A CONDORCET VOTING THEORY BASED AHP METHOD FOR … · The job of the contractors and suppliers ensures that the project is completed successfully meeting all quality and reliability

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International Journal of Civil Engineering and Technology (IJCIET) Volume 8, Issue 6, June 2017, pp. 595–604, Article ID: IJCIET_08_06_065

Available online at http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=8&IType=6 ISSN Print: 0976-6308 and ISSN Online: 0976-6316

© IAEME Publication Scopus Indexed

A CONDORCET VOTING THEORY BASED AHP

METHOD FOR CONTRACTOR SELECTION IN

CIVIL ENGINEERING PROJECTS

Sweta Bhattacharya

School of Information Technology & Engineering,

VIT University, Vellore, India

V. Raju

Institute of Industry and International Programme,

VIT University, Vellore, India

ABSTRACT

Contractor selection is an extremely important activity for successful completion

of civil engineering construction projects. The quality criteria for contractor selection

are extremely vague and majorly depend on lowest tender bids submitted by

contractors leading to quality compromises in construction projects. The paper

presents five major quality criteria expected from good contractors and derives pair

wise comparison of these quality criteria using subject matter based opinion

calibrated to standard importance scale in AHP method. The calibration to

importance scale point has chances of dilemmatic errors in deciding on scale points

causing erroneous results. This weakness is eliminated by using a Condorcet voting

method to derive the importance of the contractors over another for each quality

criteria followed by a quantitative ratio method to frame the comparison matrix. The

accuracy in framing of comparison matrix helps to get better ranking of the

contractors using the regular method of priority vector calculation of AHP. The

Condorcet Voting Theory based AHP framework thus helps to select the most suitable

contractor having capability to deliver successful civil engineering project abiding all

quality criteria.

Keywords: AHP, MCDM, Condorcet Voting Theory, Contractor Selection, Civil

Engineering Project

Cite this Article: Bhattacharya. S, and Raju V, A Condorcet Voting Theory based

AHP method for Contractor Selection in Civil Engineering Industry. International

Journal of Civil Engineering and Technology, 8(6), 2017, pp. 595–604.

http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=8&IType=6

1. INTRODUCTION

The construction industry is the second largest industry in India after agriculture holding first

position. The construction industry accounts for 11% of the total GDP in India making

Bhattacharya S and Raju V.


immense contribution towards the overall economic growth of the country. The construction

industry can be categorized into three main sectors which are real estate construction,

infrastructure construction and industrial construction [1]. The construction industry being

one of the most significant contributors in the country’s growth and infrastructure

development is a sub-practice area of civil engineering which is dependent on tools and

resources of various other inter-related industries. Thus construction industry significantly

affects employments of various other related industries in the country. Any civil engineering

project activity is highly dependent on resources supplied and work conducted by contractors

and suppliers. The job of the contractors and suppliers ensures that the project is completed

successfully meeting all quality and reliability parameters. Most of the time, project

management teams end up choosing non-performing contractors focusing more on the lowest

bid offered in the tender giving less importance on the contractor’s quality parameters. In civil

engineering, the quality parameters of good contractors are multiple and decision making

becomes dilemmatic. Hence most of the time choice of contractors gets inclined towards

tender quotations which end up being disastrous. The present paper discusses the good

qualities of contractors expected for successful project completions and uses a Condorcet

Voting method based Analytical Hierarchy Process (AHP) framework for contractor

selection. This approach would benefit the civil and construction engineering community to

select contractors without biased judgement with more satisfactory project outcomes.

1.1. The quality criteria of good contractor

Choosing an appropriate contractor can often become tedious as the preferred qualities are too

many. The following section discusses the list of qualities expected from a good contractor.

The most important qualities are [2]:

• Past experience: Civil engineering construction workers deal with architectural design

and hence past experience helps to understand their competence level in the field and

also their history of professional partnership and commitment with various companies

that they have worked in the past. A highly experienced contractor would always be

preferred for larger dimension projects in compared with the less experienced

contractors who could be given smaller assignments. Also as an example, a contractor

with experience to work in the rural areas might find it difficult to handle specialized

urban construction buildings.

• Technical Knowledge: The contractors should be technically knowledgeable with

required qualification. The qualifications should always be commensurate with the

preferred credentials expected in the tender invited.

• Financial and Technical resources: The contractor’s financial and technical resources

would help the contractor use latest technology tools and techniques necessary for

construction yielding higher quality work at faster pace. This would reduce chances of

suicidal financial bids and quality compromises in building construction using poor

quality resources leading to hazardous results.

• Present Workload: The present workload of the contractor helps to get two

perspectives of the contractor. Firstly it helps to understand the value of the contractor

in the civil engineering sector wherein if there is high workload, it could be assumed

that the contractors work is appreciated in the market. On the it would also help to

understand the level of attention and time the contractor would be able to render to the

prospective assignments keeping his financial capability and resource factor into

account.

A Condorcet Voting Theory based AHP method for Contractor Selection in Civil Engineering

Industry


• Safety Performance: The adherence of the contractor to safety measurements plays a

major role. There should be no room for compromises in the sector if the contractor

fails to perform well in safety measurement criteria.

In this paper a contractor selection method is proposed emphasizing on the above

mentioned five factors. A Condorcet Voting Theory based AHP method is used to select the

best contractor out of three contractors keeping all the five factors into consideration. The

next section provides detailed description of the two methodologies – Condorcet Voting

Method and AHP being used for the selection process.

2. RESEARCH METHOD

2.1. Analytical Hierarchy Process (AHP)

Analytical Hierarchy Process is a method developed originally by Thomal L Saaty in 1980 at

the Wharton School of Business. This method aims to solve multi-criteria decision making

(MCDM) problems based on subjective evaluation measurements [3-5]. The analytical

process method provides a framework for quantifying various criteria in a MCDM problem

and relates them to the overall goal. It evaluates the criterion against each other in order to

identify the most suitable and prioritized criteria among the alternatives concerned. It has a

hierarchical approach which enables decision makers to organize their subjective judgement

in order to achieve the most suitable decision for a dilemmatic problem [4-5]. The AHP

technique is based on “measurement through pair wise comparisons relying on the

judgements of experts to derive priority scales” [6-7].It helps to simplify the complexities of a

problem by combining various factors related to the problem to arrive at the final decision [8].

The AHP method consists of seven major steps which are mentioned below [9-10]:

Step 1: Definition of the Problem

Step 2: Define objective or outcome of the problem

Step 3: Identify the contributing factors that influence a certain affect or behavior

Step 4: Arrange the problem into a hierarchical structure based on Goal, Criteria, Sub-

Criteria/Alternatives

Step 5: Compare each factor with the other and derive at the standard importance scale

point as given by Thomas Saaty (Table 1) through proper calibration

Step 6: Calculate the Priority vector values, maximum Eigen value (Lamda-max),

Consistency Index and Consistency Ratio value.

Step 7: Calculate the value of CR and decide on the accuracy of the calculation and

judgment. If the CR value fails to meet the satisfactory criteria repeat the procedure until

desired value is achieved. The consistency ratio (CR) is calculated as shown in Equation 1, 2

and 3 [10]:

CR = CI/RI = Consistency Index (CI) / Relative Index (RI) (1)

CI = (Lamda-max – n) / (n-1) (2)

RI = 1.98(n – 2) / n (3)



The value of the Consistency Ratio (CR) evaluates the accuracy of the judgement made

when deciding on the importance scale point of the criteria. If the Consistency Ratio (CR)

value is less than 0.10, the judgement is considered to be consistent and acceptable. If not, the

revision of the process is required [11].

Table 1 Standard Importance Scale with description

Importance Scale Importance Description

1 Equal importance of “i” and “j”

3 Moderate importance of “i” over “j”

5 Strong importance of “i” over “j”

7 Very Strong importance of “i” over “j”

9 Absolute Importance of “i” over “j”

2, 4 and 6 are used for intermediate values of importance

Analytical Hierarchical Process (AHP) has been popularly used to resolve multi-criteria

decision making problems in various sectors. As an example, AHP has been used to select

suppliers focusing on three main criteria and six sub-criteria in Carglass Turkey to improve

productivity [12]. AHP method has been successfully used in contract selection based on six

criteria where ratings and aggregate based scores were used to frame the comparison matrix

[13]. Supplier selection is an area where AHP has been used extensively and one such

implementation has been in the small scale manufacturing industry sector where global

weight age and local weight age of the criterion were used to derive at the importance scale

points [14]. AHP method was also used in effective team selection process for a project which

later gave better results than the traditional selection system [15]. Choosing the best insurance

provider is often dilemmatic and AHP method was used to rank insurance provides based on

certain criteria which helped customer choose the insurance company in Turkey [16]. A

unique and uncommon use of AHP method has been in the improvisation of polygraph results

used for lie detection. The accuracy of lie detection was enhanced using AHP using actual

survey results where more authenticity was obtained [17]. AHP has been widely used in the

manufacturing industry where design plays a major role. Application of AHP in this sector

has in layout selection where the best layout is selected from various layout options [18]. The

paper uses the traditional AHP method to rank the quality criteria for the contractors.

2.2. Research gap and problem Definition

Although AHP has been used to resolve various MCDM problems but the method relies

solemnly on its ability to subjectively analyze the importance of a criteria over the other and

calibrate the importance to the standard scale.The artificial constraint in the use of 9 – point

scale makes it difficult for decision makers to differentiate between scale points and conclude

to the fact that an alternative is 6 or 7 times more important than the other. Hence there exist

chances of biased judgement making the derivations erroneous. The Condorcet voting theory

is hence used in this paper along with the traditional AHP based method to resolve chances of

error and enhance accuracy of the system. The traditional AHP based method is used to rank

the five quality criteria of the contractor and then Condorcet voting theory based AHP

approach is used to compare suppliers for a given criteria using Condorcet voting and

quantitative ratio based method. The detailed framework is discussed in the next section.

2.3. Condorcet Voting Theory

Condorcet voting theory is a method of pairwise comparison developed by philosopher and

mathematician Marquis de Condorcet. The theory is predominantly used in voting systems


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where one candidate is compared with the other based on the preference of the voter’s

preference as given in the ballot. The candidate is considered winner if it is able to win over

all the other candidates in the system following the majoritarian rule [19-20]. The algorithm

used for Condorcet voting method is:

Step 1: count = 0

Step 2: for each of the P respondents’ Tido

Step 3: If Ti ranks C1 above C2, count ++

Step 4: If Tii ranks C2 above C1, count - -

Step 5: If count > 0, rank C1 better than C2

Step 6: Else rank C2 better than C1

In this paper, the same approach is used for the pairwise comparison of the contractors

from the perspective of five quality factors mentioned earlier. Similar to the Condorcet

approach, a voting is conducted on 100 civil engineering stake holders who have provided

their preference of one constructor over the other for all the five quality factors. If a contractor

is preferred over the other, then it wins 1 point over the non-preferred contractor. The total

scores of all the voters are considered to derive the quantitative ratio based importance of one

contractor over the other. This ratio is used to frame the comparison matrix in the traditional

AHP method. Hence, Condorcet theory is used in the present paper only to derive the

importance of the contractors and framing of the comparison matrix for the contractors. The

detailed framework of the Condorcet Voting theory based AHP approach for contractor

selection is shown in Figure 1.

Figure 1 Framework for the Condorcet Voting Theory based AHP method for contract selection.



3. RESULTS AND DISCUSSION

As already mentioned the objective is to select the most appropriate contractor for a civil

engineering construction project. The quality criteria for contractor selection is already

described in the previous section and experts’ opinion in the organization was considered for

deciding the importance of one quality criteria over the other to frame the pairwise

comparison matrix following the standard importance scale point. The Table 2 represents the

pair wise comparison matrix for the five quality criteria.

Table 2 Pair wise Comparison Matrix for the Quality Criteria for Contractors

Past Experience Technical

Knowledge

Financial &

Technical

Resources

Present

Workload

Safety

Performance

Past Experience 1.000 0.333 0.500 2.000 3.000

Technical

Knowledge 3.000 1.000 2.000 3.000 2.000

Financial &

Technical

Resources 0.200 0.500 1.000 0.500 0.500

Present Workload 0.500 0.333 2.000 1.000 0.250

Safety

Performance 0.333 0.500 2.000 4.000 1.000

Once the pair wise comparison matrix was framed, the priority vectors for the criteria

were computed using the traditional steps of AHP process. The results of AHP computation

are shown in Table 3.

Table 3 Derivation of Priority Vector and CR using traditional AHP method

Past

Experience

Technical

Knowledge

Financial

& Tech.

Resources

Present

Workload

Safety

Performance

5th

Root

of

Product

Priority

Vector

(PV)

Past

Experience 1.000 0.333 0.500 2.000 3.000 1.000 0.193

Technical

Knowledge 3.000 1.000 2.000 3.000 2.000 2.048 0.394

Financial &

Tech.

Resources 0.200 0.500 1.000 0.500 0.500 0.478 0.092

Present

Workload 0.500 0.333 2.000 1.000 0.250 0.608 0.117

Safety

Performance 0.333 0.500 2.000 4.000 1.000 1.059 0.204

SUM 5.033 2.667 7.500 10.500 6.750 5.193 1.000

SUM*PV 0.969 1.051 0.691 1.230 1.377

Lamda-max

(∑Sum*PV) 5.318

CI 0.079452

CR = CI/RI,

RI for 5 =

1.12 0.070939

The weights of criteria are derived by multiplying the values in each row together and

calculating the nth

root of said product and then normalizing the aforementioned nth root of

products to get the appropriate weights termed as priority vector. The priority vector values

are multiplied to sum of each column in the comparison matrix and the total of all the

“SUM*PV” values is calculated to derive the Lamda-max. Finally the Consistency Ratio (CR)

is calculated which shows that the pairwise comparison’s made are consistent. Also from the

priority vector value it can be concluded that the Technical Knowledge of the contractor is


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most important in contractor selection followed by Safety Performance, Past Experience,

Present Workload and lastly Financial and Technical Resources of the Contractor.

Once the consistency of the quality criteria is established, the next step involves selecting

the best contractor. As part of the study, three contactor’s data are used with the objective to

select the best out of the three contractors. In order to perform the selection process

effectively, a poll was conducted among stake holders in civil construction domain to provide

their preferences for the three contractors. From the perspective of each quality criteria, voters

were asked to provide their preferences for one contractor over the other. For ease of

presentation Contractor 1, Contractor 2 and Contractor 2 are represented as C1, C2 and C3 in

the paper. As an example, from the perspective of safety performance a voter preferred

“C1>C2>C3”, which meant that C1 was preferred more than C2 and C3 in terms of safety

performance. If a contractor is preferred over the other, then it wins 1 point over the non-

preferred contractor. The total scores of all the voters are considered similarly for quantitative

ratio derivation to frame comparison matrix. The voting results, comparison matrix and

priority vectors of contractor 1, contractor 2 and Contractor 3 are shown in the following

Table 4 and Figure 2 for the five quality criteria.

Table 4 Total scores of Contractors and Quantitative Ratios for five quality criteria.

For Past Experience Votes

For Technical

Knowledge Votes

For Fin. & Tech

Resources Votes

C1 preferred over C2 37.000 C1 preferred over C2 67.000 C1 preferred over C2 36


Quantitative Ratio

(C1/C2) 0.587

Quantitative Ratio

(C1/C2) 2.030

Quantitative Ratio

(C1/C2) 0.531

Quantitative Ratio

(C2/C1) 1.703

Quantitative Ratio

(C2/C1) 0.493

Quantitative Ratio

(C2/C1) 1.777



Quantitative Ratio

(C1/C3) 0.667

Quantitative Ratio

(C1/C3) 0.587

Quantitative Ratio

(C1/C3) 0.587

Quantitative Ratio

(C3/C1) 1.500

Quantitative Ratio

(C3/C1) 1.703

Quantitative Ratio

(C3/C1) 1.702



Quantitative Ratio

(C2/C3) 2.704

Quantitative Ratio

(C2/C3) 2.333

Quantitative Ratio

(C2/C3) 2.448

Quantitative Ratio

(C3/C2) 0.370

Quantitative Ratio

(C3/C2) 0.429

Quantitative Ratio

(C3/C2) 0.408

For Present Workload Votes For Safety Performance Votes

C1 preferred over C2 35.000 C1 preferred over C2 41.000


Quantitative Ratio

(C1/C2) 0.538

Quantitative Ratio

(C1/C2) 0.695

Quantitative Ratio

(C2/C1) 1.857

Quantitative Ratio

(C2/C1) 1.439



Quantitative Ratio

(C1/C3) 0.724

Quantitative Ratio

(C1/C3) 0.563

Quantitative Ratio

(C3/C1) 1.381

Quantitative Ratio

(C3/C1) 1.778



Quantitative Ratio

(C2/C3) 0.639

Quantitative Ratio

(C2/C3) 2.125

Quantitative Ratio

(C3/C2) 1.564

Quantitative Ratio

(C3/C2) 0.471



Figure 2 Calculation of Priority Vector and CR for Contractor 1, 2 and 3 for each quality criteria

The final ranking of the Contractors are computed following the traditional AHP based

approach using the above derived priority vectors for each quality criteria for the three

contractor options. The detailed derivation of the rankings is shown in Figure 2.

Figure 3 Final Ranking of Contractors in the Civil Engineering Project considering five quality

criteria.


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The final scores are calculated by multiplying the priority vectors of each quality criteria

with priority vectors of the contractor. The scores revealed Contractor 2 as the highest ranked

and most suitable option for construction engineering projects abiding all quality criterion of a

good contractor. Also the consistency Ratio values for all the five criteria factors are less than

0.10 which established the consistency of the judgement.

4. CONCLUSION

The proposed Condorcet voting theory based AHP in the paper successfully resolves the

weakness of the traditional AHP method due to use of standard importance scale based

derivation with chances of biased result. Selection of suitable contractor in a civil and

construction engineering domain is extremely critical considering multiple criteria for

contractor selection leading to dilemma and confusion. The use of Condorcet voting technique

for contractor preferences for each quality criteria followed by the quantitative ratio based

approach eliminates chances of such bias and anomaly in converting subjective judgement to

standard importance scale point. The final rankings of the contractor using the proposed

method could be considered more trust worthy in comparison to the traditional AHP based

approach. The same approach can be used to resolve multi-criteria decision making problems

in various other domains pertaining to selection and ranking of alternatives. As an extension

to the study, deep learning methods could be combined with the proposed approach to provide

more insight and reveal patterns and predictions on the same.

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A CONDORCET VOTING THEORY BASED AHP METHOD FOR … · The job of the contractors and suppliers ensures that the project is completed successfully meeting all quality and reliability