hierarchical structure.
The pair-wise comparison usually involves much inexact, uncertain or incomplete information
that is very difficult to measure the judgments and preferences of decision-maker. Based on
Fuzzy Set Theory, assessments are described subjectively inappropriate standard linguistic
variable set is built to help experts to assess the relative importance of criteria pairwise.
Since linguistic terms are not mathematically operable, to cope with this difficulty, each
linguistic term is associated with a fuzzy number, which represents the meaning of each generic
verbal term. This representation does not only depend on the concept but also on the context in
which it is used. Even for similar contexts, fuzzy numbers representing the same concept may
vary considerably, therefore, it must be carefully defined by the characteristics of the project.
Generally, the preference information about criteria expressed as a fuzzy preference relation
presents inconsistency problems. The lack of consistency in the pair-wise criteria comparison
matrices can lead to an inconsistent set of local weights of criteria. Therefore, a method to get a
minimum consistency must be applied. The most of the research studies which apply the
concepts of Analytic Hierarchy Process (AHP) determine if the comparison matrix is consistent
or not by calculating the consistency ratio. If a matrix is not consistent experts must reevaluate
the relative importance of each pair of criteria, therefore, the expert's judgments are modified.
Since the preference information between criteria Ci and Cj, υ’ij, can also be reflected in their
ranking values wi and wj, there exists an explicit function relation between υ’ij and wi and wj
defined as: where ψ (wi) can be any non-decreasing function. To keep the simplicity of the
method, if then weak transitivity, i.e. υik≥0.5 for υij≥0.5 and υjk≥0.5, is the property that is
usually accepted to deal with problems of fuzzy preference relations consistency. Due to the
fuzziness of the opinions and the weak transitivity restrictionconsidered, an accurate solution for
21
.
this problem could not be found. The wi and wj values are calculated by difference minimization
method of the value υij, obtained directly from the experts, and the value υ’ij, defined as:
(1)
(2) & (3)
i and j are criteria of group g and level l and represent fuzzy addition and subtraction defined in
equations (A4) and (A5), respectively. Once the local weight of all criteria, wi, are calculated,
the global weight, Wi, of each criterion at the bottom level of the hierarchy is calculated as
( 4)
where i is each one of the criteria at the lowest level of the hierarchy, t is the upper groups at
different level in the criteria hierarchy, w(j) group is the group weight of the jth upper group
which contain the criterion Ci in the hierarchy and
represents fuzzy multiplication defined in
Eq.(A6). Another important and crucial task is to evaluate the rating of the contractor for each
evaluation criterion, i.e., to define the decision-making matrix, especially when evaluation
criteria may have quantitative and qualitative dimensions. When the evaluation criterion is
qualitative, most of the times, the decision-maker is not capable of defining rigorously how good
the contractor is, about this criterion. In these situations, the decision-maker prefers assessments
that are not exact but approximate and which are adjusted to the reality.
Therefore, in these cases, in general, the decision-makers should evaluate their judgments
utilizing linguistic terms instead of real numbers. Therefore, two types of assessments are
proposed: (i) when the evaluation criterion is quantitative, assessment are real numbers, and (ii)
22
.
when the evaluation criterion is qualitative, assessment are linguistic terms. In the same way, that
linguistic assessments on the relative importance of pair of criteria are transformed into fuzzy
numbers, the linguistic ratings of the contractors concerning qualitative evaluation criteria are
transformed into corresponding fuzzy numbers. Although "a priori" it seems no-sense the
fuzzification of an exact value, to operate mathematically it is necessary to convert assessment in
terms of real numbers into fuzzy number as well.
To define adequately the decision-making matrix, two aspects have to be considered: (i) the
evaluation criteria are their characteristics and each one of criteria data has their dimension and
distribution and (ii) the evaluation criterion have different importance on the final decision.
When each one of the criteria data has its dimension and distribution, it is difficult to directly
compare or operate. As a result, the original data of criteria evaluation should be dimensionless
and unit-free by normalization method. The normalized fuzzy decision matrix can be represented
as Ğ = [Ğij] and its elements defined as:
On the other hand, when criteria have not the same importance the rating of the contractor with
respect each criterion must be recalculated using the multiplication of the original rating by the
criteria weight. By taking into account these two considerations, the weighted-normalized
decision-making matrix is defined as:
23
.
where Wj is the weight of criteria Cj , Ğij are the elements of the normalized decision-making
matrix and
represents the fuzzy multiplication defined in Eq. (A6). Finally, Technique for
Order Performance by Similarity to Ideal Solution (TOPSIS) method may provide the basis for
classifying contractors. This method is based on the concept that the best alternative should have
a shorter distance from the Positive Ideal Solution (PIS) and the farthest from the Negative Ideal
Solution (NIS). For each contactor, a closeness coefficient (CC) is calculated as:
where di* is the distance of each contractor from PIS and di─ is the distance of each contractor
from NIS defined as:
where dυ is the distance measurement between two fuzzy numbers defined in Eq. (A8) and
where J1 and J2 are the sets of benefit criteria and cost criteria, respectively. According to the
descending order of CC, the ranking order of all contractors can be determined, although a more
realistic approach may be to use a linguistic variable to describe the current assessment status of
each contractor per its closeness coefficient. The interval [0,1] is divided into certain subintervals which are corresponded with each one of the proposed assessment status that maybe
"Do not recommended", "Recommended with risk” and “Approved” (Ana Nieto-Morote et al
2012)
Once final fuzzy assessment of contractors has been obtained, four approaches, i.e., fuzzy
number recognition (FNR) method, fuzzy TOPSIS (FT) method, fuzzy number weight center
(FNWC) method and simple defuzzification method are applied to rank contractors.
2.3.3.1 Fuzzy AHP (Synthetic Extent Method)
A fuzzy set is a class of objects with a continuum of grades of membership. Such a set is
characterized by a membership (characteristic) function, which assigns to each object a grade of
24
.
membership ranging between zero and one. Two triangular fuzzy number M1 (m1-, m1, m1+) and
M2 (m2-, m2, m2+) shown in Fig. below are compared. When m1-≥m2-, m1≥m2, m+≥m2+, we define
the degree of possibility V (M1 ≥M2) = 1. Otherwise, we can calculate the ordinate of the highest
intersection point(Ahmad Zaki Mohamed Noor et al, 2018)
Table 2.1:Triangular Fuzzy Numbers
25
.
2.3.3.2 Selection Criteria
2.3.3.2.1 Selection Criteria Overview
A crucial task in contractor prequalification process is to establish a set of decision criteria
through which the capabilities of contractors are measured and judged. Criteria for
prequalification may vary between projects since the characteristics of them are distinct although
there are some common characteristics of contractor prequalification. All the projects have a
reasonable cost, require a reasonable quality, within a reasonable time and with reasonable
security(Ana Nieto-Morote et al 2012).
Most of the major criteria used for contractor selection are similar but the weight given to those
criteria to evaluate contractors vary from project to project and from place to place due to
variability of factors due to many reasons.
Ana Nieto-Morote et al, (2012) described the major contractor prequalification criteria and
subcriteria as follows.
Technical capacity: The contractor must demonstrate that it has the technical capacity to
perform the activities of the specific project for which it is seeking prequalification.
Experience: The contractor must demonstrate its participation in other previous projects,
especially if they are similar to the project that will be executed.
Management capability: The contractor must demonstrate that it is capable of planning,
organizing and controlling a project.
Financial stability: The client must reach an informed opinion regarding the overall financial
position and capability of the contractor.
26
.
Past performance: Considering the past performance of each contractor, the project manager
will have a higher or lower degree of confidence in the possible contractors regarding the quality,
time and cost control requirements
Occupational health and safety: To encourage contractors to establish and maintain effective
systems to manage the risks to the health and safety of their employees, arising from the nature
of the work.
Table2.3:Main and sub-criteria
Rahmatollah et al,(2014) included "facilities and support service" which includes education and
training of the clients' technicians as one of the selection criteria. Company reputation is also
considered to be one of the selection criteria by Kolekar P. B et al (2014).
PATRICK SIK-W. et al, (1999) had identified those major criteria that attract clients' interest
and described as follows.
27
.
Fig. 2.6:Most important criteria considered by clients(PATRICK SIK et al, 1999)
2.3.3.2.2 Selection Criteria and Evaluation Methodology in Ethiopia
The overall evaluation methodology varies from client to client and vary depending on the
project characteristics. The major steps that are under practice currently are common and
described as follows (FPPA, 2011).
I.
Preliminary Screening:
Major Criteria
1
Legal Qualification
Sub-criteria
1
Nationality
2
Conflict of Interest
3
Registration in the FPPA's Suppliers List
4
Debarred by decision of the FPPA
5
Valid trade license or business organization
registration certificate
6
VAT registration certificate
7
Valid tax clearance certificate
8
Government Owned Entity
28
.
2
3
4
II.
Professional Qualification and
Capability
Technical Qualification,
Competence, and Experience
Financial Standing
1
Number of staff
2
Personnel for the key positions
1
General experience
2
Specific Experience
3
History of non-performing contracts
4
Pending litigation
5
Equipment for the implementation of the
contract
1
Historical Financial Performance
2
Average Annual Turnover
3
Financial Resources
Bid Evaluation
According to the methodology defined in the Public Procurement Proclamation and Directive,
the Public Body shall select the successful Bid by applying the following method:
A.
The Bid that is found to be substantially responsive to the professional, technical, and
financial qualification requirements,technically compliant to the technical specifications,
and with the lowest price.
B.
The Bid that is found to be substantially responsive to the professional, technical, and
financial qualification requirements,technically compliant in relation to the technical
specifications, and with the lowest evaluated bid The lowest evaluated Bid shall be the bid
offering better economic advantage ascertained on the basis of factors affecting the
economic value of the bid.
The section of the type of methodology, to be guided by procedure A or B is the right of the
client. If procedure A is selected, there will not be any further evaluation and the lowest bidder
will be awarded after checking arithmetical errors. If the selected procedure is B, there will be
further technical and financial evaluation that is why it is called two-staged evaluation
methodology.
29
.
Table 2.4: Technical Evaluation (FPPA, 2011)
Priority
Proportional
points in %
Name of criteria
Adequacy of Technical Proposal in responding to the Schedule
of Requirements:
(a) Technical capacity to mobilize equipment and personnel
1
(b) Technical approach and methodology
(c) Work plan and scheduling
(d) Organization and staffing
Total points for criterion (1):
2
Specific experience of the Bidder relevant to the Schedule of
Requirements
Qualifications and competence of the key professional staff
engaged in the works:
(a) Team Leader
(b)
Total points for criterion (3):
3
The number of points to be assigned to each of the above positions
or disciplines shall be determined considering the following three
sub-criteria and relevant percentage weights:
(a) General qualifications
20-30%
(b) Adequacy for the assignment
50-60%
(c) Experience in region and language
10-20%
Total weight:
100%
4
Total points for criterion (4):
Σ
Total Points for the Four Criteria (1+2+3+4)
30
100
.
Financial Evaluation
In the financial evaluation, the highest point shall be given to the lowest priced Bid, and
conversely, the lowest point shall be given to the highest-priced Bid; among technically qualified
Bids. The points given to other Bidders shall be determined depending on their price offers.
From the total merit points to be given for proposals submitted by Bidders in a bid for
procurement of Works, the share of Technical Proposal shall be percent and the remaining
percent shall be the share of the Bid Price. The formula for determining the financial score is the
following:
LFP
FS =
100
CFP
Where:
FS
= The Bid Price Score;
LFP = The lowest Bid Price;
CFP = The Bid Price under consideration
The Public Body shall then add the technical score to the Bid Price score to determine the
aggregated (total) Bid score and final ranking of Bids by applying the following method:
For each Technical Proposal, its technical evaluation score shall be normalized according to the
highest evaluated technical score that will get 100 points according to which other scores of
technical criteria shall be proportionally ranked. The Public Body shall apply the following
formula for the normalization of values of the technical evaluation results:
CTP
TSN =
100
HTP
Where:
TSN = Normalized Bid Technical Proposal Score;
CTP = The technical evaluation score for the Bid under consideration
HTP = The highest evaluated Technical Proposal score
31
.
This paper considers all significant criteria, which have been ignored and not incorporated as
evaluation criteria but very important for employers in Ethiopia in the construction contractor
selection process.
2.4.
Summary of the Literature Review
As part of the procurement process, selection of contractors for construction start from
procurement planning and then follows preparation of tender document, advertising the tender,
submission of bids by the tenderers, evaluation of the submitting tender and award of the
contract.In the selection of contractors, the client shall prepare the tender document considering
the specific nature of projects and avoid ambiguities, mistakes, and inconsistencies in the
document.
Contractor selection is a critical and crucial task for any client that may help to control some of
these risks and manage the complexities. Various procedures such as open tendering, selective
tendering, restricted tendering, registration/ pre-qualification, post-qualification are followed for
selecting contractors. In addition to the above, to select a contractor for a project it is required to
develop necessary and sufficient criteria to investigate and assess the capabilities of the
contractors to carry out a job if it is awarded to them.
Generally, the Analytical Hierarchy Process (AHP)Decision Models are becoming helpful tools
nowadays for decision-makers/evaluators which can assist group decision making. Fuzzy
Analytical Hierarchy Process (FAHP) is the most recent and important decision model as it
alleviatesthe uncertainties in the group decision-making process and it enables to rank
participating contractors.
32
.
CHAPTER THREE
RESEARCH METHODOLOGY
3.1 Introduction
A decision model for contractor selection based on Fuzzy Analytical Hierarchy Process is
offered in this paper. The model involves a multi-criteria evaluation of contractors and the
establishment of a classification of all the feasible contractors. At the first stage, a set of criteria
for evaluating the potential contactors is established by taking into account the nature of the
construction project. The establishment of a proper evaluation criteria system is basic for an
adequate classification of contractors, therefore, decision criteria must be reflected the project
objectives, the needs of the clients and all the factors that influence the adequate project
performance. To be efficiently assessed, decision criteria is decomposed into sub-criteria and a
hierarchical structure of criteria generated.
In many decision problems, decision criteria have not the same importance so a weight which
represents its importance is assigned to each criterion. With a hierarchical structure of criteria,
each criterion is associated with a local weight and a global weight. The local weight of a
criterion is referred to the weight relative to other criteria at the same group and level, which is to
be assessed using the pair-wise comparison process. The global weight of a criterion is referred
to the weight relative to all other criteria for the overall objective of the decision problem.
In this environment, based on Fuzzy Set Theory, assessments are described subjectively in
linguistic terms such as "more important", "equally important", etc. An appropriate standard
linguistic variable set is built to help expert to assess the relative importance of criteria pairwise.
Since linguistic terms are not mathematically operable, to cope with this difficulty, each
linguistic term is associated with a fuzzy number, which represents the meaning of each generic
verbal term. This representation does not only depend on the concept but also on the context in
which it is used. Generally, the preference information about criteria expressed as a fuzzy
preference relation presents inconsistency problems. The lack of consistency in the pair-wise
criteria comparison matrices can lead to an inconsistent set of local weights of criteria, therefore,
a method to get a minimum consistency must be applied.
Most of the research studies which apply the concepts of Analytic Hierarchy Process (AHP)
determine if the comparison matrix is consistent or not by calculating the consistency ratio. If a
33
.
matrix is not consistent experts must reevaluate the relative importance of each pair of criteria,
therefore, the expert's judgments are modified.
3.2 Research Design
There are two fundamental research approaches, qualitative and quantitative approaches.
Advancement in research methodology recommends that, the two approaches shall be
assimilated in broad research designs to improve in research thoroughness and report several of
the epistemological and methodological criticism (kelle, 2006 cited in (Gathaiya, 2007)). This
study applied both qualitative and quantitative approaches to satisfactorily answer the research
questions.
3.3 Sampling (Data Collection)
The data was collected using primary data collection system which were:
1) Direct interview with procurement experts with an experience of 10 to 25 years in the
construction industry and more than 6 years of experience in procurement and related works.
2) Document review (tender documents, standard bidding documents, manuals, contract
documents, and different journals)
As the respondents (interviewees) of this research are experts from different stakeholders of the
construction industry (from Employer companies, Contractors and Consulting firms), the method
of sampling to be applied is a kind of detailed interview and well-organized questionnaire.
The sample size is 12 (5interviewees from Employer, 3 from Contractors and 4 from consulting
firms). The research area chosen is at Addis Ababa Ethiopia since most of the headquarters of
contractors, consulting firms and Employers are seated there and most of the experts related to
this research objective are available at Addis Ababa.
3.4 Methods
The major activity steps followed for the systematic fuzzy AHP during contractors’ selection are:
Contractors selection criteria were identified based on the acquired knowledge from
different literatures and experts from different stakeholders of the construction industry
Well, organized interview questions prepared and conducted with the selected
interviewees (experts).
The relative importance of each major criteria and sub-criteria filled in the table form in
linguistic terms by experts
34
.
3.5 Data Analysis
The steps established for the creation of our model Fuzzy AHP system in the construction
industry service is as shown bellow
Step1.Determining critical factors (most important criteria) in the process of Contractors’
selection from the related literature
Step2. Experts are asked to identify the most important criteria that involve in contractors'
selection
Step3. A questionnaire was designed for interview based on criteria that exploited in steeps
1&2 to pairwise compare elements
Step4. Experts were asked to fill out the nine scale questionnaires by choosing the most
appropriate linguistic comparison variable. In this step, the experts compare two criteria
respect to their capability in supporting contractor selection goals.
Step5. Transform experts respond into nine scale fuzzy numbers Calculate the final
comparative value (weight) of each criterion by pair-wise comparison matrix with the
help of the scale of relative importance.
Step6. Calculate the final comparative value (weight) of each criterion by pair-wise
comparison matrix with the help of scale of relative importance.
Step7. Calculate the Consistency ratio to check whether the calculated criteria weight is correct
or not.
Step8. A formula (fuzzy IF-THEN rule) is created for the sake of checking the validity of the
criteria weights obtained above.
Step9. Validity of the Model is tested in A Case Study supported by MATLAB software,
(Preference Score Weighted Sum and Preference Score Weighted Product Model, IFTHEN rule) and Finally, the rank of Participating Contractors (bidders) is tabulated and
the winner of the tender is known.
35
.
CHAPTER FOUR
RESULTS AND DISCUSSION
4.1 Identifying Criteria & Developing a hierarchical structure
According to the Ethiopian Federal Procurement and Property Administration (FPPA), the first
stage of bidding is to check legal qualification of the bidder which is known as the preliminary
screening stage and it includes compliance checking with regard to Nationality, Conflict of
interest, Registration in the FPPA's suppliers list, debarred by the decision of FPPA, Valid trade
license or business organization registration certificate, VAT registration certificate, Valid tax
clearance certificate, and Government Owned Entity. A contractor who fulfilled the above
requirements is legally qualified to be considered in the next selection process.
After a comprehensive review of different literatures related to this work, the government
procurement manual of Ethiopia (FPPA, Version 1, August 2011), different contract documents,
many factors or selection criteria bring in to being that could affect the prequalification and
selection process of participating contractor. The importance of different factors may vary from
place to place. Those factors with high influence in another country might have low influence in
Ethiopia.
Accordingly, after the collection of these criteria from literatures, semi-structured interviews
were conducted with 10 construction experts working under different stakeholders of the
construction industry (5 from the Employer, 3 from the consulting firms and 2 from contractors)
whose experiences are from 10 to 25 yearsto select the most important criteria from the collected
ones and to add other important criteria which has to be included. Also, some factors may be
considered not effective at all. So, to choose and identify the most factors that have a high effect
in selecting the appropriate contractor, the factors had to be revised by experts in Ethiopia. In
these interviews, criteria were listed and then combined, and finally selected to suit the
construction industry in Ethiopia. The final 32-criteria list that is believed to affect the contractor
selection is determined. These criteria are classified into eightmajor groups as shown in Fig.7
below. The preliminary screening, legal qualification, is not included in the criteria list and
criteria weight calculation as it is a must to meet requirement.
36
.
Major and Sub-criteria for Contractor Selection
Technical
Ability
Financial
Soundness
Bid
Value
Management
Capabilty
Resources
Reputation
Health, Safety &
Environment
General suitability
1. Relevant
Expereince
1. Financial
Stability
1. Management
Knowledge
1.Technical
Expertise
1. Length of time 1. Health, safety& 1. Works at hand
in bussiness
environment
and status of
management plan works
2. Built
Technology
capability
3. Research &
Develeopment
ability
4. Information
Technology
Application
2.Creditability
2. Quality, Time &
Cost Management
2. Key personel
2. Past failures
3. Banking
arrangment &
bonding
4. Liquidity
3. Contract
Management
2. Previous safety 2. Experience in
records
the region
3.Sub contractors 3. Past owner List
contractor
relationship
4. Coordintion with 4. Specialist
4. Contractorthe Employer
Equipment
suplier
and/or consultant
relationship
5. Inovation
5. Risk Mangement 5. Fcailities
6. Staff training
6. Organizational
Structure
Major criteria
3. Technical
approach and
work methodology
4. Work plan and
scheduling
Sub-criteria
5. Other
reltionships
Fig.4.1:Major and sub-criteria for contractor selection
4.2 Modeling in Fuzzy AHP
The critical factors are identified and the hierarchical structure is created as shown above in
fig.6.The next step is to determine the relative importance (criteria weight) using fuzzy pair-wise
comparison matrix based on the experts’ determinations and check whether the criteria weights
are consistent or not.
4.2.1 Determining Relative Importance
Experts are asked to fill the pair-wise comparison matrix in linguistic terms as listed below from
1 to 25 and these linguistic terms are changed into fuzzy numbers and tabulated to fuzzy pairwise matrix.
37
.
Table 4.1:Linguistic terms
No.
Criteria to be compared
Experts determinations
1
Technical capability with respect to Financial
Soundness
Strong important
2
Technical capability with respect to Bid value
Weak
3
Technical with respect to Management ability
Very Strong Important
4
Technical capability with respect to Reputability
Equally Important
5
Technical capability with respect to Resources
Very Strong important
6
Technical capability with respect to HSE
Extremely Strong important
7
Technical capability with respect to General
Suitability
Moderate important
8
Financial soundness with respect to bid value
Equally Important
9
Financial soundness with respect to management
ability
Moderately important
10
Financial soundness with respect to Reputability
Equally important
11
Financial soundness with respect to Resources
Strong Important
12
Financial soundness with respect to HSE
Strong important
13
Financial soundness with respect to General
suitability
Equally important
14
Bid value with respect to management ability
Strong important
15
Bid value with respect to Resource
Strong important
16
Bid value with respect to HSE
Strong important
17
Bid value with respect to General suitability
Moderate important
18
Management ability with respect to resources
Moderate important
19
Management ability with respect to HSE
Equally important
20
Management ability with respect to General
suitability
Equally important
21
Reputability with respect to Resource
Strong Important
22
Reputability with respect to HSE
Moderate important
23
Reputability with respect to General Suitability
Equally important
24
Resource with respect to HSE
Equally important
25
HSE with respect to General suitability
Equally important
38
.
The scale of relative importance is expressed in triangular fuzzy number representation which is
designated as X for the Variables (criteria) in the fuzzy et A and µ A(X) for the membership
function as follows.
Fig.4.2: Fuzzy scale of relative importance
The fuzzy triangular relative importance is as shown in the above figure and is described as
follows.
Linguistic Term
Crisp Value
Fuzzy Value
Equal importance
1
(1, 1, 1)
Moderate importance
3
(2, 3, 4)
Strong importance
5
(4, 5, 6)
Very strong importance
7
(6, 7, 8)
Extremely strong importance
9 (8, 9, 9)
2
(1, 2, 3)
4
(3, 4, 5)
Intermediate values
8
6
(5, 6, 7)
(7, 8, 9)
39
.
Table 4.2: Fuzzified Pair-wise comparison matrix
Technical
capability
Financial
Soundness
Bid Vale
Technical Financial
Bid
Capability Soundness value
(1, 1, 1)
(4 , 5, 6)
,
)
Manageme
nt Ability
Reputabil
ity
Resourc
es
HSE
General
Suitability
(6, 7, 8)
(1,1, 1)
(6, 7, 8) (8, 9, 9) (2, 3, 4)
)
(1, 1, 1)
(1, 1, 1)
(2, 3, 4)
(1, 1, 1)
(4, 5, 6) (4, 5, 6) (1, 1, 1)
(2, 3, 4)
(1, 1, 1)
(1, 1, 1)
(4, 5, 6)
(2,3, 4)
(4, 5, 6) (4, 5, 6) (2, 3, 4)
,
Management
,
)
ability
Reputability (1,1, 1)
,
,
)
(1, 1, 1)
,
)
(1, 1, 1)
(4, 5, 6)
)
Resources
,
)
,
)
,
)
HSE
,
)
,
)
,
General
Suitability
,
)
(1, 1, 1)
,
)
(2, 3, 4) (1, 1, 1) (1, 1, 1)
(1, 1, 1)
(4, 5, 6) (2, 3, 4) (2, 3, 4)
,
)
,
)
(1, 1, 1) (1, 1, 1)
)
(1, 1, 1)
,
)
(1, 1, 1) (1, 1, 1) (1, 1, 1)
)
(1, 1, 1)
,
)
(2, 3, 4) (1, 1, 1) (1, 1, 1)
,
,
Note: Fraction values of the relative importance is fuzzified by the following inverse comparison
formula.
(Chang D.Y, 1996)
where, u = upper value, m = middle and l = lower values of fuzzy numbers
40
)
.
Table 4.3: Fuzzy Geometric mean
Technical
capability
Financial
Soundness
Bid Vale
Managem
ent ability
Reputabili
ty
Resources
T.Capab
ility
F.Soundn
ess
Bid
value
(1, 1, 1)
(4 , 5, 6)
,
,
)
(1, 1, 1)
(2, 3, 4) (1, 1, 1)
,
)
(1, 1, 1)
Manage
ment
Ability
(6, 7, 8)
Reputab
ility
Resourc
es
HSE
(1,1, 1)
(6, 7, 8)
(1, 1, 1) (2, 3, 4)
(1, 1, 1)
(1, 1, 1)
(2, 3, 4)
)
(4, 5, 6)
)
,
)
(1, 1, 1)
(1, 1, 1)
,
)
(4, 5, 6)
,
Geometric Mean
(8, 9, 9)
General
Suitabili
ty
(2, 3, 4)
(4, 5, 6)
(4, 5, 6)
(1, 1, 1)
(1.23, 1.40, 1.56)
(4, 5, 6)
(4, 5, 6)
(2, 3, 4)
(2.18, 2.76, 3.29)
)
(2, 3, 4)
(1, 1, 1)
(1, 1, 1)
(0.45, 0.52, 0.62)
(1, 1, 1)
(4, 5, 6)
(2, 3, 4)
(2, 3, 4)
(1.41, 1.71, 2.03)
,
)
,
)
(1, 1, 1)
(1, 1, 1)
)
(1, 1, 1)
,
)
(1, 1, 1)
)
(1, 1, 1)
,
)
(2, 3, 4)
,
)
,
)
,
)
HSE
,
)
,
)
,
General
Suitability
,
)
(1, 1, 1)
,
,
(2.21, 2.62, 3.02)
)
(0.28, 0.32, 0.40)
(1, 1, 1)
(1, 1, 1)
(0.41, 0.44, 0.50)
(1, 1, 1)
(1, 1, 1)
(0.71, 0.76, 0.91)
,
Note: The Geometric mean of two fuzzy numbers is expressed as follows
(Buckley 1985)
Now, the Fuzzy Geometric weight is calculated by adding the Fuzzy Geometric mean values
vertically and the sum is:
Fuzzy Geometric Weight = (8.88, 10.53, 12.33)
Then the geometric mean value for each criterion shall be multiplied by the inverse of the
geometric weight = (
,
,
)
41
.
Table4.4: Calculation of Fuzzy Weight
Criteria
Geometric Mean
Weight inverse
Result (Fuzzy weight)
Technical capability
(2.21, 2.62, 3.02)
(
,
,
)
(0.18, 0.25, 0.34)
Financial Soundness
(1.23, 1.40, 1.56)
(
,
,
)
(0.10, 0.13, 0.18)
Bid Vale
(2.18, 2.76, 3.29)
(
,
,
)
(0.18, 0.26, 0.37)
Management ability
(0.45, 0.52, 0.62)
(
,
,
)
(0.04, 0.05, 0.07)
Reputability
(1.41, 1.71, 2.03)
(
,
,
)
(0.11, 0.16, 0.23)
Resources
(0.28, 0.32, 0.40)
(
,
,
)
(0.02, 0.03, 0.05)
HSE
(0.41, 0.44, 0.50)
(
,
,
)
(0.03, 0.04, 0.06)
General Suitability
(0.71, 0.76, 0.91)
(
,
,
)
(0.06, 0.07, 0.10)
The rightmost column in the above table 5 Shows the fuzzy weight for each criterion. It can be
defuzzzified into crisp values as follows if necessary by the Center of Area (COA) method to be
used for further calculations.
Where,
wi=Criteria Weight
l= lower value
m = middle value
u= upper value
(Manoj 2018)
42
.
Table 4.5: Fuzzified and Defuzzzified (crisp value) criteria weights
Criteria
Result (Fuzzy weight)
Defuzzzified Weight
Technical capability
(0.18, 0.25, 0.34)
0.256
Financial Soundness
(0.10, 0.13, 0.18)
0.136
Bid Vale
(0.18, 0.26, 0.37)
0.270
Management ability
(0.04, 0.05, 0.07)
0.052
Reputability
(0.11, 0.16, 0.23)
0.168
Resources
(0.02, 0.03, 0.05)
0.033
HSE
(0.03, 0.04, 0.06)
0.044
General Suitability
(0.06, 0.07, 0.10)
0.077
The Sum of the above crisp value is 1.036. So, it has to be normalized to 1 by dividing to 1.036
all the criteria weights and the final normalized weight of each criteria is tabulated below.
Table 4.6: Normalized and rounded weight for criteria
Criteria
Normalized weight
Technical capability
0.25
Financial Soundness
0.13
Bid Vale
0.26
Management ability
0.05
Reputability
0.16
Resources
0.03
HSE
0.05
General Suitability
0.07
43
.
4.2.2 Model Formulation
Based on the above criteria weight obtained, the following rating formula is developed which
can serve to calculate the Contractors’ score.
Variables:
SCi = Scoreof the ith Contractor (i = 1…n, where n is number of candidate contractors)
BV = Bid Value
LBV = Lowest Bid Value
EBV = Estimated Bid Value
TC = Technical Capability
FS = Financial Soundness
MA = Management Ability
R = Reputability
RS = Resource
HSE = Health Safety and Environment
GS = General Suitability
SCi = 0.26
) + 0.25TCi + 0.13FS + 0.05MA + 0.16R + 0.03RS + .05HSE+ 0.07GS)
Maximum Possible Score Rating = (8, 9, 9)
Taking the mean = (8+9+9)/3 = 26/3;
SCi=
) + 0.25TCi + 0.13FS + 0.05MA + 0.16R + 0.03RS +0.05HSE+ 0.07GS)
x3/26...(1)
SCi = 0.26
) + 0.25TCi + 0.13FS + 0.05MA + 0.16R + 0.03RS+0.05HSE+ 0.07GS) x 3/26....
(2)
44
.
Depending on the interest of the employer (owner), there might be an estimated bid value. If
there is an estimated bid value, the second equation shall be used to calculate the score of
candidates and the first equation shall be used in case of the absence of any bid estimation.
4.3 Ranking Contractors
4.3.1 Determining Linguistic terms for Contractors rating
The linguistic terms used for contractors rating with the corresponding fuzzy numbers are shown
in fig.9 bellow and the linguistic values with the corresponding fuzzy numbers and crisp values
are indicated in table 11 below.
Fig.4.3:Linguistic terms with Fuzzy values
Table 4.7: Linguistic Variables for the Rating with fuzzy values
Linguistic Terms
Poor
Medium Poor
Fair
Medium Good
Good
Very Good
Excellent
Symbol
P
MP
F
MG
G
VG
E
45
Fuzzy Value
(0, 1, 2)
(1, 2, 3)
(2, 3 ,4)
(3, 4, 5)
(4, 5, 6)
(6, 7, 8)
(8, 9, 9)
Crisp Value
1
2
3
4
5
7
8.67
.
4.3.2 Developing Codes (IF-THEN rule) in MATLAB Software
The IF-THEN rule is the rule which has to be an input for the MATLAB software to obtain the
final rank of contractors considered for the evaluation stage as per the same formula created by
Manoj Mathew (2018).
Three Variables are created (Mathew, https://mathewmanoj.wordpress.com/multi-criteriadecission-making/)
X = Represents all the contractors’ ratings for each criteria
W = Weightage for each criterion, which is determined by experts and calculated and ranked in
fuzzy pair-wise comparison matrix above.
Wcriteria = is a variable used to separate the beneficial and non-beneficial criteria. The nonbeneficial criterion is bid value from which the lowest value is preferred. The other
criteria are beneficial from which the higher value shall be selected. We have to feed
0 for non-beneficial criteria and 1 for beneficial criteria.
Xval=length(X(:,1));
for i=1:Xval
for j= 1:length(W)
if Wcriteria(1,j)== 0
Y(i,j)=min(X(:,j))/X(i,j);
else
Y(i,j)=X(i,j)/max(X(:,j));
end
end
end
for i=1:Xval
PWSM(i,1)=sum(Y(i,:).*W);
PWPM(i,1)=prod(Y(i,:).^W);
end
Preference_Score_of_Weighted_Sum_Model = num2str([PWSM])
Preference_Score_of_Weighted_Product_Model= num2str([PWPM])
46
.
4.4 MODEL VALIDATION (Case Study)
4.4.1 Introduction
A case study was conducted for the tender which was issued in a Magazine (Ethiopian Herald
dated 26 May 2015) for the Construction of Office Building, Bull Barn Building, and Small
Diversion Dam which is part of Holeta and Kality access road project. The employer wanted to
evaluate candidate contractors who can realize the project. Seven Contractors had participated
and 4 Contractors passed the Preliminary screening. Based on the instruction to bidders, the
bidder should score a minimum of 80/100 in the technical evaluation and 3 of the participating
contractors become nonresponsive. Here in this case study all the seven contractors will be
participated in the newly developed model and evaluated. Firstly, the contractors were evaluated
based on the current selection methodology and then evaluated by the new model and the outputs
are compared for illustration.
The list of Contractors and their financial offer in ETB was as follows
1. Contractor A = 675,256,453.2
2. Contractor B = 610,730,807.77
3. Contractor C = 742,376,280.30
4. Contractor D = 605,648,372.36
5. Contractor E = 712,724,235.48
6. Contractor F = 680,889,642.90
7. Contractor G = 655,078,752.81
4.4.2 Contractors rating for each criterion
After reviewing the technical evaluation documents, the following linguistic and Crisp values for
the contractor ratings were recorded.
4.4.2.1 Contractors Selection based on the current practice
Step-1: Preliminary Screening
From the offers of the tender, seven contractors are found responsive for preliminary
screening and considered for further Bid Evaluation stage.
Step-2: Bid Evaluation
The Evaluation methodology adopted in this tender is a two-staged evaluation and
scoring method.
47
.
Step-3: Technical Evaluation
Technical Proposals had been be evaluated using the following criteria:
(1)
The company's general experience in the construction industry of Building
Construction (30%)
(2)
The adequacy of the proposed work plan, methodology, work schedule and
the completeness of the qualification document (5%)
(3)
The qualification and competence of the personnel proposed for the project
(20%)
(4)
The availability and adequacy of rented/leased/owned construction
equipment (30%).
(5)
Declaration of Site visit (5%)
(6)
Financial situation (15%).
The sum of the above points is 105% shall be converted into 100% during comparison of
bidders.
The Technical Evaluation was done for each Contractor for each criterion and the result is as
shown in the table bellow
Table 4.8: Technical Evaluation
No
1
1.1
1.2
Evaluating Criteria
General Qualification
Marking
Point
Cont. A
Cont. B
Cont. C
Cont. D
Cont. E
Cont. F
Cont. G
55
37
42
52
35
50
50
17.5
Must meet requirement
Legal Status
30
25
25
30
23
30
27
12.5
20
7
12
17
7
15
18
0
Proposal of work methods
and programs.
5
5
5
5
5
5
5
5
2
Financial Situation
15
15
15
15
15
15
15
7
3
Experience
30
17
29
20
28
25
24
22
1.3
1.4
4
Major Equipment
Key personnel
Site Visit
Total weight point out of
105%
Remark
5
5
5
0
0
5
5
5
105%
74%
91%
87%
78%
95%
94%
52%
100%
70%
87%
83%
74%
90%
90%
49%
Not responsiveResponsive
Responsive
Not responsiveResponsive
Responsive
Not responsive
As it is observed in the above table the three contractors were not responsive and only four
contractors considered for Financial Evaluation.
The technical score is calculated as follows:
48
.
CTP
TSN =
100
HTP
TSNB =(
)x100 = 96.67%
TSNC =(
)x100 = 92.22%
TSNE =(
)x100 = 100%
TSNF =(
)x100 = 100%
Step-4: Financial Evaluation
The Financial Score is calculated as follows:
LFP
FS =
100
CFP
FSB = (
) x100 = 100 %
FSC = (
) x100 = 82.26 %
FSE = (
) x100 = 85.68 %
FSF = (
) x100 = 89.69 %
Step-5: Weight of Scores
In our case study, the client procurement team explained that the weight of financial evaluation is
70 % and the remaining 30% is for Technical evaluation.
The final score is calculated as follows
S = FS x 0.7 + TSN x 0.3
SB = 100 x 0.7 + 96.67 x 0.3 = 99.01 %
SC = 82.26 x 0.7 + 92.22 x 0.3 = 85.25 %
SE = 85.68 x 0.7 + 100 x 0.3 = 89.98 %
SF = 89.69 x 0.7 + 100 x 0.3 = 92.78 %
The Final score and Rank of Contractors is tabulated bellow
49
.
Table 4.9: Score and rank of Contractors
Candidate Contractor
Score
Rank
Contractor B
99.01
1
Contractor C
85.25
4
Contractor E
89.98
3
Contractor F
92.78
2
4.4.3 Contractors Selection Based on the New Model
Step-1: Contractors Linguistic Rating for each criterion
Table 4.10: Bid evaluators’ linguistic rating
Technical
Financial
Bid
Management
Reput
Resou
HSE
General
Capability
Soundness
Value
Ability
ability
rces
Contractor A
G
E
F
G
VG
F
G
VG
Contractor B
E
VG
VG
VG
VG
G
VG
VG
Contractor C
VG
E
P
G
G
VG
G
G
Contractor D
E
E
VG
G
G
MP
G
G
Contractor E
E
VG
P
VG
G
VG
G
E
Contractor F
E
E
MP
G
MG
VG
MG
G
Contractor G
F
F
G
G
MG
P
G
G
Suitability
Step – 2: Transforming Linguistic rating to the corresponding Crisp Value
Table 4.11: Crisp Values
Technical
Financial
Bid
Manageme
Reputabili
Resou
Capability
Soundness
Value
nt Ability
ty
rces
Contractor A
4
8.67
3
5
7
3
5
7
Contractor B
8.67
7
7
7
7
5
7
7
Contractor C
7
8.67
1
5
5
7
5
5
Contractor D
8.67
8.67
7
5
5
2
5
5
Contractor E
8.67
7
1
7
5
7
5
8.67
Contractor F
8.67
8.67
2
5
7
7
4
5
Contractor G
3
3
5
5
4
1
5
5
50
HSE
General
Suitability
.
Step-3: Calculation of Scores
Based on the above mathematical formula created (4.2.2) and the contractors’ data rated by the
bid evaluators and the bid value offered by the candidate contractors, the evaluation is done as
follows without the support of any software
4.4.3.1 Contractors Ranking (without software)
In this case study, the first equation is applied as the employer did not have an estimated bid
amount.
SCA = 0.26
) + (0.25TCA + 0.13FSA + 0.05MAA + 0.16R A+ 0.03RSA +0.05HSEB+ 0.07GSA) x3/26
) + (0.25x4+0.13x8.67+0.05x5+0.16x7+0.03x 3+0.05x5+.07x7)x3/26
= 0.26
= 0.7325
The scores of other contractors is calculated with the same manner and outputs (scores) from the
above calculation are converted to a percentage and ranked as shown in the table below.
Table 4.12: Score and Rank of Contractors
No
Name of Contractor Score
Score %
Rank
1
Contractor A
0.7325
73.25
6
2
Contractor B
0.8967
89.67
1
3
Contractor C
0.7587
75.87
5
4
Contractor D
0.8374
83.74
3
5
Contractor E
0.8318
83.19
4
6
Contractor F
0.8572
85.72
2
7
Contractor G
0.5473
54.73
7
51
.
4.4.3.2 Ranking supported by software (MATLAB)
4.4.3.2.1 Variable Creation & Assigning Values
Three variables X, W, and Wcriteria are created as it is described above and all the values for the
Variables filled in MATLAB workspace.
Fig.4.4:Variables and the corresponding values (screen hot)
As it is shown in the above figure, the three variables which are an input for the Matlab software
are created and the data, that is the decision makers’ ratings for each criteria to individual
contractors, is fed in to Matlab. The value “0” is given for bid value for each contractor for
Wcriteria due to the reason that bid value is non beneficiary but for the other Wcriteria is given
“1” due to the beneficiary characteristics of the criteria.
52
.
4.4.3.2.2 Running the Software and data interpretation
Once the Variables are created and the data are fed, the next step is to write the formula in the
command window and run the software. The output is given in two models and shown in the
consecutive figures bellow.
Fig.4.5: Formula(code) fed into MATLAB command window (screenshot)
The above figure shows the created Matlab codes which is fed in to Matlab command window
and it is ready for running the software.
53
.
Fig.4.6: MATLAB output in Weighted Product Model (screenshot)
As it is shown in the above figure (Matlab output in weighed product model), the software
resulted in the score of each contractor within a fraction of seconds. The result stipulated in the
order which is fed in the command window. This shows Contractor A scored 74.399 % and
contractor G scored 52.531 % which is the combination of technical and financial evaluation.
54
.
Fig.4.6: MATLAB output in Weighted Sum Model (Screenshot)
Table 4.13: Score and Rank of Contractors
No
Name of Contractor
Result Based
on WSM
Result based
on WPM
1
Contractor A
0.7793
0.7439
6
2
Contractor B
0.9507
0.9464
1
3
Contractor C
0.8000
0.7926
5
4
Contractor D
0.8746
0.8490
4
5
Contractor E
0.8759
0.8686
3
6
Contractor F
0.9059
0.8924
2
7
Contractor G
0.5793
0.5253
7
55
Rank
.
4.4.4 Discussion and Interpretations
4.4.4.1 Based on the current practice
Rating Methodology:
The rating methodology is numerical but as works of literature portrayed, human beings are
excellent in linguistic rating than numeric. The rating methodology for the current practice takes
more time and it is a very tedious work for evaluators as group decision making is time taking
and boring by itself.
Technical Evaluation:
The criteria considered for technical ignored some important sub-criteria such as innovation,
research & development, HSE, Risk management, etc. As it is more clarified in the literature
review, the employer wanted to evaluate candidate contractors who can realize the project. Seven
Contractors had participated and 4 Contractors passed the Preliminary screening. Based on the
instruction to bidders, the bidder should score a minimum of 80/100 in the technical evaluation
and 3 of the participating contractors become nonresponsive. This showed that, the three
contractors become out of competition since they lose insignificant points(scores) at the technical
evaluation stage. This makes the currently applied way of evaluation doesn’t entertain the
vagueness of the decision making problem.
Weightage for scoring:
The criteria weight for financial score is 70 % and the remaining 30 % for technical evaluation.
This encourages contractors to focus on financial competition and did not encourage to improve
technical requirements which are described in selection criteria (fig.7). If we make the weight to
the reverse, the scores will be changed and Contractor F will be the winner.
4.4.4.2 Scores based on the new model
Rating Methodology:
The rating methodology adopted in the new model is linguistic. That is, the bid evaluators (decision
makers) rate the contractors in linguistic terms and this linguistic terms are changed in to crisp value, then
this crisp value will go through fuzzy analytical hierarchy process. Human beings are excellent in
linguistic type of rating and decision by nature.
56
.
Technical Evaluation:
The major and sub-criteria considered encourages contractors to compete for new technologies, IT
applications, research, and innovation, to pay attention to health, safety, and environment, to build better
company reputation. In this new model, the coefficients for the developed model make the technical
evaluation stage very easy due to the reason that, the experts finalized the ratio of those criteria to be
applied.
Weightage for scoring:
The weights for technical evaluation is 74 % and the remaining 26 % is for bid price. The 70% includes
those criteria which are identified at the first stage except bid value, which are: technical capability,
financial soundness, Management ability, Reputability, Resource, HSE, and General suitability
With and without Software:
As it is shown in the above two figures 12 & 13 and Table 16 the rank of participating Contractors is
tabulated both in weighted sum and weighted product model outputs. Even though it didn't make rank
difference in this case study, it might make changes in other evaluation cases as long as the numerical
value of the outputs of the two models is different. The weighted sum model generalizes the arithmetic
mean and the weighted product generalized the geometric mean of values. For such kind of application
where the criteria are fuzzy, the weighted Product Model is Preferable and the winner of the bid is chosen
based on the weighted product. Based on the Evaluation Result Contractor is B the winner.
57
.
CHAPTER FIVE:
CONCLUSSION AND RECOMMENDATION
5.1 Conclusions
Most of real-world contractor prequalification problems involve uncertainty and imprecision in
the estimates of performance ratings and criteria weights due to the own nature of construction
projects and subjectivity of decision-makers' judgments.
The selection criteria which are under practice in our country encourage financial competition
and pay less attention to technical prequalification criteria such as new technologies, research
and development, training, innovation and health, safety and environmental protection and others
which are listed in chapter 3 fig.7. The current practice is also not supported by models and
software which can reduce repeated and tedious works and human errors during tender
evaluation.
Analytical Hierarchy Process is an effective decision-making technique based on multi-criteria
decision making which is a method successfully used as it incorporates all the attributes of
contractor selection and then prioritizes each attribute resulting in an easy judgment of best
contractor.
But, in some complex decision problems, it is difficult for the decision-maker to compare
alternatives with crisp value, because of the ambiguity in human experience and knowledge.
Fuzzy methodology used to tackle this type of problem. Consistency of the outcome regarding
the selection of the contractor in the AHP checked in FGDM, the uncertainty involved in rating a
contractor overcome using Fuzzy methodology and this makes Fuzzy Analytical Hierarchy
Process (FAHP) is more preferable as an extended AHP decision-making tool
Through works of literature and thorough interviews, it was understood that many factors could
affect the selection and evaluation process. The Selection criteria were identified and grouped
into 8 major criteria.
The importance weight of the selection criteria was calculated as per the experts’ rating and
weighted and ranked based on AHP pair-wise comparison matrix which is the basic part to
formulate our mathematical model. A mathematical model was developed based on the selected
criteria and the corresponding weights.
58
.
The developed mathematical model was tested in a case study and selection of contractors was
conducted and compared in three ways. Contractors were evaluated based on the current practice
and based on the developed mathematical model. The developed mathematical model is tested
with and without software.
The developed mathematical model had incorporated additional criteria that can create more
competition field for contractors instead of fighting on bid prices and it is easy for decisionmakers to rate candidates in linguistic terms and the mathematical model can save more time and
reduces human errors. A code (IF-THEN rule) was developed to support the mathematical model
by software (MATLAB, R2008a). Even though there is some difference in the output of the
scores of candidates in the second option, it was found that the evaluation resulted in an
insignificant difference in the Ranks of Contractors. The software (MATLAB) saves more time
and reduce errors. As it is observed, using the software is more preferable than manually
calculating scores.
5.2 Recommendation
Recommended from this Study:
The employers and consulting firms are suggested to test, improve and use the mathematical
model and Matlab software which can be addressed through short-term training or by video
tutorials and manuals which are available online
Recommendations for further Study:
Further study is recommended in this research area by incorporating more experts using data and
specifications from more sources, stakeholders and covering more areas in addition to
procurement management.
59
.
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Appendices
Appendix 1: Introduction
Request to Participate in MSc Research Interview
I am a MSc student in Addis Ababa Science and Technology University Civil Engineering
Department, Construction Technology and Management stream. I am conducting a research
study entitled “Development of Fuzzy Decision Model for Ethiopian Construction Contractors
Selection”.
Choosing the right contractor to deliver a project in time, within budget and with better quality is
the most significant decision-making process to ensure the successful completion of construction
projects. As we are observing from day to day, many contractors failed to accomplish projects
due to different reasons like labor problems, financial problems, poor performance, social and
political problems, lack of safety considerations at worksite, management capability, etc. All
these cases have led to the impression that the current scenario of awarding the contracts is
inefficient in selecting the contractor capable of meeting the demands and challenges of present
times and hence needs to be reviewed accordingly.
The construction contractors’ selection under practice currently in Ethiopia screen out and makes
out of competition those capable contractors at the time of technical evaluation which is not fair
to lose the chance of competing for financial evaluation due to missing insignificant scores at the
time of technical evaluation.
The objectives of this research is to determine the most important criteria in construction
contractor selection and develop decision support model using fuzzy analytical hierarchy process
(FAHP).
I am so happy that, you are willing to assist me to do my research by making yourself ready for
the interview and making yourself as one of the participants who played the most important roll
for the successfulness of this research and I hope that this interview will not take more than an
hour.
63
.
Appendix 2: Interview Questions
A. First Round Interview:
1. Name of your Organization: ________________________________
2. Which Position do you hold?
3. What is your experience in the construction industry in years?
a). ≤ 5
b) 5 – 10 c) 10 – 15 d) 15 – 20 e) ≥ 20
4. What is your specific experience in Contract/Procurement management in years?
a). ≤ 5
b) 5 – 10 c) 10 – 15 d) 15 – 20 e) ≥ 20
5. How is contractors’ selection done in your organization?
a) Manually
software
b) manually guided by mathematical models c) using computer
e) I don’t know
6. Please discuss the Contractors’ selection steps and methodology that your company used
to evaluate candidate contractors.
7. Please discuss the Contractors’ selection steps and methodology that you know in your
previous organization.
8. How long does it take to undertake contractors’ selection using the current method?
9. What are the main challenges that face in contractors’ selection evaluation in your
Company/Organization?
10. Please list out those criteria that your company is using currently to evaluate candidate
contractors.
11. Do your company have fixed weight for each criteria to evaluate contractors? If so,
please tell me the weight of each criteria.
12. Do you think that the criteria that are under practice currently in your company and
others in Ethiopia are inclusive?
13. What additional criteria do you want to be included as part of the contractors’ selection
evaluation?
64
.
B. Second Round Interview
14. Please rate the relative importance of the following Contractor’s Selection Criteria from 1
to 9.
Important
------------------------------ 1
Moderately important ------------------ 3
Strongly important ---------------------- 5
Very strongly important ---------------- 7
Extremely strongly important ---------- 9
No
Importance weight
Criteria
1
1
Relevant Experience
2
Built in Technology capability
3
Research & Development ability
4
Information Technology application
5
Innovation
6
Staff Training
7
Financial Stability
8
Creditability
9
Banking arrangement & Bonding
10
Liquidity
11
Bid Value
12
Management Knowledge
13
Quality, Time, and Cost Management
14
Contract Management
15
Coordination with the Employer and /or
consultant
65
3
5
7
9
.
16
Risk Management
17
Organizational Structure
18
Technical Expertise
19
Key Personnel
20
Sub-contractors List
21
Specialist Equipment
22
Facilities
23
Length of time in Business
24
Past Failures
25
Past owner-contractor relationship
26
Contractor-supplier relationship
27
Other relationships
28
HSE management plan
29
Previous safety records
30
Work at hand and status of works
31
Experience in the region
32
Technical approach & work methodology
33
Work plan & scheduling
66
.
C. Third Round Interview
15. Please rate the pairwise relative importance of those criteria which are listed below in the
table in linguistic terms.
Linguistic Term
Crisp Value
Equal importance 1
Moderate importance
3
Strong importance 5
Very strong importance
7
Extremely strong importance
9
Experts determinations
No.
Criteria to be compared
1
Technical capability with respect to Financial
Soundness
2
Technical capability with respect to Bid value
3
Technical with respect to Management ability
4
Technical capability with respect to Reputability
5
Technical capability with respect to Resources
6
Technical capability with respect to HSE
7
Technical capability with respect to General
Suitability
8
Financial soundness with respect to bid value
9
Financial soundness with respect to management
ability
10
Financial soundness with respect to Reputability
11
Financial soundness with respect to Resources
12
Financial soundness with respect to HSE
13
Financial soundness with respect to General
suitability
14
Bid value with respect to management ability
67
.
15
Bid value with respect to Resource
16
Bid value with respect to HSE
17
Bid value with respect to General suitability
18
Management ability with respect to resources
19
Management ability with respect to HSE
20
Management ability with respect to General
suitability
21
Reputability with respect to Resource
22
Reputability with respect to HSE
23
Reputability with respect to General Suitability
24
Resource with respect to HSE
25
HSE with respect to General suitability
68
Siferew Bishaw