Research Article A Novel Hybrid MCDM Procedure...

Research ArticleA Novel Hybrid MCDM Procedure for Achieving AspiredEarned Value Project Performance

Shou-Yan Chou1 Chien-Chou Yu1 and Gwo-Hshiung Tzeng23

1Department of Industrial Management National Taiwan University of Science and Technology No 43 Section 4Keelung Road Taipei 106 Taiwan2Graduate Institute of Urban Planning College of Public Affairs National Taipei University No 151 University RoadSan Shia New Taipei City 23741 Taiwan3Institute of Management of Technology National Chiao Tung University No 1001 Ta-Hsueh RoadHsinchu 300 Taiwan

Correspondence should be addressed to Gwo-Hshiung Tzeng ghtzengmailntpuedutw

Received 30 December 2015 Revised 14 April 2016 Accepted 19 April 2016

Academic Editor Danielle Morais

Copyright copy 2016 Shou-Yan Chou et alThis is an open access article distributed under the Creative CommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

A better-performing project gains more subsequent businesses Many organizations worldwide apply an earned value management(EVM) system to monitor and control their projectsrsquo performance However a successful EVM application requires handlingmultiple interinfluenced criteria with feedback effects for decision-making and continuous improvements throughout theapplication life cycleThe conventional decision approaches assume that preferences between criteria are independent and put theirfocuses on decision-making This study employs a hybrid multiple criteria decision-making (HMCDM) method to devise a novelprocedure to fulfil the deficiencies The proposed procedure enables us to evaluate interinfluence effects and gap indices amongcriteriadimensionsalternatives and then systemize the evaluation results in a context of influential network relation map (INRM)The INRM provides managers with visual information to find a route in making application decisions while identifying criticalgaps for continuous improvements A numerical example is presented to illustrate the applicability of the proposed procedureTheresults show that by employing the HMCDM method the proposed procedure can provide organizations with a foundation toensure that the aspired EVM application outcomes are achieved at different levels within an organization

1 Introduction

A project is ldquoa temporary endeavor undertaken to transformlimited resources into a unique product service or resultrdquo inorder to satisfy the needs of society users and customers [1]A better-performing project gainsmore subsequent business-es and is ultimately of strategic importance to an organization[2 3] To attain high performances many organizationsworldwide apply an earned valuemanagement (EVM) systemto monitor and control their projects [4 5] A successfulEVM application enables us to produce reliable performanceindices at initial stages of a project as early as 15 to 20 percentof the project process [6 7] thus allowing organizations tounderstand project health predict future trends and takerequired control actions to minimize deviations thereby

attaining the aspired performances throughout the projectlife cycle [8ndash10]

According to Kim et al [11] EVM application can beformulated as a multiple criteria decision-making (MCDM)problem which requires experts to analyze a set of interin-fluenced application criteria with feedback effects through-out the application process Some of these criteria includethe following using information systems to report projectprogress in an accurate and timely manner [11] using aproject management process to break down the project scopeand organizational structure [7] training stakeholders in theeffective use of EVM [12] and providing ongoing efforts toimprove the application of EVM [10] According to Flemingand Koppelman [7] a lack of accurate understanding ofthe above-mentioned interinfluenced criteria can lead to

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2016 Article ID 9721726 16 pageshttpdxdoiorg10115520169721726

2 Mathematical Problems in Engineering

a series of shortcomings in the implementation of an EVMKwak and Anbari [5] have also noted that without adequateanalysis upfront even after an application decision has beenconceived and implemented unanticipated efforts will berequired to solve new problems as the implementation pro-ceedsThese studies demonstrate the importance of adoptinga systematic procedure to analyze interinfluenced criteriaassociated with the EVM application decision Additionallyto obtain aspired application outcomes continuous improve-ments should be also early considered in order to preventthe selected decisions from producing negative outcomes[2 13 14]

However according to the literature review of this studymost traditional MCDM approaches assume that the pref-erences between decision variables are independent andput their emphasis on evaluation and selection of decisionalternativeswithout addressing practicalmeans to implementrequired improvements [15ndash20] Yet as discussed previouslyEVM application requires a decision approach that addressesthese issues Consequently this study employs a hybrid mul-tiple criteria decision-making (HMCDM) method to devisea novel procedure to fulfil the above-mentioned deficienciesThe HMCDM method contains a decision-making trial andevaluation (DEMATAEL) technique [21] aDEMATEL-basedanalytical network procedure (DANP) [22] and a mod-ified multicriteria optimization and compromise solution(ViseKriterijumska Optimizacija I Kompromisno Resenje inSerbian VIKOR) method [23] This combined approach wasintroduced by Tzeng [17] as a new trend of decision-makingRecently it has been successfully applied in different businessfields to solve and improve complex and interdependent real-world problems [18 22 24ndash27] and is thus examined in thisstudy

The proposed novel procedure uses expertsrsquo judgmentsto model interdependent EVM application problems witha decision framework considering improvement require-ments The procedure then employs the HMCDM methodto quantify gap indices with respect to aspiration levels ofEVM application based on interinfluence effects among fac-torsdimensionsalternatives within the decision frameworkFinally the HMCDM method systemizes the quantitativeresults in the context of influential network relation maps(INRM) The INRM helps managers find a route for EVMapplication decisions while identifying critical gaps for priorimprovements throughout the life of the decisions implemen-tation A numerical example is presented to illustrate how theproposed procedure operates in practice The results showthat by employing the HMCDMmethod the proposed pro-cedure can provide organizations with a foundation to ensurethat the aspired EVM application outcomes are achievedat different levels within an organization The remainder ofthis paper is organized as follows In Section 2 the EVMliterature is reviewed in relation to the proposed procedurein Section 3 essential concepts of the HMCDM model arepresented and the proposed procedure is introduced inSection 4 a numerical example showing the applicability ofthe proposed procedure is presented and main findings arediscussed conclusions are provided in the final section

2 The Literature Review aboutEarned Value Management

This section briefly reviews research literature associatedwith EVM application and then identifies the dimensionsand factorscriteria for establishing a decision frameworkin formulating the proposed procedure for pursuing theaspiration levels of EVM application through better decision-making and continuous improvements

The EVM was originally developed as a technique bythe United States Department of Defense (DoD) in the1960s to manage the financial aspects of major acquisitionprojects In 1967 the DoD adopted the 35 standardizedEVM managerial criteria defined by the United StatesAir Force as the Cost Schedule Control System Criteria(CSCSC) This regulatory system was used by the DoD andits contractors to monitor and control various projects overthe next three decades [7] In 1996 the National DefenseIndustrial Association reduced the EVM criteria to a totalof 32 which were formally accepted by ANSIEIA in 1998 intheir publication of the ANSIEIA 748-98 standard knownas EVM system [6] During the following year the ProjectManagement Institute (PMI) adopted EVM as a managerialtool and technique to monitor projects as stated in itspublication titled A Guide to the Project Management Bodyof Knowledge (PMBOKGuide) and subsequently describedin a separate publication Practice Standards for EarnedValueManagementThese publications and the promotion of EVMprinciples including their regulation standardization andsimplification have led to increasing interest in the useand development of innovative applications of EVM amongorganizations and experts worldwide [3 5 6 8 11]

However while EVM has been widely accepted as oneof the most pragmatic systems for managing project perfor-mances in both public and private organizations the studieshave also noted that the development of EVM elements andthe wide acceptance of EVM do not in themselves guaranteethat the EVM application will be successful for projects in allorganizations [2 6] Some of the common issues arising inprojects managed through EVM in different organizationsincluding the US government and its subsidiary agenciesinclude overbudgeting schedule delays and unsatisfactoryperformance [5 11] These phenomena indicate that evenin organizations with long-term operational experiencethe implementation of EVM can result in deviations fromorganizationsrsquo aspiration level [7] Hence the subject of theeffective EVM application requires further study to assistorganizations in obtaining intended outcomes In particularorganizationmust enable us to assess the current capability ofeach subordinate unit to understand whether EVM applica-tion decisions could eventually help the unit to bettermanageproject performance What application factors should be inplace for each unit to apply EVM and to avoid the needfor unintended efforts during the implementation of EVMdecisions Furthermore if the EVM application is justified asinappropriate then how can each unit improve its weaknessto facilitate benefits through EVM application in the future

According to the American National Standards InstituteElectric Industries Association a reliable EVM application

Mathematical Problems in Engineering 3

should consider 32 criteria belonging to five categories (1)organization (2) planning and budgeting (3) accounting(4) analysis and revision and (5) data maintenance [28]Fleming and Koppelman [7] who conducted research onmany software projects proposed ten ldquomust-havesrdquo thatare required to fully grasp and apply the critical earnedvalue concept in enhancing the management of all types ofprojects in an industry These ten ldquomust-havesrdquo require thecomplete definition of a projectrsquos scope of work using a workbreakdown structure (WBS) at the outset of project planningas well as through the continuous management of all changesduring project execution Another study by Kwak and Anbari[5] based on the National Aeronautics and Space Association(NASA) indicated that key success factors for the imple-mentation of EVM included the early introduction of EVMthe full involvement of users and consistent communicationwith all stakeholders Lipke [10] argued that the elementsrequired for executing projects and facilitating continuousimprovement are necessary ingredients for EVM applicationto ensure successful project outcomes These studies haveprovided useful information for understanding the factorsinfluencing the successful EVM application from differentperspectives but lack an integrated or systematic procedurefor analyzing level of readiness of these factors when makingapplication and improvement decisions

Stratton [12] proposed a five-stepmaturemodel of earnedvalue management to enhance the quality and use of EVMwithin an organization This model can be linked to theANSIESI standard 748 to create assessment matrices thathelp users to evolve an EVM within their own organizationsand to assess the relative strengths of various EVM appli-cations This study has focused on developing a systematicprocedure for analyzing effectively EVM implementationwhile assuming the independence of the factors in theassessment matrices This assumption conflicts with the real-world application situations discussed in many other studies[3 5 10]

A more comprehensive study by Kim et al [11] used sur-veys mailed to 2500 individuals and on-site case studies con-ducted within six organizations and concluded that approx-imately 40 interactive factors in four dimensions (the EVMuser the EVM methodology the implementation processand the project environment) could influence significantlythe EVM application in four ways (1) accepting the concept(2) applying EVM by project managers and team members(3) enabling projects to be completed within constraints andwith satisfactory performance and (4) bringing overall sat-isfaction to users of this methodology The study concludedby proposing an implementation framework to assist bothindustrial and government agencies applying EVM moreeffectively for different sizes and types of projects Howeverthe proposedmodel and frameworkwere qualitative in natureand did not provide a systematic mean to quantitativelyanalyze interrelated effects among the dimensionsfactors forapplication decisions and management actions

According to the literatures discussed above the fac-torscriteria influencing the effective EVM application canbe grouped into four dimensions the EVM user the EVMmethodology the implementation process and the project

environment Each dimension contains respective factors asshown in Table 1 In the next section a novel procedurebased on the HMADM method is proposed to evaluate andanalyze these interdependent application dimensionsfactorsin relation to the selection and improvement of applicationdecisions with the goal of obtaining aspiration levels of EVMapplication

3 The Proposed Procedures for Obtainingthe Aspiration Levels of EVM Application

To explain the proposed procedure this section first brieflyintroduces the essential concepts related to the HMCDMmodel that combines the following elements DEMATELtechnique DEMATEL-base ANP andmodifiedVIKOR sub-sequently this section discusses how the model is employedto develop the proposed procedure

The HMCDM model was proposed by Tzeng [17] whocombined new concepts and techniques to handle complicateand dynamic real-world problems First theHMCDMmodelemploys the DEMATEL technique to quantify interinfluenceeffects among decision variables and visualize the effects onan influential network relationmap (INRM)TheDEMATELtechnique was developed by the Battelle Geneva Institute in1972 for assessing and solving complex groups of problems[29] This technique used Boolean operation and MarkovProcess to quantify cause and effect relationships on eachdimensioncriterion within a system (or subsystem) Quan-titative values results are then systemized on a single mapshowing degree and direction that each dimensioncriterioncan influence each other and to the overall system per-formance [30] The interinfluence values of DEMATELcan not only help managers gain valuable information forunderstanding specific societal problems but also be furtherused with other methods to obtain more precise weight-ing values and gap indices in dealing with the real-worlddecision and improvement problems [21 31] Second thismodel provides a procedure known as DANP that appliesa basic concept of the analytic network procedure (ANP)to transform the interinfluence value of DEMATEL intoinfluential weights (IWs) for prioritizing decision variablesANP was proposed by Saaty [32] to address interdependenceand feedback among the factors dimensions or alternativesassociated with a decision-making problem However ANPassigns identical weights for each cluster per group on thenormalized supermatrix neglecting the influence in differentdegree DANP used DEMATEL technique to adjust the ANPequal weighting assumption for better communication ofreal interdependent situations and improvement alternativesand decisions [22 31] These features avoid the assumptionof traditional decision models such as AHP TOPSIS pathanalysis and SEM that the value creation criteria are inde-pendently and hierarchically structured thereby enablinginterdependent decision situations to be viewed as decisionprocess and outcomes [18]

Third this model adopts the principle of ldquoaspirationlevelsrdquo [33] to replace the traditional maxmin approach [1534] through a modified VIKOR method when choosing


Table 1 Evaluation factors and dimensions

Dimensionsfactors DescriptionsEVM users (119863

1)

Experience (1198621) Experience in using EVMS

Training (1198622) Training at school and on-job training to understand how to use

EVMSAdministrative capabilities (119862

3) Administrative expertise of project managers

Technical capabilities (1198624) Technical expertise of project managers

Changes in work contents (1198625) Acceptance of power shift after implementing EVMS

EVM methodology (1198632)

WBS (1198626) Using work breakdown structure (WBS) details project scopes

CPM (1198627) Using the Critical Path Method (CPM) as scheduling tool of

projects

IPT (1198628) Using Integrated Project Team (IPT) facilitates understanding

among project participantsComputer system (119862

9) Using automated computer system as part of EVMS process

Integrated project management (11986210) Using a project management system including EVMS

Implementation process (1198633)

Open communication (11986211) Open communications among project team players including

customersSufficient resources (119862

12) Provision of sufficient resources in the EVMS process

Top-down approach (11986213) Top management perceives EVMS as a pragmatic way in managing

project effectively

Integrated change control system (11986214) Using separated office to handle required changes justified by

EVMSContinuous improvement (119862

15) Providing ongoing efforts to improve application of the EVMS

Project management environment (1198634)

Colleague-based work environment (11986216) A colleague-based project management environment as opposed

to bureaucratic cultureOwnership of EVM to lower level project managers (119862

17) Flexibility allowed lower level project managers

Risk free (11986218) Allowing project players to select their own form of EVMS use

within a general frameworkCulture (119862

19) A strong trust and supportive culture in which project is performed

Regulations (11986220) Complete regulations for implementing EVMS

a relatively good solution from existing alternatives Thisfeature produces the size of performance gaps to aspirationlevels on each criteriondimensionalternative thus enablingmanagers to use a single value for both decision-makingand continuous improvements [25]The VIKORmethod wasproposed by Opricovic [35] to solve problems that involveincommensurable and conflicting factors Originally thismethod focused on analyzing a set of alternatives and select-ing a compromise solution closest to the ideal state [34] Theideal state was defined as a set of maximumminimum valuesrelating to each benefitcost criterion among all alternativesHowever these traditional compromises can entail ldquochoosingthe best among inferior optionsalternativesrdquo that is pick thebest apple in a barrel of rotten apples thus the traditionalprocedure has to entail ldquoimprovingrdquo the potential solutions[18] Hence Tzeng [17] proposed the modified VIKORmethod to replace the maximumminimum approach withldquoaspired-worstrdquo by setting 119891

lowast

119895= 10 and 119891minus

119895= 0 as the

aspiration level and the worst level respectively for criterion

119895 if performance scores with measuring range are from 0to 10 in questionnaires of each criterion as complete dis-satisfactionbad larr 0 1 2 4 5 6 8 9 10 rarr extremesatisfactiongood Recently this method has been used to aiddecisionmakers in identifying critical gaps in need of furtherimprovement [36 37]

Combining all these concepts and techniques theHMCDMmodel allowsmanagers to avoid ldquochoosing the bestamong inferior optionsalternativesrdquo (ie avoiding ldquopickingthe best apple among a barrel of rotten applesrdquo) [17] Moreimportantly the HMCDMmodel extends the evaluation andselection of decision functions to include identification ofcritical gaps for continuous improvement over the life ofdecision implementation [24 27 37] The detailed descrip-tions notations and computational processes can be foundin [17 19 26 38]

This study applies the HMCDM model to devise a novelprocedure for obtaining aspiration levels of EVM applica-tion through four main stages (1) form an expert team


Develop a decision framework

Compute initial-average influence relation matrix AExpert questionnaire

Form expert team

User questionnaire

Construct influentialnetwork relation map

INRM

Top management

Make decisions and determine strategies

for continuousimprovements

DEMATEL technique

DANP

Modified VIKOR methodCompute gap indices using Rl = Sl + (1 minus )Ql

the maximal regret using Ql = maxjrlj | j = 1 n

Normalize flj using rlj = (|flowast

jminus flj|)(|f

lowast

jminus f

minus

j|)

Set aspiration level and the worst level fminusj

f+

j

Performance values flj

Compute weighted supermatrix W120572= T120572

DW

Transpose into W = (T120572C)998400 Normalize into T120572

D

Normalize A into initial-influence matrix D = As

Compute total-influence matrix T = D(I minus D)minus1

Classify factors into correspondent dimension TC

Average each dimension into TDNormalize into T120572C

Compute influential weights (IWs) on factorsdimensions(W120572

)urArr w = (w1 wj wn)limurarrinfin

Compute the average value using Sl = sumn

j=1wjrlj and

Figure 1 A graphical representation of the proposed procedure

(2) develop a decision framework (3) systemize and visualizedecision information using HMCDM model and (4) makeapplication decisions and determine improvement strategiesbased on INRM A graphical representation of our procedureis depicted in Figure 1

As shown in Figure 1 the proposed procedure first formsan expert team (ET) through a top management commit-tee according to the predetermined qualifications Secondthe ET identifies influencing criteria to develop a noveldecision framework (Figure 2) which considers both thedecision-making and continuous improvements associatedwith an interrelated decision problem The decision frame-work developed in this stage is different from traditionalones which only consider decision-making Third based on

the decision framework the procedure uses the HMCDMmodel to evaluate systemize and visualize decision andimprovement information including the following comput-ing interinfluence effects using the DEMATEL techniquecomputing influential weights using DANP computing gapindices using modified VIKOR method and lastly sys-temizing the decision information obtained from the pre-vious steps on the visualized DEMATELrsquos INRM showingpreference of alternatives and how much improvement isrequired for each criterion and dimension associated witheach alternative Finally referring to the INRM the ETgains valuable information to finalize application decisionswith top management and stakeholders while determiningstrategies for continuous improvements in achieving the


Goal

Dimensions

Criteria(factors)

Alternatives

Gaps

Implementationprocess

Opencommunication

Sufficient resources

Top-down approach

Integrated changecontrol

Continuousimprovement

Unit 2

EVM users

Experience

Training

Administrativecapabilities

Technicalcapabilities

Changes in workcontents

EVMmethodology

WBS

CPM

IPT

Computersystem

Integratedproject

management

Unit 1

Projectenvironment

Colleague-basedwork environment

Ownership of EVMto lower level

project managers

Risk free

Culture

Regulations

z units in an organization

D1

D2 D3D4

C1

C2

C3

C4

C5

C6

C7

C8

C9

C10

C11

C12

C13

C14

C15

C16

C17

C18

C19

C20

U3 Uz

Unit 3 Unit zU1 U2

D1 D2

D3D4

C1 C2 C3

C4 C5

C6 C7 C8

C9 C10

C11 C12

C13

C14 C15

C16 C17

C18

C19 C20

Obtaining aspiration levels of EVM application across an organization for z units

Figure 2 The decision framework for EVM application

aspired EVM application outcomes in an organization In thenext section a numerical example is presented to illustratehow the proposed procedure operates in practice

4 A Numerical Example to Illustratethe Proposed Procedure

In this section we use an empirical example from a defenseorganization to illustrate the application of the proposedprocedure to a real-world problem To preserve confidential-ity all data related to the example have been transformedinto equivalent units by normalization which does notcompromise the analysis or gap measurement for each factor

and dimension and overall alternatives in order to reach thedesired aspiration levels

41 Problem Descriptions The Ministry of National Defense(MND) of a country has been experiencing difficultiesobtaining sufficient defense funding during the economicrecession and is consequently considering whether to applyEVM to its acquisition units to sustain superior defensecapacities with limited resources by ensuring better reg-ulation of the performance and progress of its projectsHowever the MND has many acquisition units As a resultof the multisourcing strategy adopted by theMND to acquireits projects from manufacturers in the US Europe and


the domestic market each unit exhibits certain differencesin infrastructure for the management of the projects fromdifferent sources These differences have made EVM appli-cation in the MND more complicated than in organizationswith mature or identical project management infrastructuresfor their subordinates To better manage this complicatedsituation theMND required a comprehensive and systematicevaluation to analyze select and improve the appropriatedecisions that would enable the aspired EVM applicationoutcomes to be achieved in the different units The MNDtherefore applied the proposed procedure in a pilot projectto assess two units and obtain satisfactory outcomes

42 Application of the Procedure Here we illustrate thestepwise process by which the MND applied our procedureto obtain application decisions and improvement strategies toassist subordinate units in determining how to accept and useEVM to manage project performances with aspired results

421 Form a Team The MND formed an ET with sevenexperts one from each of following sectors acquisitiontechnology manufacturing logistics end users procure-ment and finance All experts were selected based on theirproficiency in relation to EVM as assessed by a top manage-ment MND committee according to a set of predeterminedqualifications

422 Develop a Novel Decision Framework In this stage theET members identify 20 influencing factors as evaluationcriteria in 4 dimensions and develop a decision frameworkas shown in Figure 2

In Figure 2 the highest level of the decision frameworkis the goal obtaining aspiration levels of EVM applicationacross MND for two acquisition units (two alternatives)denoted by 119880

1and 119880

2 where two units also represent the

alternatives to be evaluated at the fourth level of the decisionframework The second and third levels contain dimensionsand factors (groups of interinfluence factors) used to evaluatethe alternatives The fifth and final levels include the gaps foreach dimension and factor to be measured in terms of how toreach aspiration levels through continuous improvements

423 Systemize and Visualize Decision Information UsingHMCDM Model In this stage the ET members firstemployed the DEMATEL technique to evaluate the interin-fluence effects among 20 factors within the DF and averagedthe results in an initial-average 20-by-20matrixA = [119886

119894119895]20times20

(Table 2)The initial-average matrix was further normalized as an

initial-influence matrixD (Table 3) using

D =A119904

= [119889119894119895]119899times119899

(1)

where 119904 = max(max1le119894le119899

sum119899

119895=1119886119894119895max1le119895le119899

sum119899

119894=1119886119894119895)

Subsequently throughmatrix operation using (2) a total-influence matrix T was obtained as in Table 4 In Table 4all factors in T were further classified into the corresponding

dimensions as matrix T119862 and each dimension was averaged

to obtain matrix T119863

T = D (I minus D)minus1

when lim119906rarrinfin

D119906 = [0]119899times119899 (2)

where I is an identity matrix D = [119889119894119895]119899times119899

0 le 119889119894119895

lt 1 0 lt

sum119899

119895=1119889119894119895

le 1 0 lt sum119899

119894=1119889119894119895

le 1 If the summation of at leastone column or one row (but not all) is equal to one then wecan guarantee that lim

119906rarrinfinD119906 = [0]

119899times119899

In matrix T the inconsistency rate (IR) of the evaluationresults from all experts was only 270 which is less than 5This result implied that the inclusion of an additional expertin this study would not influence the findings and that thesignificant confidence level is 9730

According toTable 4 the ET employedDANP to computethe influential weights (IWs) for the dimensions and factorsDuring this process the matrices T

119862and T

119863obtained

throughDEMATELwere normalized asT120572119862andT120572

119863 and then

we transposed matrix T120572119862into an unweighted supermatrix

W = (T120572119862)1015840 Subsequently T120572

119863was multiplied byW to obtain

a weighted supermatrix W120572 = T120572119863W as shown in Table 5

and finally multiplied by W120572 until it converged into IWs forfactors and dimensions as shown in Table 6

As shown in Table 6 the ET generally agreed that interms of the IWs of DANP all dimensions and factors havethe similar level of importance for effective EVM applicationHowever the DEMATEL results (Table 4) provide managerswith additional information to justify the level of interinflu-ence among factorsdimensions to achieve the aspired EVMapplication

After the DANP steps the ET administered a question-naire to collect the opinions of users at different units regard-ing the outcomes that their units can achieve through EVMapplication based on their current operational capabilitiesTypically the main components of the questionnaire canbe designed as shown in Table 7 set scores to evaluate therespective performance outcomes on a scale from 1 to 5 ldquoNA(1)rdquo ldquoA (2)rdquo ldquoAU (3)rdquo ldquoAUP (4)rdquo and ldquoAUPS (5)rdquo

In this case 18 and 20 respondents in 1198801and 119880

2were

interviewed respectively The ET averaged all responses asperformance value 119891

119897119895and then set the worst value 119891minus

119895= 1

and the aspiration level (best value) 119891lowast119895

= 5 Subsequentlythe modified VIKOR method was employed to compute thegap indices through using (3)sim(6)The computational resultsare summarized in Table 8

119903119897119895=

(10038161003816100381610038161003816119891lowast119895

minus 119891119897119895

10038161003816100381610038161003816)

(10038161003816100381610038161003816119891lowast119895

minus 119891minus119895

10038161003816100381610038161003816) (3)

119878119897=

119899

sum119895=1

119908119895119903119897119895 119897 = 1 2 119898 (4)

where 119908119895is the IWs of the factor from DANP

119876119897= max119895

119903119897119895| 119895 = 1 2 119899 119897 = 1 2 119898 (5)

119877119897= V (119878

119897) + (1 minus V) (119876

119897) (6)


Table 2 The initial-average matrix A obtained through the DEMATEL

A 1198621

1198622

1198623

1198624

1198625

1198626

1198627

1198628

1198629

11986210

11986211

11986212

11986213

11986214

11986215

11986216

11986217

11986218

11986219

11986220

1198621

0000 2857 2857 3429 3143 3286 2857 3000 2714 2571 2714 2143 3571 3571 3429 3000 2714 3000 2571 24291198622

2714 0000 3143 3857 2857 3429 3429 3429 2571 3286 2429 1857 2571 2857 3286 2714 2571 3000 2714 21431198623

2429 2000 0000 2143 2714 2286 2286 2571 2000 2571 2571 2429 2286 2571 2571 2143 2714 2857 2286 21431198624

3143 2286 2143 0000 2286 3429 3286 3429 3000 2571 2286 2143 2571 3000 3000 2857 3143 3286 2714 21431198625

2857 2286 2571 2429 0000 2429 1571 3000 2143 2857 3000 2143 2571 3286 3286 3000 2714 2857 3286 30001198626

3000 2429 2857 2571 2714 0000 3143 3143 2571 3429 3286 3000 3000 3429 3286 3143 3143 3000 2714 28571198627

2286 2286 2286 2714 2000 3143 0000 3286 2714 3000 2571 2571 2143 2429 2429 2143 2143 2000 2143 20001198628

2857 2429 2429 2714 2714 3429 3143 0000 2429 3000 3571 2714 3143 3143 3143 2857 2571 3000 3143 22861198629

2857 3286 3429 3429 2286 3571 3286 3571 0000 3571 2429 3143 2429 3000 3286 2714 2571 2286 2429 214311986210

2857 2429 2429 2714 2571 3286 3143 3143 2571 0000 2857 2000 2571 3429 2857 2714 2429 2571 2857 228611986211

3000 3286 2714 3143 2857 2857 3000 3286 2000 3286 0000 3000 2714 3571 3571 3000 3143 3143 3286 271411986212

2000 3143 2714 3000 2714 2429 2571 3143 2571 2857 3286 0000 2429 2857 3571 2714 2714 2714 2714 242911986213

2429 3143 2571 2714 2857 2714 2571 2571 2286 2714 2857 3286 0000 3571 2857 3571 3000 2857 3000 242911986214

2143 2286 3000 3143 2429 2857 2286 3000 2571 2571 2857 2429 2286 0000 3143 2143 2143 2286 2286 228611986215

3286 3429 3000 3286 2857 2571 2571 2857 2143 2857 3286 2714 2571 3429 0000 2714 2143 2857 2571 228611986216

3000 2571 2714 2571 3000 2714 2857 2571 2857 3000 3143 2571 2143 3143 3143 0000 3429 2714 3286 228611986217

3286 3000 2714 3000 2714 2714 2429 3286 2143 2714 2857 2714 2571 2857 3000 3286 0000 2857 2714 257111986218

3429 3286 3000 3571 3143 3000 2857 3143 2429 3000 3286 2571 2714 3143 3429 3000 3286 0000 3286 228611986219

3143 2571 3000 2857 3143 2429 2429 3286 1857 2714 3571 2286 3000 2714 3429 3000 3000 3714 0000 285711986220

2429 2857 3000 2571 2429 2143 2143 2429 1857 2429 2714 2286 2286 2571 2857 2429 2286 2571 3000 0000

Table 3 The initial-influence matrixD obtained through the DEMATEL

D 1198621

1198622

1198623

1198624

1198625

1198626

1198627

1198628

1198629

11986210

11986211

11986212

11986213

11986214

11986215

11986216

11986217

11986218

11986219

11986220

1198621

0000 0048 0048 0058 0053 0055 0048 0050 0046 0043 0046 0036 0060 0060 0058 0050 0046 0050 0043 00411198622

0046 0000 0053 0065 0048 0058 0058 0058 0043 0055 0041 0031 0043 0048 0055 0046 0043 0050 0046 00361198623

0041 0034 0000 0036 0046 0038 0038 0043 0034 0043 0043 0041 0038 0043 0043 0036 0046 0048 0038 00361198624

0053 0038 0036 0000 0038 0058 0055 0058 0050 0043 0038 0036 0043 0050 0050 0048 0053 0055 0046 00361198625

0048 0038 0043 0041 0000 0041 0026 0050 0036 0048 0050 0036 0043 0055 0055 0050 0046 0048 0055 00501198626

0050 0041 0048 0043 0046 0000 0053 0053 0043 0058 0055 0050 0050 0058 0055 0053 0053 0050 0046 00481198627

0038 0038 0038 0046 0034 0053 0000 0055 0046 0050 0043 0043 0036 0041 0041 0036 0036 0034 0036 00341198628

0048 0041 0041 0046 0046 0058 0053 0000 0041 0050 0060 0046 0053 0053 0053 0048 0043 0050 0053 00381198629

0048 0055 0058 0058 0038 0060 0055 0060 0000 0060 0041 0053 0041 0050 0055 0046 0043 0038 0041 003611986210

0048 0041 0041 0046 0043 0055 0053 0053 0043 0000 0048 0034 0043 0058 0048 0046 0041 0043 0048 003811986211

0050 0055 0046 0053 0048 0048 0050 0055 0034 0055 0000 0050 0046 0060 0060 0050 0053 0053 0055 004611986212

0034 0053 0046 0050 0046 0041 0043 0053 0043 0048 0055 0000 0041 0048 0060 0046 0046 0046 0046 004111986213

0041 0053 0043 0046 0048 0046 0043 0043 0038 0046 0048 0055 0000 0060 0048 0060 0050 0048 0050 004111986214

0036 0038 0050 0053 0041 0048 0038 0050 0043 0043 0048 0041 0038 0000 0053 0036 0036 0038 0038 003811986215

0055 0058 0050 0055 0048 0043 0043 0048 0036 0048 0055 0046 0043 0058 0000 0046 0036 0048 0043 003811986216

0050 0043 0046 0043 0050 0046 0048 0043 0048 0050 0053 0043 0036 0053 0053 0000 0058 0046 0055 003811986217

0055 0050 0046 0050 0046 0046 0041 0055 0036 0046 0048 0046 0043 0048 0050 0055 0000 0048 0046 004311986218

0058 0055 0050 0060 0053 0050 0048 0053 0041 0050 0055 0043 0046 0053 0058 0050 0055 0000 0055 003811986219

0053 0043 0050 0048 0053 0041 0041 0055 0031 0046 0060 0038 0050 0046 0058 0050 0050 0062 0000 004811986220

0041 0048 0050 0043 0041 0036 0036 0041 0031 0041 0046 0038 0038 0043 0048 0041 0038 0043 0050 0000


Table 4 The total-influence matrix T for factors T119862and for dimensions T

119863obtained through DEMATEL

T(T119862) 1198621

1198622

1198623

1198624

1198625

1198626

1198627

1198628

1198629

11986210

11986211

11986212

11986213

11986214

11986215

11986216

11986217

11986218

11986219

11986220

1198621

0379 0414 0419 0450 0416 0441 0415 0459 0369 0431 0438 0377 0411 0472 0475 0425 0412 0429 0418 03651198622

0416 0361 0416 0450 0405 0437 0418 0459 0361 0435 0427 0366 0389 0454 0465 0414 0403 0422 0413 03551198623

0351 0335 0307 0361 0345 0357 0341 0380 0300 0362 0367 0321 0328 0383 0388 0345 0347 0359 0347 03031198624

0410 0386 0388 0376 0384 0424 0403 0445 0357 0411 0412 0360 0377 0442 0447 0404 0400 0414 0401 03441198625

0395 0377 0386 0405 0338 0398 0367 0427 0335 0405 0413 0350 0368 0436 0441 0396 0384 0398 0400 03491198626

0432 0412 0424 0443 0415 0394 0424 0467 0371 0450 0453 0395 0407 0476 0479 0433 0424 0434 0425 03761198627

0354 0345 0349 0375 0339 0376 0309 0397 0316 0374 0372 0328 0331 0387 0391 0350 0343 0351 0350 03051198628

0418 0401 0405 0433 0403 0437 0413 0404 0359 0431 0445 0380 0398 0458 0464 0417 0404 0422 0420 03571198629

0423 0418 0426 0449 0401 0444 0421 0467 0324 0445 0432 0391 0392 0461 0471 0419 0408 0416 0414 035911986210

0398 0381 0386 0411 0382 0414 0393 0432 0344 0362 0413 0351 0370 0440 0437 0394 0382 0395 0395 034011986211

0438 0431 0427 0458 0423 0446 0428 0476 0367 0453 0407 0400 0408 0484 0490 0436 0429 0442 0440 037911986212

0390 0398 0396 0422 0389 0406 0390 0439 0348 0414 0425 0323 0373 0438 0454 0400 0392 0403 0399 034711986213

0406 0406 0402 0427 0400 0420 0399 0440 0352 0421 0428 0383 0342 0459 0453 0422 0405 0415 0413 035511986214

0363 0356 0371 0393 0357 0383 0357 0405 0323 0379 0388 0336 0344 0360 0415 0362 0354 0368 0363 031911986215

0415 0407 0405 0432 0397 0414 0396 0440 0347 0419 0431 0371 0381 0453 0404 0405 0388 0411 0402 034911986216

0413 0396 0403 0423 0401 0418 0402 0438 0359 0424 0431 0371 0376 0450 0456 0364 0410 0411 0415 035111986217

0416 0401 0401 0428 0395 0417 0394 0447 0347 0418 0425 0372 0381 0444 0452 0415 0354 0412 0405 035411986218

0447 0433 0434 0467 0430 0451 0428 0476 0376 0452 0461 0395 0410 0480 0491 0439 0434 0395 0442 037411986219

0424 0405 0416 0437 0412 0423 0404 0458 0351 0428 0447 0375 0398 0454 0470 0421 0412 0435 0372 036711986220

0362 0359 0366 0379 0351 0366 0349 0390 0307 0371 0380 0328 0339 0395 0404 0361 0351 0366 0369 0278T119863

1198631

1198632

1198633

1198634

1198631

0387 0397 0404 03861198632

0401 0399 0413 03891198633

0404 0403 0406 03921198634

0408 0404 0415 0388Note where 119905119901

119894119895and 119905119901minus1119894119895

denote the average influence of factor 119894 on 119895 according to 119901 = 7 and 119901 minus 1 = 6 experts respectively and 119899 = 20 denotes the number offactors thus the results above are significant at a significant confidence level of 9730 in gaps which is greater than the 95 level used to test for significancethat is IR = (11198992)sum119899

119894=1sum119899

119895=1(|119905119901

119894119895minus 119905119901minus1

119894119895|119905119901

119894119895) times 100 = 27 (0027) and significant confidence level = 1 minus IR = 9730

where 119897 = 1 2 119898 V is presented as the weight of thestrategy of maximum group utility (priority improvement)and 1 minus V is the weight of individual regret

As shown in Table 8 the gap indices for alternatives 1198801

and1198802are 0520 and 0739 respectivelyThese values revealed

the gap size that each unit would need to be improvedto reach the aspiration level These values imply that theEVM application with required continuous improvementswould enhance performance of the acquisition projects in119880

1

however the EVM application may not help 1198802to enhance

the performance of projects unless the current operationalcapabilities of 119880

2are further improved

Additionally the ET developed the INRM with the useof the results of the DEMATEL and the modified VIKORmethod (Tables 4 and 8) During this process using Table 4the ET computed the degree of total influence that a factorexerted on the other factors (sum of each row) 119903

119894 and the

degree of total influence that a factor received from the otherfactors (sum of each column) 119888

119894 The ET also derived 119903

119894+

119888119894 indicating the degree of the central role that respective

dimensionfactor 119894 plays in the system and 119903119894minus 119888119894 indicating

the degree of net influence that respective dimensionfactor119894 contributes to the system If 119903

119894minus 119888119894is positive then the

dimensionfactor 119894 affects other dimensionsfactors and if119903119894minus 119888119894is negative then the dimensionfactor 119894 is influenced

by other dimensionsfactorsThe results were summarized asshown in Table 9

In Table 9 the degree of the central role (119903119894+ 119888119894) of the

EVM users (1198631) the EVM methodology (119863

2) the imple-

mentation process (1198633) and the project management envi-

ronment (1198634) are 3174 3201 3243 and 3171 respectively

These values indicate that all members of the ET generallyagreed that all 4 dimensions play a central role in achievingthe MNDrsquos EVM application at aspiration levels Howeveramong the 4 dimensions the degree of net influence (119903

119894minus 119888119894)

on the project management environment (1198634) is 0060 and

an emphasis on this dimension is the basic requirement forthe MND to apply EVM in managing projects effectivelyThis finding also implies that if the project managementenvironment is not well established EVM application wouldbe affected negatively Table 9 also contains the interinfluenceeffects on factors showing valuable indications for better


Table 5 The weighted supermatrixW120572 derived from DANP

W120572 1198621

1198622

1198623

1198624

1198625

1198626

1198627

1198628

1198629

11986210

11986211

11986212

11986213

11986214

11986215

11986216

11986217

11986218

11986219

11986220

1198621

0045 0050 0051 0052 0051 0051 0050 0051 0050 0051 0051 0049 0050 0050 0051 0051 0051 0051 0051 00501198622

0049 0043 0049 0049 0049 0049 0049 0049 0049 0049 0050 0050 0050 0049 0050 0049 0050 0049 0049 00501198623

0049 0050 0044 0049 0050 0050 0050 0049 0050 0049 0049 0050 0050 0051 0050 0050 0050 0050 0050 00511198624

0053 0054 0052 0047 0052 0052 0053 0053 0053 0053 0053 0053 0053 0054 0053 0052 0053 0053 0053 00531198625

0049 0049 0050 0049 0044 0049 0048 0049 0047 0049 0049 0049 0049 0049 0049 0050 0049 0049 0050 00491198626

0053 0052 0052 0052 0052 0047 0053 0053 0053 0053 0052 0051 0052 0052 0052 0051 0052 0052 0051 00511198627

0050 0050 0049 0050 0048 0050 0043 0050 0050 0050 0049 0049 0049 0049 0049 0049 0049 0049 0049 00491198628

0055 0055 0055 0055 0056 0055 0056 0049 0055 0055 0055 0055 0054 0055 0055 0054 0055 0055 0055 00551198629

0044 0043 0044 0044 0044 0044 0044 0044 0038 0044 0042 0044 0043 0044 0043 0044 0043 0043 0043 004311986210

0051 0052 0053 0051 0053 0053 0053 0053 0053 0046 0052 0052 0052 0052 0052 0052 0052 0052 0052 005211986211

0052 0052 0053 0052 0053 0053 0053 0053 0052 0053 0047 0053 0052 0053 0053 0053 0053 0053 0054 005311986212

0045 0045 0046 0045 0045 0046 0047 0046 0047 0045 0046 0041 0047 0046 0046 0046 0046 0045 0045 004611986213

0049 0048 0047 0048 0047 0047 0047 0048 0047 0047 0047 0047 0042 0047 0047 0046 0047 0047 0048 004711986214

0056 0055 0055 0056 0056 0055 0055 0055 0055 0056 0056 0055 0056 0049 0056 0056 0055 0055 0054 005511986215

0056 0057 0056 0056 0056 0056 0056 0056 0057 0056 0057 0057 0056 0057 0050 0056 0056 0056 0056 005611986216

0051 0051 0050 0050 0050 0050 0050 0050 0051 0050 0050 0050 0051 0050 0051 0045 0051 0051 0050 005011986217

0049 0049 0050 0050 0049 0049 0049 0049 0049 0049 0049 0049 0049 0049 0048 0050 0044 0050 0049 004911986218

0051 0052 0052 0052 0051 0050 0050 0051 0050 0050 0051 0051 0050 0051 0051 0051 0051 0046 0052 005111986219

0050 0050 0050 0050 0051 0049 0050 0051 0050 0050 0051 0050 0050 0050 0050 0051 0050 0051 0045 005111986220

0044 0043 0044 0043 0044 0044 0044 0043 0043 0043 0044 0044 0043 0044 0044 0043 0044 0043 0044 0039

understanding critical elements in EVM application in dif-ferent units within MND

Based on Tables 8 and 9 the INRM was developed asshown in Figure 3 Taking the dimensions as an example (onthe top center in Figure 3) the 119909-coordinate is the degree ofcentral role 119903

119894+ 119888119894 and the 119910-coordinate is the degree of net

influence 119903119894minus119888119894 First we marked the coordinates of the EVM

users (1198631) the EVMmethodology (119863

2) the implementation

process (1198633) and the projectmanagement environment (119863

4)

which are (3174 minus0025) (3204 minus0001) (3243 minus0034)and (3171 0060) respectively The process then referred toTable 4 to determine the arrow directions based on the degreeof total influence between each dimension For instanceaccording to Table 4 the degree of total influence of EVMusers (119863

1) on the project management environment (119863

4) is

0386 conversely the degree of total influence of the projectmanagement environment (119863

4) on EVM users (119863

1) is 0408

The arrow direction is then drawn from project managementenvironment (119863

4) to EVMusers (119863

1) because 0408 is greater

than 0386 Likewise the influential directions among allthe dimensions and factors are determined and depictedaccordingly Additionally the ET marked the gap indiceson the INRM for factorsdimensions with respect to eachalternative based on Table 8

As shown in Figure 3 the INRM quantified and sys-temized the gap indices and the degree and direction ofinterinfluence effects among 20 factors within 4 dimensionsassociated with the aspired EVM application in the MNDTherefore it helps managers easily analyze EVM applicationsituations that are essential to make better application deci-sions For example the visualized interinfluence effects at the

dimensional level on the INRM(on the top center in Figure 3)revealed that the project management environment (119863

4) and

the EVM methodology (1198632) were prerequisites for qualified

EVM users (1198631) to implement an effective process (119863

3) to

achieve the aspired application outcome When adoptingthe same approach systematic information associated withdecisions to accomplish the aspired EVM application can berealized comprehensively

424 Make Application Decisions and Determine Improve-ment Strategies In this stage the ET arranged a series ofmeetings chaired by the MNDrsquos top management includingrepresentatives from related functional divisions All of theparticipants reviewed Tables 1ndash9 and with reference tothe INRM discussed application situations for each unitand which factors or dimensions should be prioritized forimprovements The participants also discussed the afford-ability and availability of the resources required for potentialimprovements The eventual outcome of these meetings wasto apply EVM at 119880

1and to delay its application in 119880

2until

the dimensions factors andor overall gaps for that unitcould be improved to a level below 0500 Additionally theparticipants determined the improvement strategies to beadopted including allocation of the priority of and respon-sibility for a set of improvement activities For instanceaccording to the size of the gap to the aspiration on thedimensions in Table 8 the ET classified the respectivedimensional levels for 119880

1and 119880

2in descending order as

follows 1198801 1198634(0518) ≻ 119863

3(0488) ≻ 119863

1(0408) ≻

1198632(0395) and 119880

2 1198634(0753) ≻ 119863

1(0653) ≻

1198633(0633) ≻ 119863

2(0600) These values revealed that the


Table6Th

einfl

uentialw

eightsob

tained

throug

hDANP

Influ

entia

lweightsforfactors(119862119895)d

imensio

ns(119863119895)

Factors

1198621

1198622

1198623

1198624

1198625

1198626

1198627

1198628

1198629

11986210

11986211

11986212

11986213

11986214

11986215

11986216

11986217

11986218

11986219

11986220

0050

0049

0050

0053

0049

0052

0049

0055

0043

0052

0053

0045

0047

0055

0056

0050

0049

0051

0050

0043

Dim

ensio

ns1198631

1198632

1198633

1198634

0250

0251

0256

0243


Table 7 Sample questionnaire responses

Factors States of outcome ScoresNA A AU AUP AUPS

Experience (1198621) x 1

Training (1198622) x 2

Administrative capabilities (1198623) x 3

Technical capabilities (1198624) x 4

Changes in work contents (1198625) x 5

Note ldquoNArdquo not available as score 1 ldquoArdquo accepted as score 2 ldquoAUrdquo accepted and used as score 3 ldquoAUPrdquo accepted used and enhanced performance as score 4ldquoAUPSrdquo accepted used and enhanced performance and satisfied all users as score 5

Table 8 Gaps indices obtained through the modified VIKOR method

Dimensionfactor Influential weights (IWs) Performance values The size of gap toaspiration level

Local Global 1198801

1198802

1198801

1198802

EVM users (1198631) 0250 0408 0653

Experience (1198621) 0201 0050 3350 1944 0413 0764

Training (1198622) 0196 0049 3750 2667 0313 0583

Administrative capabilities (1198623) 0198 0050 3550 2722 0363 0569

Technical capabilities (1198624) 0210 0053 3200 2778 0450 0556

Changes in work contents (1198625) 0195 0049 3000 1833 0500 0792

EVM methodology (1198632) 0251 0395 0600

WBS (1198626) 0206 0052 4000 2833 0250 0542

CPM (1198627) 0196 0049 3500 1722 0375 0819

IPT (1198628) 0218 0055 3300 2889 0425 0528

Computer system (1198629) 0173 0043 3100 3056 0475 0486

Integrated project management (11986210) 0207 0052 3200 2500 0450 0625

Implementation process (1198633) 0256 0488 0633

Open communication (11986211) 0205 0053 3000 3056 0500 0486

Sufficient resources (11986212) 0178 0045 2950 2056 0513 0736

Top-down approach (11986213) 0184 0047 3300 2444 0425 0639

Integrated change control system (11986214) 0215 0055 3350 2500 0413 0625

Continuous improvement (11986215) 0218 0056 2650 2278 0588 0681

Project management environment (1198634) 0243 0518 0753

Colleague-based work environment (11986216) 0206 0050 3000 1722 0500 0819

Ownership of EVM to lower level projectmanagers (119862

17) 0201 0049 2900 2278 0525 0681

Risk free (11986218) 0208 0051 2800 1833 0550 0792

Culture (11986219) 0206 0050 2750 2389 0563 0653

Regulations (11986220) 0178 0043 3200 1722 0450 0819

Gap indices 0520 0739

project management environment (1198634) was a problem that

arose for both 1198801and 119880

2 In addition with reference to

the INRM 1198634(3171 0060) was located in the cause group

thus improvements in the project management environment(1198634) would have the greatest effects in terms of improving

the other dimensions and the selected application decisionsFurthermore the INRM (Figure 3) showed that all fivefactors under the project management environment (119863

4)

also belonged to the cause group the colleague-based workenvironment119862

16(16132 0091) ownership of EVMby lower

level project managers 11986217

(15913 0241) being risk free11986218

(16817 0616) culture 11986219

(16310 0305) and regula-tions 119862

20(14095 0245) These values suggested that all

factors under the project management environment (1198634)

should be accorded top priority for improvement and that theMND should be able to achieve the strongest improvementeffects Additionally with the cross-referencing of Table 8and the INRM the factors needing prior improvements inthe respective units were as follows 119880

1 sufficient resources

(11986212) and open communication (119862

11) in the dimension of


Table 9 The total influence given and received on dimensions and factors obtained through DEMATEL

Dimensionfactor 119903119894

119888119894

119903119894+ 119888119894

119903119894minus 119888119894

EVM users (1198631) 1574 1600 3174 minus0025

Experience (1198621) 8416 8046 16463 0370

Training (1198622) 8265 7821 16086 0445

Administrative capabilities (1198623) 6928 7925 14853 minus0997

Technical capabilities (1198624) 7984 8418 16402 minus0434

Changes in work contents (1198625) 7768 7785 15552 minus0017

EVM methodology (1198632) 1602 1602 3204 minus0001

WBS (1198626) 8532 8265 16796 0267

CPM (1198627) 7040 7850 14890 minus0810

IPT (1198628) 8269 8745 17014 minus0476

Computer system (1198629) 8382 6914 15296 1467

Integrated project management (11986210) 7819 8287 16106 minus0467

Implementation process (1198633) 1605 1639 3243 minus0034

Open communication (11986211) 8660 8393 17053 0266

Sufficient resources (11986212) 7946 7272 15218 0674

Top-down procedure (11986213) 8148 7523 15671 0625

Integrated change control system (11986214) 7298 8826 16124 minus1528

Continuous improvement (11986215) 8067 8948 17015 minus0881

Project management environment (1198634) 1615 1555 3171 0060

Colleague-based work environment (11986216) 8111 8020 16132 0091

Ownership of EVM to lower level project managers (11986217) 8077 7836 15913 0241

Risk free (11986218) 8716 8101 16817 0616

Culture (11986219) 8308 8003 16310 0305

Regulations (11986220) 7170 6925 14095 0245

implementation process (1198633) and119880

2 experience (119862

1) in the

dimension of EVM use (1198631) sufficient resources (119862

12) in the

dimension of implementation process (1198633)These factors are

classified as part of the cause group and the size of their gapsis greater than that of the other factors In a similar fashionthe improvement strategies were determined accordingly

43 Discussions and Implications Several critical results werederived from the above-described numerical example andfrom the discussion with the ET members concerning theEVM application First according to the DEMATEL results(Tables 5 9 and Figure 3) the interdependent relationshipsamong 20 factors and 4 dimensions can influence the aspiredEVM application outcomes This finding is consistent withthe arguments made by many studies that a set of interin-fluenced criteria would significantly influence the effectiveEVM application and ultimately project performance [511] However using the DEMATEL technique can analyzesystemize and visualize these interdependencies in a singlepicture thus revealing the degree and direction of interinflu-ence effects that each dimension and factor would exert onone another and on the aspired EVM application outcomesConsequently for users to be satisfied with the use of EVM toenhance their project performance organizations require adeep understanding of these interrelationships when makingapplication decisions Additionally using the DEMATELtechnique can help managers to better analyze and under-stand interdependent application situations in detail

Second according to the results from the modifiedVIKOR method with the IWs of the DANP (Table 8)decisions regarding the MNDrsquos application of EVM maydiffer for different units in terms of their capabilities in themanagement of different projects The results confirm thatthe development of EVM elements and the wide acceptanceof EVM worldwide may not guarantee that EVM applicationwill be successful for all projects in all organizations In otherwords organizations will use a systematic procedure to thor-oughly analyze application situations at different levels whenmaking suitable application decisions for all units within anorganization The members of the ET emphasized the factthat the numerical results from the modified VIKORmethodand the DANP were essential for the MND which had noprior experience in applying the EVMand encounteredmanydifferent application situations in each subordinate unit Ifthe HMCDM procedure had not been used the applicationdecisions would have been identical for all units once topmanagement had made the decision to apply EVM

Third according to the DANP results (Table 7) amongthe 20 factors continuous improvement (119862

15) an integrated

change control system (11986214) and an integrated product

team (IPT) (1198628) are prioritized as the top three factors

with IWs of 0056 0055 and 0055 respectively This resultechoes the findings obtained from the previously reviewedstudies indicating that the EVM application is not merelythe delivery of a system in an organization [11] Rather thereis considerable potential for improvement which includes


EVM users (D1)EVM methodology (D2)

Implementation process (D3)Project management environment (D4)

D4 (3171 0060)Gaps

U1 0518U2 0753

minus004

minus002

000

002

004

006

316

INRM_dimensions

D1 (3174 minus0025)Gaps

U1 0408U2 0653


U1 0395U2 0600


U1 0488U2 0633

317 318 319 320 321 322 323 324 325

riminusc i

ri + ci

(a)

INRM_factors in D1

Experience (C1)Training ( )C2

Administrative capabilities (C3)

Technical capabilities ( )C4

change work contents (C5)

minus104

minus074

minus044

minus014

016

046

1450 1500 1550 1600 1650 1700

C2 (16086 0445)Gaps

U1 0313U2 0583

C4 (16402 minus0434)Gaps

U1 0450U2 0556


U1 0343U2 0569

C1 (16463 0370)Gaps

U1 0413U2 0764


U1 0500U2 0792

riminusc i ri + ci

(b)

riminusc i

ri + ci

INRM_factors in D2

WBS ( )C6

CPM ( )C7

IPT (C8)

)Computer system (C9Integrated project management (C10)

minus090

minus040

010

060

110

160

147 152 157 162 167 172

C9 (15296 1467)Gaps

U1 0475U2 0468

C6 (16796 0267)Gaps

U1 0250U2 0542


U1 0450U2 0625


U1 0374U2 0819


U1 0425U2 0528

(c)

riminusc i ri + ci

070

1510 1560 1610 1660 1710


U1 0413U2 0625

C12 (15218 0674)Gaps

U1 0513U2 0736


U1 0588U2 0681

C13 (15671 0625)Gaps

U1 0425U2 0639

C11 (17503 0266)Gaps

U1 0500U2 0486

minus180

minus130

minus080

minus030

020

INRM_factors in D3

Sufficient resources (C12)

Integrated change control system (C14)Top-down approach (C13)

Open communication (C11)

Continuous improvement (C15)

(d)

riminusc i

ri + ci

INRM_factors in D4

Risk free (C18)

Regulations (C20)Culture (C19)

Ownership of EVM to lower level project managers (C17)Colleague-based work environment (C16 )

C18 (16817 0616)Gaps

U1 0550U2 0792

C19 (16310 0305)Gaps

U1 0563U2 0653

C15 (16132 0091)Gaps

U1 0500U2 0819

C17 (15913 0241)Gaps

U1 0525U2 0681

C20 (14095 0245)Gaps

U1 0450U2 0819

1390 1440 1490 1540 1590 1640 1690

000

030

060

(e)

Figure 3 The INRM


continuing to identify weaknesses in EVM and regard themas opportunities for improvements [5] Additionally accord-ing to the results of the modified VIKOR method (Table 8)each dimensionfactor can create different sizes of gaps toimpact aspired EVM application in each acquisition unit(alternative) However the proposed procedure based on theHMCDM model combining the DEMATEL technique theDANP and the modified VIKOR method enables a cross-functional team to analyze capability gaps with respect todimensionsfactors of respective application units Analyzingthese gaps is useful in developing strategies to enable eachapplication unit to take the most influential improvementactions to facilitate the EVM application decisions and toensure the aspired results

Finally based on the above example we argue thatwithout the full support and participation of the variousunits within an organization the proposed approach couldnot have been applied in the pragmatic manner describedabove In particular in the MND case it is essential tohave a small ET (with five to seven members) that includesgenuine experts with full authorization from the topmanage-ment to handle the application project on a full-time basisldquoGenuine expertsrdquo refer to experts who are committed totaking the appropriate actions when rendering their opinionsand judgments regarding the EVM application In additionthe end users who apply the EVM must have progressiveintentions to pursue performance improvement in theirprojects Overall the EVM application is not an easy taskindeed it involves an array of interdependent variables thatinfluence the application processes and outcomesThis exam-ple however has demonstrated that the procedure based onthe HMCDM model combining the DEMATEL techniquethe DANP and the modified VIKOR method can not onlybetter address application problems but also easily identifycritical factors that are highly influential in solving EVMapplication problems to achieve the aspiration level

5 Conclusions

Although EVM has been widely accepted and applied tomanage project performance in different types of organiza-tions worldwide many studies have indicated that a set ofinterdependent application factors can influence the EVMapplication process and outcomes This study proposed anovel procedure based on the HMCDM method enablingorganizations to obtain aspired outcomes through betterdecision-making and continuous improvements over the lifeof the application process

A numerical example was used to demonstrate the appli-cability of the proposed procedure The results showed thefollowing merits of this study (1) it alone measures theinterinfluence effects and gap indices to support decision-making and continuous improvements in pursuing aspiredEVM application outcomes (2) the traditional concept ofldquoeffective EVM applicationrdquo is extended from ldquoillustrating ofsuccess factors and analysis framework for decision-makingrdquoto ldquoanalyzing selecting and improving selected decisionsover application life cyclerdquo and (3) managers obtain a visu-alized route showing decision information at different levels

within a decision framework allowing EVM application tobe adapted to different application situations existing withinthe organization These merits indicate that the proposedprocedure can provide a significant foundation for ensuringthat aspiration levels of EVM application are achieved atdifferent levels in an organization

This study has several limitations First the dimensionsand factors used to establish the decision framework for theproposed procedure were obtained from a limited reviewof the literature thus this study may have excluded otherpotential influences on the decision process associated withthe effective EVM application Further research could useother approaches such as interviews or case studies to selectadditional factors and explore the differences and similaritiesbetween these approaches Second the conclusions drawnare based on a case from a national defense organizationThus future research could apply our procedure to othercases such as organizations in the private sector to examineour procedure across a wider range of application situationsthus making comparisons to gain additional insights into theusefulness of the proposed procedure Finally the improve-ment strategies determined from our procedure are a set ofstrategic guidelines Future research can identify substantialimprovement activities This work can be characterized asan MODM problem and future research can adopt theDINOV method with a changeable objective and decisionspaces to obtain more valuable improvement outcomesThese limitations provide directions for future research tobroaden the applicability of the proposed procedure

Competing Interests

The authors declare that they have no competing interests

References

[1] PMI A Guide to the Project Management Body of KnowledgeProject Management Institute Newtown Square Pa USA 5thedition 2013

[2] J R Meredith S M Shafer S J Mantel and M M SuttonProject Management in Practice John Wiley amp Sons HobokenNJ USA 5th edition 2013

[3] J K Pinto Project Management Achieving Competitive Advan-tage PearsonPrentice Hall Upper Saddle River NJ USA 2007

[4] J Batselier and M Vanhoucke ldquoEvaluation of deterministicstate-of-the-art forecasting approaches for project durationbased on earned value managementrdquo International Journal ofProject Management vol 33 no 7 pp 1588ndash1596 2015

[5] Y H Kwak and F T Anbari ldquoHistory practices and future ofearned value management in government perspectives fromNASArdquo Project Management Journal vol 43 no 1 pp 77ndash902012

[6] F T Anbari ldquoEarned value project management method andextensionsrdquo Project Management Journal vol 34 no 4 pp 12ndash23 2003

[7] Q W Fleming and J M Koppelman Earned Value ProjectManagement Project Management Institute Newtown SquarePa USA 2nd edition 2000


[8] J Colin and M Vanhoucke ldquoSetting tolerance limits for statis-tical project control using earned value managementrdquo Omegavol 49 pp 107ndash122 2014

[9] J-S Lee ldquoCalculating cumulative inefficiency using earnedvalue management in construction projectsrdquo Canadian Journalof Civil Engineering vol 42 no 4 pp 222ndash232 2015

[10] W Lipke ldquoIs something missing from project managementrdquoCrosstalk The Journal of Defense Software Engineering pp 16ndash19 2013

[11] E Kim W G Wells Jr and M R Duffey ldquoA model for effectiveimplementation of Earned Value Management methodologyrdquoInternational Journal of Project Management vol 21 no 5 pp375ndash382 2003

[12] R W StrattonThe Earned Value Management Maturity ModelManagement Concepts Inc Vienna Austria 2006

[13] J Colin and M Vanhoucke ldquoA comparison of the performanceof various project control methods using earned value manage-ment systemsrdquo Expert Systems with Applications vol 42 no 6pp 3159ndash3175 2015

[14] P Rayner and G Reiss Portfolio and Programme ManagementDemystifiedManagingMultiple Projects Successfully RoutledgeNew York NY USA 2nd edition 2013

[15] K P Yoon and C L HwangMultiple-Criteria Decision MakingAn Introduction vol 104 Sage Thousand Oaks Calif USA1995

[16] R Ley-Borras ldquoDeciding on the decision situation to analyzethe critical first step of a decision analysisrdquo Decision Analysisvol 12 no 1 pp 46ndash58 2015

[17] J J H Liou ldquoNew concepts and trends of MCDM fortomorrowmdashin honor of Professor Gwo-Hshiung Tzeng on theoccasion of his 70th birthdayrdquo Technological and EconomicDevelopment of Economy vol 19 no 2 pp 367ndash375 2013

[18] J J H Liou and G H Tzeng ldquoComments on multiplecriteria decision making (MCDM) methods in economics anoverviewrdquo Technological and Economic Development of Econ-omy vol 18 no 4 pp 672ndash695 2012

[19] F-K Wang C-H Hsu and G-H Tzeng ldquoApplying a hybridMCDM model for six sigma project selectionrdquo MathematicalProblems in Engineering vol 2014 Article ID 730934 13 pages2014

[20] S H Zanakis A Solomon N Wishart and S Dublish ldquoMulti-attribute decision making a simulation comparison of selectmethodsrdquo European Journal of Operational Research vol 107no 3 pp 507ndash529 1998

[21] C-W Hsu T-C Kuo S-H Chen and A H Hu ldquoUsingDEMATEL to develop a carbonmanagement model of supplierselection in green supply chainmanagementrdquo Journal of CleanerProduction vol 56 pp 164ndash172 2013

[22] K Govindan D Kannan and M Shankar ldquoEvaluation ofgreen manufacturing practices using a hybrid MCDM modelcombiningDANPwith PROMETHEErdquo International Journal ofProduction Research vol 53 no 21 pp 6344ndash6371 2015

[23] J J H Liou C-Y Tsai R-H Lin and G-H Tzeng ldquoA mod-ified VIKOR multiple-criteria decision method for improvingdomestic airlines service qualityrdquo Journal of Air TransportManagement vol 17 no 2 pp 57ndash61 2011

[24] W-Y Chiu G-H Tzeng and H-L Li ldquoA new hybrid MCDMmodel combining DANP with VIKOR to improve e-storebusinessrdquo Knowledge-Based Systems vol 37 no 1 pp 48ndash612013

[25] Y-P Ou Yang H-M Shieh and G-H Tzeng ldquoA VIKORtechnique based on DEMATEL and ANP for informationsecurity risk control assessmentrdquo Information Sciences vol 232pp 482ndash500 2013

[26] G-H Tzeng and J-J Huang Multiple Attribute Decision Mak-ing CRC Press Boca Raton Fla USA 2011

[27] M-T Lu S-K Hu L-H Huang and G-H Tzeng ldquoEvaluatingthe implementation of business-to-business m-commerce bySMEs based on a new hybrid MADM modelrdquo ManagementDecision vol 53 no 2 pp 290ndash317 2015

[28] ANSI-EIA Earned Value Management Systems ANSI-EIA-748-98 A N S I E I Alliance American National StandardsInstitute Arlington Va USA 1998

[29] A Gabus and E Fontela World Problems an Invitation toAdditionally Thought within the Framework of DEMATELBattelle Geneva Research Center Geneva Switzerland 1972

[30] M-T Lu G-H Tzeng H Cheng and C-C Hsu ldquoExploringmobile banking services for user behavior in intention adop-tion using new hybrid MADMmodelrdquo Service Business vol 9no 3 pp 541ndash565 2015

[31] S Y Chou G H Tzeng and C C Yu ldquoA novel hybridmultiple attribute decision making procedure for aspired agileapplicationrdquo in Proceedings of the 22nd ISPE Inc InternationalConference on Concurrent Engineering Transdisciplinary Lifecy-cle Analysis of Systems vol 2 pp 152ndash161 July 2015

[32] T L Saaty Decision Making with Dependence and FeedbackTheAnalytic Network Process RWSPublications Pittsburgh PaUSA 1996

[33] H A Simon ldquoA behavioral model of rational choicerdquo TheQuarterly Journal of Economics vol 69 no 1 pp 99ndash118 1955

[34] S Opricovic and G-H Tzeng ldquoCompromise solution byMCDM methods a comparative analysis of VIKOR and TOP-SISrdquo European Journal of Operational Research vol 156 no 2pp 445ndash455 2004

[35] S Opricovic Multicriteria Optimization of Civil EngineeringSystems vol 2 Faculty of Civil Engineering Belgrade Serbia1998

[36] F-H Chen and G-H Tzeng ldquoProbing organization perfor-mance using a new hybrid dynamic MCDM method basedon the balanced scorecard approachrdquo Journal of Testing andEvaluation vol 43 no 4 pp 924ndash937 2015

[37] K-Y Shen M-R Yan and G-H Tzeng ldquoCombining VIKOR-DANPmodel for glamor stock selection and stock performanceimprovementrdquo Knowledge-Based Systems vol 58 pp 86ndash972014

[38] K W Huang J H Huang and G H Tzeng ldquoNew hybridmultiple attribute decision-making model for improving com-petence sets enhancing a companyrsquos core competitivenessrdquoSustainability vol 8 no 2 p 175 2016

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


a series of shortcomings in the implementation of an EVMKwak and Anbari [5] have also noted that without adequateanalysis upfront even after an application decision has beenconceived and implemented unanticipated efforts will berequired to solve new problems as the implementation pro-ceedsThese studies demonstrate the importance of adoptinga systematic procedure to analyze interinfluenced criteriaassociated with the EVM application decision Additionallyto obtain aspired application outcomes continuous improve-ments should be also early considered in order to preventthe selected decisions from producing negative outcomes[2 13 14]

However according to the literature review of this studymost traditional MCDM approaches assume that the pref-erences between decision variables are independent andput their emphasis on evaluation and selection of decisionalternativeswithout addressing practicalmeans to implementrequired improvements [15ndash20] Yet as discussed previouslyEVM application requires a decision approach that addressesthese issues Consequently this study employs a hybrid mul-tiple criteria decision-making (HMCDM) method to devisea novel procedure to fulfil the above-mentioned deficienciesThe HMCDM method contains a decision-making trial andevaluation (DEMATAEL) technique [21] aDEMATEL-basedanalytical network procedure (DANP) [22] and a mod-ified multicriteria optimization and compromise solution(ViseKriterijumska Optimizacija I Kompromisno Resenje inSerbian VIKOR) method [23] This combined approach wasintroduced by Tzeng [17] as a new trend of decision-makingRecently it has been successfully applied in different businessfields to solve and improve complex and interdependent real-world problems [18 22 24ndash27] and is thus examined in thisstudy

The proposed novel procedure uses expertsrsquo judgmentsto model interdependent EVM application problems witha decision framework considering improvement require-ments The procedure then employs the HMCDM methodto quantify gap indices with respect to aspiration levels ofEVM application based on interinfluence effects among fac-torsdimensionsalternatives within the decision frameworkFinally the HMCDM method systemizes the quantitativeresults in the context of influential network relation maps(INRM) The INRM helps managers find a route for EVMapplication decisions while identifying critical gaps for priorimprovements throughout the life of the decisions implemen-tation A numerical example is presented to illustrate how theproposed procedure operates in practice The results showthat by employing the HMCDMmethod the proposed pro-cedure can provide organizations with a foundation to ensurethat the aspired EVM application outcomes are achievedat different levels within an organization The remainder ofthis paper is organized as follows In Section 2 the EVMliterature is reviewed in relation to the proposed procedurein Section 3 essential concepts of the HMCDM model arepresented and the proposed procedure is introduced inSection 4 a numerical example showing the applicability ofthe proposed procedure is presented and main findings arediscussed conclusions are provided in the final section

2 The Literature Review aboutEarned Value Management

This section briefly reviews research literature associatedwith EVM application and then identifies the dimensionsand factorscriteria for establishing a decision frameworkin formulating the proposed procedure for pursuing theaspiration levels of EVM application through better decision-making and continuous improvements

The EVM was originally developed as a technique bythe United States Department of Defense (DoD) in the1960s to manage the financial aspects of major acquisitionprojects In 1967 the DoD adopted the 35 standardizedEVM managerial criteria defined by the United StatesAir Force as the Cost Schedule Control System Criteria(CSCSC) This regulatory system was used by the DoD andits contractors to monitor and control various projects overthe next three decades [7] In 1996 the National DefenseIndustrial Association reduced the EVM criteria to a totalof 32 which were formally accepted by ANSIEIA in 1998 intheir publication of the ANSIEIA 748-98 standard knownas EVM system [6] During the following year the ProjectManagement Institute (PMI) adopted EVM as a managerialtool and technique to monitor projects as stated in itspublication titled A Guide to the Project Management Bodyof Knowledge (PMBOKGuide) and subsequently describedin a separate publication Practice Standards for EarnedValueManagementThese publications and the promotion of EVMprinciples including their regulation standardization andsimplification have led to increasing interest in the useand development of innovative applications of EVM amongorganizations and experts worldwide [3 5 6 8 11]

However while EVM has been widely accepted as oneof the most pragmatic systems for managing project perfor-mances in both public and private organizations the studieshave also noted that the development of EVM elements andthe wide acceptance of EVM do not in themselves guaranteethat the EVM application will be successful for projects in allorganizations [2 6] Some of the common issues arising inprojects managed through EVM in different organizationsincluding the US government and its subsidiary agenciesinclude overbudgeting schedule delays and unsatisfactoryperformance [5 11] These phenomena indicate that evenin organizations with long-term operational experiencethe implementation of EVM can result in deviations fromorganizationsrsquo aspiration level [7] Hence the subject of theeffective EVM application requires further study to assistorganizations in obtaining intended outcomes In particularorganizationmust enable us to assess the current capability ofeach subordinate unit to understand whether EVM applica-tion decisions could eventually help the unit to bettermanageproject performance What application factors should be inplace for each unit to apply EVM and to avoid the needfor unintended efforts during the implementation of EVMdecisions Furthermore if the EVM application is justified asinappropriate then how can each unit improve its weaknessto facilitate benefits through EVM application in the future

According to the American National Standards InstituteElectric Industries Association a reliable EVM application














1)










projects










project effectively













lowast

119895= 10 and 119891minus

119895= 0 as the








Form expert team

User questionnaire


INRM

Top management



DEMATEL technique

DANP




jminus flj|)(|f

lowast

jminus f

minus

j|)


f+

j



DW


D








j=1wjrlj and






Goal

Dimensions

Criteria(factors)

Alternatives

Gaps


Opencommunication


Top-down approach



Unit 2

EVM users

Experience

Training




EVMmethodology

WBS

CPM

IPT

Computersystem

Integratedproject

management

Unit 1

Projectenvironment



project managers

Risk free

Culture

Regulations


D1

D2 D3D4

C1

C2

C3

C4

C5

C6

C7

C8

C9

C10

C11

C12

C13

C14

C15

C16

C17

C18

C19

C20

U3 Uz

Unit 3 Unit zU1 U2

D1 D2

D3D4

C1 C2 C3

C4 C5

C6 C7 C8

C9 C10

C11 C12

C13

C14 C15

C16 C17

C18

C19 C20














1and 119880




119894119895]20times20



D =A119904

= [119889119894119895]119899times119899

(1)


sum119899

119895=1119886119894119895max1le119895le119899

sum119899

119894=1119886119894119895)






D119906 = [0]119899times119899 (2)


0 le 119889119894119895

lt 1 0 lt

sum119899

119895=1119889119894119895

le 1 0 lt sum119899

119894=1119889119894119895


119906rarrinfinD119906 = [0]

119899times119899



119862and T

119863obtained


119863 and then









2were



119895= 1



119903119897119895=

(10038161003816100381610038161003816119891lowast119895

minus 119891119897119895

10038161003816100381610038161003816)

(10038161003816100381610038161003816119891lowast119895


10038161003816100381610038161003816) (3)

119878119897=

119899

sum119895=1

119908119895119903119897119895 119897 = 1 2 119898 (4)


119876119897= max119895

119903119897119895| 119895 = 1 2 119899 119897 = 1 2 119898 (5)

119877119897= V (119878

119897) + (1 minus V) (119876

119897) (6)



A 1198621

1198622

1198623

1198624

1198625

1198626

1198627

1198628

1198629

11986210

11986211

11986212

11986213

11986214

11986215

11986216

11986217

11986218

11986219

11986220

1198621

0000 2857 2857 3429 3143 3286 2857 3000 2714 2571 2714 2143 3571 3571 3429 3000 2714 3000 2571 24291198622

2714 0000 3143 3857 2857 3429 3429 3429 2571 3286 2429 1857 2571 2857 3286 2714 2571 3000 2714 21431198623

2429 2000 0000 2143 2714 2286 2286 2571 2000 2571 2571 2429 2286 2571 2571 2143 2714 2857 2286 21431198624

3143 2286 2143 0000 2286 3429 3286 3429 3000 2571 2286 2143 2571 3000 3000 2857 3143 3286 2714 21431198625

2857 2286 2571 2429 0000 2429 1571 3000 2143 2857 3000 2143 2571 3286 3286 3000 2714 2857 3286 30001198626

3000 2429 2857 2571 2714 0000 3143 3143 2571 3429 3286 3000 3000 3429 3286 3143 3143 3000 2714 28571198627

2286 2286 2286 2714 2000 3143 0000 3286 2714 3000 2571 2571 2143 2429 2429 2143 2143 2000 2143 20001198628

2857 2429 2429 2714 2714 3429 3143 0000 2429 3000 3571 2714 3143 3143 3143 2857 2571 3000 3143 22861198629

2857 3286 3429 3429 2286 3571 3286 3571 0000 3571 2429 3143 2429 3000 3286 2714 2571 2286 2429 214311986210

2857 2429 2429 2714 2571 3286 3143 3143 2571 0000 2857 2000 2571 3429 2857 2714 2429 2571 2857 228611986211

3000 3286 2714 3143 2857 2857 3000 3286 2000 3286 0000 3000 2714 3571 3571 3000 3143 3143 3286 271411986212

2000 3143 2714 3000 2714 2429 2571 3143 2571 2857 3286 0000 2429 2857 3571 2714 2714 2714 2714 242911986213

2429 3143 2571 2714 2857 2714 2571 2571 2286 2714 2857 3286 0000 3571 2857 3571 3000 2857 3000 242911986214

2143 2286 3000 3143 2429 2857 2286 3000 2571 2571 2857 2429 2286 0000 3143 2143 2143 2286 2286 228611986215

3286 3429 3000 3286 2857 2571 2571 2857 2143 2857 3286 2714 2571 3429 0000 2714 2143 2857 2571 228611986216

3000 2571 2714 2571 3000 2714 2857 2571 2857 3000 3143 2571 2143 3143 3143 0000 3429 2714 3286 228611986217

3286 3000 2714 3000 2714 2714 2429 3286 2143 2714 2857 2714 2571 2857 3000 3286 0000 2857 2714 257111986218

3429 3286 3000 3571 3143 3000 2857 3143 2429 3000 3286 2571 2714 3143 3429 3000 3286 0000 3286 228611986219

3143 2571 3000 2857 3143 2429 2429 3286 1857 2714 3571 2286 3000 2714 3429 3000 3000 3714 0000 285711986220

2429 2857 3000 2571 2429 2143 2143 2429 1857 2429 2714 2286 2286 2571 2857 2429 2286 2571 3000 0000


D 1198621

1198622

1198623

1198624

1198625

1198626

1198627

1198628

1198629

11986210

11986211

11986212

11986213

11986214

11986215

11986216

11986217

11986218

11986219

11986220

1198621

0000 0048 0048 0058 0053 0055 0048 0050 0046 0043 0046 0036 0060 0060 0058 0050 0046 0050 0043 00411198622

0046 0000 0053 0065 0048 0058 0058 0058 0043 0055 0041 0031 0043 0048 0055 0046 0043 0050 0046 00361198623

0041 0034 0000 0036 0046 0038 0038 0043 0034 0043 0043 0041 0038 0043 0043 0036 0046 0048 0038 00361198624

0053 0038 0036 0000 0038 0058 0055 0058 0050 0043 0038 0036 0043 0050 0050 0048 0053 0055 0046 00361198625

0048 0038 0043 0041 0000 0041 0026 0050 0036 0048 0050 0036 0043 0055 0055 0050 0046 0048 0055 00501198626

0050 0041 0048 0043 0046 0000 0053 0053 0043 0058 0055 0050 0050 0058 0055 0053 0053 0050 0046 00481198627

0038 0038 0038 0046 0034 0053 0000 0055 0046 0050 0043 0043 0036 0041 0041 0036 0036 0034 0036 00341198628

0048 0041 0041 0046 0046 0058 0053 0000 0041 0050 0060 0046 0053 0053 0053 0048 0043 0050 0053 00381198629

0048 0055 0058 0058 0038 0060 0055 0060 0000 0060 0041 0053 0041 0050 0055 0046 0043 0038 0041 003611986210

0048 0041 0041 0046 0043 0055 0053 0053 0043 0000 0048 0034 0043 0058 0048 0046 0041 0043 0048 003811986211

0050 0055 0046 0053 0048 0048 0050 0055 0034 0055 0000 0050 0046 0060 0060 0050 0053 0053 0055 004611986212

0034 0053 0046 0050 0046 0041 0043 0053 0043 0048 0055 0000 0041 0048 0060 0046 0046 0046 0046 004111986213

0041 0053 0043 0046 0048 0046 0043 0043 0038 0046 0048 0055 0000 0060 0048 0060 0050 0048 0050 004111986214

0036 0038 0050 0053 0041 0048 0038 0050 0043 0043 0048 0041 0038 0000 0053 0036 0036 0038 0038 003811986215

0055 0058 0050 0055 0048 0043 0043 0048 0036 0048 0055 0046 0043 0058 0000 0046 0036 0048 0043 003811986216

0050 0043 0046 0043 0050 0046 0048 0043 0048 0050 0053 0043 0036 0053 0053 0000 0058 0046 0055 003811986217

0055 0050 0046 0050 0046 0046 0041 0055 0036 0046 0048 0046 0043 0048 0050 0055 0000 0048 0046 004311986218

0058 0055 0050 0060 0053 0050 0048 0053 0041 0050 0055 0043 0046 0053 0058 0050 0055 0000 0055 003811986219

0053 0043 0050 0048 0053 0041 0041 0055 0031 0046 0060 0038 0050 0046 0058 0050 0050 0062 0000 004811986220

0041 0048 0050 0043 0041 0036 0036 0041 0031 0041 0046 0038 0038 0043 0048 0041 0038 0043 0050 0000




T(T119862) 1198621

1198622

1198623

1198624

1198625

1198626

1198627

1198628

1198629

11986210

11986211

11986212

11986213

11986214

11986215

11986216

11986217

11986218

11986219

11986220

1198621

0379 0414 0419 0450 0416 0441 0415 0459 0369 0431 0438 0377 0411 0472 0475 0425 0412 0429 0418 03651198622

0416 0361 0416 0450 0405 0437 0418 0459 0361 0435 0427 0366 0389 0454 0465 0414 0403 0422 0413 03551198623

0351 0335 0307 0361 0345 0357 0341 0380 0300 0362 0367 0321 0328 0383 0388 0345 0347 0359 0347 03031198624

0410 0386 0388 0376 0384 0424 0403 0445 0357 0411 0412 0360 0377 0442 0447 0404 0400 0414 0401 03441198625

0395 0377 0386 0405 0338 0398 0367 0427 0335 0405 0413 0350 0368 0436 0441 0396 0384 0398 0400 03491198626

0432 0412 0424 0443 0415 0394 0424 0467 0371 0450 0453 0395 0407 0476 0479 0433 0424 0434 0425 03761198627

0354 0345 0349 0375 0339 0376 0309 0397 0316 0374 0372 0328 0331 0387 0391 0350 0343 0351 0350 03051198628

0418 0401 0405 0433 0403 0437 0413 0404 0359 0431 0445 0380 0398 0458 0464 0417 0404 0422 0420 03571198629

0423 0418 0426 0449 0401 0444 0421 0467 0324 0445 0432 0391 0392 0461 0471 0419 0408 0416 0414 035911986210

0398 0381 0386 0411 0382 0414 0393 0432 0344 0362 0413 0351 0370 0440 0437 0394 0382 0395 0395 034011986211

0438 0431 0427 0458 0423 0446 0428 0476 0367 0453 0407 0400 0408 0484 0490 0436 0429 0442 0440 037911986212

0390 0398 0396 0422 0389 0406 0390 0439 0348 0414 0425 0323 0373 0438 0454 0400 0392 0403 0399 034711986213

0406 0406 0402 0427 0400 0420 0399 0440 0352 0421 0428 0383 0342 0459 0453 0422 0405 0415 0413 035511986214

0363 0356 0371 0393 0357 0383 0357 0405 0323 0379 0388 0336 0344 0360 0415 0362 0354 0368 0363 031911986215

0415 0407 0405 0432 0397 0414 0396 0440 0347 0419 0431 0371 0381 0453 0404 0405 0388 0411 0402 034911986216

0413 0396 0403 0423 0401 0418 0402 0438 0359 0424 0431 0371 0376 0450 0456 0364 0410 0411 0415 035111986217

0416 0401 0401 0428 0395 0417 0394 0447 0347 0418 0425 0372 0381 0444 0452 0415 0354 0412 0405 035411986218

0447 0433 0434 0467 0430 0451 0428 0476 0376 0452 0461 0395 0410 0480 0491 0439 0434 0395 0442 037411986219

0424 0405 0416 0437 0412 0423 0404 0458 0351 0428 0447 0375 0398 0454 0470 0421 0412 0435 0372 036711986220

0362 0359 0366 0379 0351 0366 0349 0390 0307 0371 0380 0328 0339 0395 0404 0361 0351 0366 0369 0278T119863

1198631

1198632

1198633

1198634

1198631

0387 0397 0404 03861198632

0401 0399 0413 03891198633

0404 0403 0406 03921198634

0408 0404 0415 0388Note where 119905119901

119894119895and 119905119901minus1119894119895


119894=1sum119899

119895=1(|119905119901

119894119895minus 119905119901minus1

119894119895|119905119901






1





119894 and the



119894+









2) the imple-




119894minus 119888119894)





W120572 1198621

1198622

1198623

1198624

1198625

1198626

1198627

1198628

1198629

11986210

11986211

11986212

11986213

11986214

11986215

11986216

11986217

11986218

11986219

11986220

1198621

0045 0050 0051 0052 0051 0051 0050 0051 0050 0051 0051 0049 0050 0050 0051 0051 0051 0051 0051 00501198622

0049 0043 0049 0049 0049 0049 0049 0049 0049 0049 0050 0050 0050 0049 0050 0049 0050 0049 0049 00501198623

0049 0050 0044 0049 0050 0050 0050 0049 0050 0049 0049 0050 0050 0051 0050 0050 0050 0050 0050 00511198624

0053 0054 0052 0047 0052 0052 0053 0053 0053 0053 0053 0053 0053 0054 0053 0052 0053 0053 0053 00531198625

0049 0049 0050 0049 0044 0049 0048 0049 0047 0049 0049 0049 0049 0049 0049 0050 0049 0049 0050 00491198626

0053 0052 0052 0052 0052 0047 0053 0053 0053 0053 0052 0051 0052 0052 0052 0051 0052 0052 0051 00511198627

0050 0050 0049 0050 0048 0050 0043 0050 0050 0050 0049 0049 0049 0049 0049 0049 0049 0049 0049 00491198628

0055 0055 0055 0055 0056 0055 0056 0049 0055 0055 0055 0055 0054 0055 0055 0054 0055 0055 0055 00551198629

0044 0043 0044 0044 0044 0044 0044 0044 0038 0044 0042 0044 0043 0044 0043 0044 0043 0043 0043 004311986210

0051 0052 0053 0051 0053 0053 0053 0053 0053 0046 0052 0052 0052 0052 0052 0052 0052 0052 0052 005211986211

0052 0052 0053 0052 0053 0053 0053 0053 0052 0053 0047 0053 0052 0053 0053 0053 0053 0053 0054 005311986212

0045 0045 0046 0045 0045 0046 0047 0046 0047 0045 0046 0041 0047 0046 0046 0046 0046 0045 0045 004611986213

0049 0048 0047 0048 0047 0047 0047 0048 0047 0047 0047 0047 0042 0047 0047 0046 0047 0047 0048 004711986214

0056 0055 0055 0056 0056 0055 0055 0055 0055 0056 0056 0055 0056 0049 0056 0056 0055 0055 0054 005511986215

0056 0057 0056 0056 0056 0056 0056 0056 0057 0056 0057 0057 0056 0057 0050 0056 0056 0056 0056 005611986216

0051 0051 0050 0050 0050 0050 0050 0050 0051 0050 0050 0050 0051 0050 0051 0045 0051 0051 0050 005011986217

0049 0049 0050 0050 0049 0049 0049 0049 0049 0049 0049 0049 0049 0049 0048 0050 0044 0050 0049 004911986218

0051 0052 0052 0052 0051 0050 0050 0051 0050 0050 0051 0051 0050 0051 0051 0051 0051 0046 0052 005111986219

0050 0050 0050 0050 0051 0049 0050 0051 0050 0050 0051 0050 0050 0050 0050 0051 0050 0051 0045 005111986220

0044 0043 0044 0043 0044 0044 0044 0043 0043 0043 0044 0044 0043 0044 0044 0043 0044 0043 0044 0039








4)



4) is



1) is 0408







4) and



3) to




2until


1and 119880


follows 1198801 1198634(0518) ≻ 119863

3(0488) ≻ 119863

1(0408) ≻

1198632(0395) and 119880

2 1198634(0753) ≻ 119863

1(0653) ≻

1198633(0633) ≻ 119863



Table6Th

einfl

uentialw

eightsob

tained

throug

hDANP

Influ

entia


imensio

ns(119863119895)

Factors

1198621

1198622

1198623

1198624

1198625

1198626

1198627

1198628

1198629

11986210

11986211

11986212

11986213

11986214

11986215

11986216

11986217

11986218

11986219

11986220

0050

0049

0050

0053

0049

0052

0049

0055

0043

0052

0053

0045

0047

0055

0056

0050

0049

0051

0050

0043

Dim

ensio

ns1198631

1198632

1198633

1198634

0250

0251

0256

0243













1198802

1198801

1198802

EVM users (1198631) 0250 0408 0653

Experience (1198621) 0201 0050 3350 1944 0413 0764

Training (1198622) 0196 0049 3750 2667 0313 0583




EVM methodology (1198632) 0251 0395 0600

WBS (1198626) 0206 0052 4000 2833 0250 0542

CPM (1198627) 0196 0049 3500 1722 0375 0819

IPT (1198628) 0218 0055 3300 2889 0425 0528

Computer system (1198629) 0173 0043 3100 3056 0475 0486











17) 0201 0049 2900 2278 0525 0681

Risk free (11986218) 0208 0051 2800 1833 0550 0792

Culture (11986219) 0206 0050 2750 2389 0563 0653

Regulations (11986220) 0178 0043 3200 1722 0450 0819








4)




(15913 0241) being risk free11986218

(16817 0616) culture 11986219

(16310 0305) and regula-tions 119862










119888119894

119903119894+ 119888119894

119903119894minus 119888119894

EVM users (1198631) 1574 1600 3174 minus0025

Experience (1198621) 8416 8046 16463 0370

Training (1198622) 8265 7821 16086 0445





WBS (1198626) 8532 8265 16796 0267

CPM (1198627) 7040 7850 14890 minus0810

IPT (1198628) 8269 8745 17014 minus0476

Computer system (1198629) 8382 6914 15296 1467











Risk free (11986218) 8716 8101 16817 0616

Culture (11986219) 8308 8003 16310 0305

Regulations (11986220) 7170 6925 14095 0245



1) in the


12) in the






15) an integrated







D4 (3171 0060)Gaps

U1 0518U2 0753

minus004

minus002

000

002

004

006

316

INRM_dimensions


U1 0408U2 0653


U1 0395U2 0600


U1 0488U2 0633

317 318 319 320 321 322 323 324 325

riminusc i

ri + ci

(a)

INRM_factors in D1





minus104

minus074

minus044

minus014

016

046

1450 1500 1550 1600 1650 1700

C2 (16086 0445)Gaps

U1 0313U2 0583


U1 0450U2 0556


U1 0343U2 0569

C1 (16463 0370)Gaps

U1 0413U2 0764


U1 0500U2 0792

riminusc i ri + ci

(b)

riminusc i

ri + ci

INRM_factors in D2

WBS ( )C6

CPM ( )C7

IPT (C8)


minus090

minus040

010

060

110

160

147 152 157 162 167 172

C9 (15296 1467)Gaps

U1 0475U2 0468

C6 (16796 0267)Gaps

U1 0250U2 0542


U1 0450U2 0625


U1 0374U2 0819


U1 0425U2 0528

(c)

riminusc i ri + ci

070

1510 1560 1610 1660 1710


U1 0413U2 0625

C12 (15218 0674)Gaps

U1 0513U2 0736


U1 0588U2 0681

C13 (15671 0625)Gaps

U1 0425U2 0639

C11 (17503 0266)Gaps

U1 0500U2 0486

minus180

minus130

minus080

minus030

020

INRM_factors in D3





(d)

riminusc i

ri + ci

INRM_factors in D4

Risk free (C18)



C18 (16817 0616)Gaps

U1 0550U2 0792

C19 (16310 0305)Gaps

U1 0563U2 0653

C15 (16132 0091)Gaps

U1 0500U2 0819

C17 (15913 0241)Gaps

U1 0525U2 0681

C20 (14095 0245)Gaps

U1 0450U2 0819

1390 1440 1490 1540 1590 1640 1690

000

030

060

(e)

Figure 3 The INRM




5 Conclusions





Competing Interests


References















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra






















1)










projects










project effectively













lowast

119895= 10 and 119891minus

119895= 0 as the








Form expert team

User questionnaire


INRM

Top management



DEMATEL technique

DANP




jminus flj|)(|f

lowast

jminus f

minus

j|)


f+

j



DW


D








j=1wjrlj and






Goal

Dimensions

Criteria(factors)

Alternatives

Gaps


Opencommunication


Top-down approach



Unit 2

EVM users

Experience

Training




EVMmethodology

WBS

CPM

IPT

Computersystem

Integratedproject

management

Unit 1

Projectenvironment



project managers

Risk free

Culture

Regulations


D1

D2 D3D4

C1

C2

C3

C4

C5

C6

C7

C8

C9

C10

C11

C12

C13

C14

C15

C16

C17

C18

C19

C20

U3 Uz

Unit 3 Unit zU1 U2

D1 D2

D3D4

C1 C2 C3

C4 C5

C6 C7 C8

C9 C10

C11 C12

C13

C14 C15

C16 C17

C18

C19 C20














1and 119880




119894119895]20times20



D =A119904

= [119889119894119895]119899times119899

(1)


sum119899

119895=1119886119894119895max1le119895le119899

sum119899

119894=1119886119894119895)






D119906 = [0]119899times119899 (2)


0 le 119889119894119895

lt 1 0 lt

sum119899

119895=1119889119894119895

le 1 0 lt sum119899

119894=1119889119894119895


119906rarrinfinD119906 = [0]

119899times119899



119862and T

119863obtained


119863 and then









2were



119895= 1



119903119897119895=

(10038161003816100381610038161003816119891lowast119895

minus 119891119897119895

10038161003816100381610038161003816)

(10038161003816100381610038161003816119891lowast119895


10038161003816100381610038161003816) (3)

119878119897=

119899

sum119895=1

119908119895119903119897119895 119897 = 1 2 119898 (4)


119876119897= max119895

119903119897119895| 119895 = 1 2 119899 119897 = 1 2 119898 (5)

119877119897= V (119878

119897) + (1 minus V) (119876

119897) (6)



A 1198621

1198622

1198623

1198624

1198625

1198626

1198627

1198628

1198629

11986210

11986211

11986212

11986213

11986214

11986215

11986216

11986217

11986218

11986219

11986220

1198621

0000 2857 2857 3429 3143 3286 2857 3000 2714 2571 2714 2143 3571 3571 3429 3000 2714 3000 2571 24291198622

2714 0000 3143 3857 2857 3429 3429 3429 2571 3286 2429 1857 2571 2857 3286 2714 2571 3000 2714 21431198623

2429 2000 0000 2143 2714 2286 2286 2571 2000 2571 2571 2429 2286 2571 2571 2143 2714 2857 2286 21431198624

3143 2286 2143 0000 2286 3429 3286 3429 3000 2571 2286 2143 2571 3000 3000 2857 3143 3286 2714 21431198625

2857 2286 2571 2429 0000 2429 1571 3000 2143 2857 3000 2143 2571 3286 3286 3000 2714 2857 3286 30001198626

3000 2429 2857 2571 2714 0000 3143 3143 2571 3429 3286 3000 3000 3429 3286 3143 3143 3000 2714 28571198627

2286 2286 2286 2714 2000 3143 0000 3286 2714 3000 2571 2571 2143 2429 2429 2143 2143 2000 2143 20001198628

2857 2429 2429 2714 2714 3429 3143 0000 2429 3000 3571 2714 3143 3143 3143 2857 2571 3000 3143 22861198629

2857 3286 3429 3429 2286 3571 3286 3571 0000 3571 2429 3143 2429 3000 3286 2714 2571 2286 2429 214311986210

2857 2429 2429 2714 2571 3286 3143 3143 2571 0000 2857 2000 2571 3429 2857 2714 2429 2571 2857 228611986211

3000 3286 2714 3143 2857 2857 3000 3286 2000 3286 0000 3000 2714 3571 3571 3000 3143 3143 3286 271411986212

2000 3143 2714 3000 2714 2429 2571 3143 2571 2857 3286 0000 2429 2857 3571 2714 2714 2714 2714 242911986213

2429 3143 2571 2714 2857 2714 2571 2571 2286 2714 2857 3286 0000 3571 2857 3571 3000 2857 3000 242911986214

2143 2286 3000 3143 2429 2857 2286 3000 2571 2571 2857 2429 2286 0000 3143 2143 2143 2286 2286 228611986215

3286 3429 3000 3286 2857 2571 2571 2857 2143 2857 3286 2714 2571 3429 0000 2714 2143 2857 2571 228611986216

3000 2571 2714 2571 3000 2714 2857 2571 2857 3000 3143 2571 2143 3143 3143 0000 3429 2714 3286 228611986217

3286 3000 2714 3000 2714 2714 2429 3286 2143 2714 2857 2714 2571 2857 3000 3286 0000 2857 2714 257111986218

3429 3286 3000 3571 3143 3000 2857 3143 2429 3000 3286 2571 2714 3143 3429 3000 3286 0000 3286 228611986219

3143 2571 3000 2857 3143 2429 2429 3286 1857 2714 3571 2286 3000 2714 3429 3000 3000 3714 0000 285711986220

2429 2857 3000 2571 2429 2143 2143 2429 1857 2429 2714 2286 2286 2571 2857 2429 2286 2571 3000 0000


D 1198621

1198622

1198623

1198624

1198625

1198626

1198627

1198628

1198629

11986210

11986211

11986212

11986213

11986214

11986215

11986216

11986217

11986218

11986219

11986220

1198621

0000 0048 0048 0058 0053 0055 0048 0050 0046 0043 0046 0036 0060 0060 0058 0050 0046 0050 0043 00411198622

0046 0000 0053 0065 0048 0058 0058 0058 0043 0055 0041 0031 0043 0048 0055 0046 0043 0050 0046 00361198623

0041 0034 0000 0036 0046 0038 0038 0043 0034 0043 0043 0041 0038 0043 0043 0036 0046 0048 0038 00361198624

0053 0038 0036 0000 0038 0058 0055 0058 0050 0043 0038 0036 0043 0050 0050 0048 0053 0055 0046 00361198625

0048 0038 0043 0041 0000 0041 0026 0050 0036 0048 0050 0036 0043 0055 0055 0050 0046 0048 0055 00501198626

0050 0041 0048 0043 0046 0000 0053 0053 0043 0058 0055 0050 0050 0058 0055 0053 0053 0050 0046 00481198627

0038 0038 0038 0046 0034 0053 0000 0055 0046 0050 0043 0043 0036 0041 0041 0036 0036 0034 0036 00341198628

0048 0041 0041 0046 0046 0058 0053 0000 0041 0050 0060 0046 0053 0053 0053 0048 0043 0050 0053 00381198629

0048 0055 0058 0058 0038 0060 0055 0060 0000 0060 0041 0053 0041 0050 0055 0046 0043 0038 0041 003611986210

0048 0041 0041 0046 0043 0055 0053 0053 0043 0000 0048 0034 0043 0058 0048 0046 0041 0043 0048 003811986211

0050 0055 0046 0053 0048 0048 0050 0055 0034 0055 0000 0050 0046 0060 0060 0050 0053 0053 0055 004611986212

0034 0053 0046 0050 0046 0041 0043 0053 0043 0048 0055 0000 0041 0048 0060 0046 0046 0046 0046 004111986213

0041 0053 0043 0046 0048 0046 0043 0043 0038 0046 0048 0055 0000 0060 0048 0060 0050 0048 0050 004111986214

0036 0038 0050 0053 0041 0048 0038 0050 0043 0043 0048 0041 0038 0000 0053 0036 0036 0038 0038 003811986215

0055 0058 0050 0055 0048 0043 0043 0048 0036 0048 0055 0046 0043 0058 0000 0046 0036 0048 0043 003811986216

0050 0043 0046 0043 0050 0046 0048 0043 0048 0050 0053 0043 0036 0053 0053 0000 0058 0046 0055 003811986217

0055 0050 0046 0050 0046 0046 0041 0055 0036 0046 0048 0046 0043 0048 0050 0055 0000 0048 0046 004311986218

0058 0055 0050 0060 0053 0050 0048 0053 0041 0050 0055 0043 0046 0053 0058 0050 0055 0000 0055 003811986219

0053 0043 0050 0048 0053 0041 0041 0055 0031 0046 0060 0038 0050 0046 0058 0050 0050 0062 0000 004811986220

0041 0048 0050 0043 0041 0036 0036 0041 0031 0041 0046 0038 0038 0043 0048 0041 0038 0043 0050 0000




T(T119862) 1198621

1198622

1198623

1198624

1198625

1198626

1198627

1198628

1198629

11986210

11986211

11986212

11986213

11986214

11986215

11986216

11986217

11986218

11986219

11986220

1198621

0379 0414 0419 0450 0416 0441 0415 0459 0369 0431 0438 0377 0411 0472 0475 0425 0412 0429 0418 03651198622

0416 0361 0416 0450 0405 0437 0418 0459 0361 0435 0427 0366 0389 0454 0465 0414 0403 0422 0413 03551198623

0351 0335 0307 0361 0345 0357 0341 0380 0300 0362 0367 0321 0328 0383 0388 0345 0347 0359 0347 03031198624

0410 0386 0388 0376 0384 0424 0403 0445 0357 0411 0412 0360 0377 0442 0447 0404 0400 0414 0401 03441198625

0395 0377 0386 0405 0338 0398 0367 0427 0335 0405 0413 0350 0368 0436 0441 0396 0384 0398 0400 03491198626

0432 0412 0424 0443 0415 0394 0424 0467 0371 0450 0453 0395 0407 0476 0479 0433 0424 0434 0425 03761198627

0354 0345 0349 0375 0339 0376 0309 0397 0316 0374 0372 0328 0331 0387 0391 0350 0343 0351 0350 03051198628

0418 0401 0405 0433 0403 0437 0413 0404 0359 0431 0445 0380 0398 0458 0464 0417 0404 0422 0420 03571198629

0423 0418 0426 0449 0401 0444 0421 0467 0324 0445 0432 0391 0392 0461 0471 0419 0408 0416 0414 035911986210

0398 0381 0386 0411 0382 0414 0393 0432 0344 0362 0413 0351 0370 0440 0437 0394 0382 0395 0395 034011986211

0438 0431 0427 0458 0423 0446 0428 0476 0367 0453 0407 0400 0408 0484 0490 0436 0429 0442 0440 037911986212

0390 0398 0396 0422 0389 0406 0390 0439 0348 0414 0425 0323 0373 0438 0454 0400 0392 0403 0399 034711986213

0406 0406 0402 0427 0400 0420 0399 0440 0352 0421 0428 0383 0342 0459 0453 0422 0405 0415 0413 035511986214

0363 0356 0371 0393 0357 0383 0357 0405 0323 0379 0388 0336 0344 0360 0415 0362 0354 0368 0363 031911986215

0415 0407 0405 0432 0397 0414 0396 0440 0347 0419 0431 0371 0381 0453 0404 0405 0388 0411 0402 034911986216

0413 0396 0403 0423 0401 0418 0402 0438 0359 0424 0431 0371 0376 0450 0456 0364 0410 0411 0415 035111986217

0416 0401 0401 0428 0395 0417 0394 0447 0347 0418 0425 0372 0381 0444 0452 0415 0354 0412 0405 035411986218

0447 0433 0434 0467 0430 0451 0428 0476 0376 0452 0461 0395 0410 0480 0491 0439 0434 0395 0442 037411986219

0424 0405 0416 0437 0412 0423 0404 0458 0351 0428 0447 0375 0398 0454 0470 0421 0412 0435 0372 036711986220

0362 0359 0366 0379 0351 0366 0349 0390 0307 0371 0380 0328 0339 0395 0404 0361 0351 0366 0369 0278T119863

1198631

1198632

1198633

1198634

1198631

0387 0397 0404 03861198632

0401 0399 0413 03891198633

0404 0403 0406 03921198634

0408 0404 0415 0388Note where 119905119901

119894119895and 119905119901minus1119894119895


119894=1sum119899

119895=1(|119905119901

119894119895minus 119905119901minus1

119894119895|119905119901






1





119894 and the



119894+









2) the imple-




119894minus 119888119894)





W120572 1198621

1198622

1198623

1198624

1198625

1198626

1198627

1198628

1198629

11986210

11986211

11986212

11986213

11986214

11986215

11986216

11986217

11986218

11986219

11986220

1198621

0045 0050 0051 0052 0051 0051 0050 0051 0050 0051 0051 0049 0050 0050 0051 0051 0051 0051 0051 00501198622

0049 0043 0049 0049 0049 0049 0049 0049 0049 0049 0050 0050 0050 0049 0050 0049 0050 0049 0049 00501198623

0049 0050 0044 0049 0050 0050 0050 0049 0050 0049 0049 0050 0050 0051 0050 0050 0050 0050 0050 00511198624

0053 0054 0052 0047 0052 0052 0053 0053 0053 0053 0053 0053 0053 0054 0053 0052 0053 0053 0053 00531198625

0049 0049 0050 0049 0044 0049 0048 0049 0047 0049 0049 0049 0049 0049 0049 0050 0049 0049 0050 00491198626

0053 0052 0052 0052 0052 0047 0053 0053 0053 0053 0052 0051 0052 0052 0052 0051 0052 0052 0051 00511198627

0050 0050 0049 0050 0048 0050 0043 0050 0050 0050 0049 0049 0049 0049 0049 0049 0049 0049 0049 00491198628

0055 0055 0055 0055 0056 0055 0056 0049 0055 0055 0055 0055 0054 0055 0055 0054 0055 0055 0055 00551198629

0044 0043 0044 0044 0044 0044 0044 0044 0038 0044 0042 0044 0043 0044 0043 0044 0043 0043 0043 004311986210

0051 0052 0053 0051 0053 0053 0053 0053 0053 0046 0052 0052 0052 0052 0052 0052 0052 0052 0052 005211986211

0052 0052 0053 0052 0053 0053 0053 0053 0052 0053 0047 0053 0052 0053 0053 0053 0053 0053 0054 005311986212

0045 0045 0046 0045 0045 0046 0047 0046 0047 0045 0046 0041 0047 0046 0046 0046 0046 0045 0045 004611986213

0049 0048 0047 0048 0047 0047 0047 0048 0047 0047 0047 0047 0042 0047 0047 0046 0047 0047 0048 004711986214

0056 0055 0055 0056 0056 0055 0055 0055 0055 0056 0056 0055 0056 0049 0056 0056 0055 0055 0054 005511986215

0056 0057 0056 0056 0056 0056 0056 0056 0057 0056 0057 0057 0056 0057 0050 0056 0056 0056 0056 005611986216

0051 0051 0050 0050 0050 0050 0050 0050 0051 0050 0050 0050 0051 0050 0051 0045 0051 0051 0050 005011986217

0049 0049 0050 0050 0049 0049 0049 0049 0049 0049 0049 0049 0049 0049 0048 0050 0044 0050 0049 004911986218

0051 0052 0052 0052 0051 0050 0050 0051 0050 0050 0051 0051 0050 0051 0051 0051 0051 0046 0052 005111986219

0050 0050 0050 0050 0051 0049 0050 0051 0050 0050 0051 0050 0050 0050 0050 0051 0050 0051 0045 005111986220

0044 0043 0044 0043 0044 0044 0044 0043 0043 0043 0044 0044 0043 0044 0044 0043 0044 0043 0044 0039








4)



4) is



1) is 0408







4) and



3) to




2until


1and 119880


follows 1198801 1198634(0518) ≻ 119863

3(0488) ≻ 119863

1(0408) ≻

1198632(0395) and 119880

2 1198634(0753) ≻ 119863

1(0653) ≻

1198633(0633) ≻ 119863



Table6Th

einfl

uentialw

eightsob

tained

throug

hDANP

Influ

entia


imensio

ns(119863119895)

Factors

1198621

1198622

1198623

1198624

1198625

1198626

1198627

1198628

1198629

11986210

11986211

11986212

11986213

11986214

11986215

11986216

11986217

11986218

11986219

11986220

0050

0049

0050

0053

0049

0052

0049

0055

0043

0052

0053

0045

0047

0055

0056

0050

0049

0051

0050

0043

Dim

ensio

ns1198631

1198632

1198633

1198634

0250

0251

0256

0243













1198802

1198801

1198802

EVM users (1198631) 0250 0408 0653

Experience (1198621) 0201 0050 3350 1944 0413 0764

Training (1198622) 0196 0049 3750 2667 0313 0583




EVM methodology (1198632) 0251 0395 0600

WBS (1198626) 0206 0052 4000 2833 0250 0542

CPM (1198627) 0196 0049 3500 1722 0375 0819

IPT (1198628) 0218 0055 3300 2889 0425 0528

Computer system (1198629) 0173 0043 3100 3056 0475 0486











17) 0201 0049 2900 2278 0525 0681

Risk free (11986218) 0208 0051 2800 1833 0550 0792

Culture (11986219) 0206 0050 2750 2389 0563 0653

Regulations (11986220) 0178 0043 3200 1722 0450 0819








4)




(15913 0241) being risk free11986218

(16817 0616) culture 11986219

(16310 0305) and regula-tions 119862










119888119894

119903119894+ 119888119894

119903119894minus 119888119894

EVM users (1198631) 1574 1600 3174 minus0025

Experience (1198621) 8416 8046 16463 0370

Training (1198622) 8265 7821 16086 0445





WBS (1198626) 8532 8265 16796 0267

CPM (1198627) 7040 7850 14890 minus0810

IPT (1198628) 8269 8745 17014 minus0476

Computer system (1198629) 8382 6914 15296 1467











Risk free (11986218) 8716 8101 16817 0616

Culture (11986219) 8308 8003 16310 0305

Regulations (11986220) 7170 6925 14095 0245



1) in the


12) in the






15) an integrated







D4 (3171 0060)Gaps

U1 0518U2 0753

minus004

minus002

000

002

004

006

316

INRM_dimensions


U1 0408U2 0653


U1 0395U2 0600


U1 0488U2 0633

317 318 319 320 321 322 323 324 325

riminusc i

ri + ci

(a)

INRM_factors in D1





minus104

minus074

minus044

minus014

016

046

1450 1500 1550 1600 1650 1700

C2 (16086 0445)Gaps

U1 0313U2 0583


U1 0450U2 0556


U1 0343U2 0569

C1 (16463 0370)Gaps

U1 0413U2 0764


U1 0500U2 0792

riminusc i ri + ci

(b)

riminusc i

ri + ci

INRM_factors in D2

WBS ( )C6

CPM ( )C7

IPT (C8)


minus090

minus040

010

060

110

160

147 152 157 162 167 172

C9 (15296 1467)Gaps

U1 0475U2 0468

C6 (16796 0267)Gaps

U1 0250U2 0542


U1 0450U2 0625


U1 0374U2 0819


U1 0425U2 0528

(c)

riminusc i ri + ci

070

1510 1560 1610 1660 1710


U1 0413U2 0625

C12 (15218 0674)Gaps

U1 0513U2 0736


U1 0588U2 0681

C13 (15671 0625)Gaps

U1 0425U2 0639

C11 (17503 0266)Gaps

U1 0500U2 0486

minus180

minus130

minus080

minus030

020

INRM_factors in D3





(d)

riminusc i

ri + ci

INRM_factors in D4

Risk free (C18)



C18 (16817 0616)Gaps

U1 0550U2 0792

C19 (16310 0305)Gaps

U1 0563U2 0653

C15 (16132 0091)Gaps

U1 0500U2 0819

C17 (15913 0241)Gaps

U1 0525U2 0681

C20 (14095 0245)Gaps

U1 0450U2 0819

1390 1440 1490 1540 1590 1640 1690

000

030

060

(e)

Figure 3 The INRM




5 Conclusions





Competing Interests


References















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












Form expert team

User questionnaire


INRM

Top management



DEMATEL technique

DANP




jminus flj|)(|f

lowast

jminus f

minus

j|)


f+

j



DW


D








j=1wjrlj and






Goal

Dimensions

Criteria(factors)

Alternatives

Gaps


Opencommunication


Top-down approach



Unit 2

EVM users

Experience

Training




EVMmethodology

WBS

CPM

IPT

Computersystem

Integratedproject

management

Unit 1

Projectenvironment



project managers

Risk free

Culture

Regulations


D1

D2 D3D4

C1

C2

C3

C4

C5

C6

C7

C8

C9

C10

C11

C12

C13

C14

C15

C16

C17

C18

C19

C20

U3 Uz

Unit 3 Unit zU1 U2

D1 D2

D3D4

C1 C2 C3

C4 C5

C6 C7 C8

C9 C10

C11 C12

C13

C14 C15

C16 C17

C18

C19 C20














1and 119880




119894119895]20times20



D =A119904

= [119889119894119895]119899times119899

(1)


sum119899

119895=1119886119894119895max1le119895le119899

sum119899

119894=1119886119894119895)






D119906 = [0]119899times119899 (2)


0 le 119889119894119895

lt 1 0 lt

sum119899

119895=1119889119894119895

le 1 0 lt sum119899

119894=1119889119894119895


119906rarrinfinD119906 = [0]

119899times119899



119862and T

119863obtained


119863 and then









2were



119895= 1



119903119897119895=

(10038161003816100381610038161003816119891lowast119895

minus 119891119897119895

10038161003816100381610038161003816)

(10038161003816100381610038161003816119891lowast119895


10038161003816100381610038161003816) (3)

119878119897=

119899

sum119895=1

119908119895119903119897119895 119897 = 1 2 119898 (4)


119876119897= max119895

119903119897119895| 119895 = 1 2 119899 119897 = 1 2 119898 (5)

119877119897= V (119878

119897) + (1 minus V) (119876

119897) (6)



A 1198621

1198622

1198623

1198624

1198625

1198626

1198627

1198628

1198629

11986210

11986211

11986212

11986213

11986214

11986215

11986216

11986217

11986218

11986219

11986220

1198621

0000 2857 2857 3429 3143 3286 2857 3000 2714 2571 2714 2143 3571 3571 3429 3000 2714 3000 2571 24291198622

2714 0000 3143 3857 2857 3429 3429 3429 2571 3286 2429 1857 2571 2857 3286 2714 2571 3000 2714 21431198623

2429 2000 0000 2143 2714 2286 2286 2571 2000 2571 2571 2429 2286 2571 2571 2143 2714 2857 2286 21431198624

3143 2286 2143 0000 2286 3429 3286 3429 3000 2571 2286 2143 2571 3000 3000 2857 3143 3286 2714 21431198625

2857 2286 2571 2429 0000 2429 1571 3000 2143 2857 3000 2143 2571 3286 3286 3000 2714 2857 3286 30001198626

3000 2429 2857 2571 2714 0000 3143 3143 2571 3429 3286 3000 3000 3429 3286 3143 3143 3000 2714 28571198627

2286 2286 2286 2714 2000 3143 0000 3286 2714 3000 2571 2571 2143 2429 2429 2143 2143 2000 2143 20001198628

2857 2429 2429 2714 2714 3429 3143 0000 2429 3000 3571 2714 3143 3143 3143 2857 2571 3000 3143 22861198629

2857 3286 3429 3429 2286 3571 3286 3571 0000 3571 2429 3143 2429 3000 3286 2714 2571 2286 2429 214311986210

2857 2429 2429 2714 2571 3286 3143 3143 2571 0000 2857 2000 2571 3429 2857 2714 2429 2571 2857 228611986211

3000 3286 2714 3143 2857 2857 3000 3286 2000 3286 0000 3000 2714 3571 3571 3000 3143 3143 3286 271411986212

2000 3143 2714 3000 2714 2429 2571 3143 2571 2857 3286 0000 2429 2857 3571 2714 2714 2714 2714 242911986213

2429 3143 2571 2714 2857 2714 2571 2571 2286 2714 2857 3286 0000 3571 2857 3571 3000 2857 3000 242911986214

2143 2286 3000 3143 2429 2857 2286 3000 2571 2571 2857 2429 2286 0000 3143 2143 2143 2286 2286 228611986215

3286 3429 3000 3286 2857 2571 2571 2857 2143 2857 3286 2714 2571 3429 0000 2714 2143 2857 2571 228611986216

3000 2571 2714 2571 3000 2714 2857 2571 2857 3000 3143 2571 2143 3143 3143 0000 3429 2714 3286 228611986217

3286 3000 2714 3000 2714 2714 2429 3286 2143 2714 2857 2714 2571 2857 3000 3286 0000 2857 2714 257111986218

3429 3286 3000 3571 3143 3000 2857 3143 2429 3000 3286 2571 2714 3143 3429 3000 3286 0000 3286 228611986219

3143 2571 3000 2857 3143 2429 2429 3286 1857 2714 3571 2286 3000 2714 3429 3000 3000 3714 0000 285711986220

2429 2857 3000 2571 2429 2143 2143 2429 1857 2429 2714 2286 2286 2571 2857 2429 2286 2571 3000 0000


D 1198621

1198622

1198623

1198624

1198625

1198626

1198627

1198628

1198629

11986210

11986211

11986212

11986213

11986214

11986215

11986216

11986217

11986218

11986219

11986220

1198621

0000 0048 0048 0058 0053 0055 0048 0050 0046 0043 0046 0036 0060 0060 0058 0050 0046 0050 0043 00411198622

0046 0000 0053 0065 0048 0058 0058 0058 0043 0055 0041 0031 0043 0048 0055 0046 0043 0050 0046 00361198623

0041 0034 0000 0036 0046 0038 0038 0043 0034 0043 0043 0041 0038 0043 0043 0036 0046 0048 0038 00361198624

0053 0038 0036 0000 0038 0058 0055 0058 0050 0043 0038 0036 0043 0050 0050 0048 0053 0055 0046 00361198625

0048 0038 0043 0041 0000 0041 0026 0050 0036 0048 0050 0036 0043 0055 0055 0050 0046 0048 0055 00501198626

0050 0041 0048 0043 0046 0000 0053 0053 0043 0058 0055 0050 0050 0058 0055 0053 0053 0050 0046 00481198627

0038 0038 0038 0046 0034 0053 0000 0055 0046 0050 0043 0043 0036 0041 0041 0036 0036 0034 0036 00341198628

0048 0041 0041 0046 0046 0058 0053 0000 0041 0050 0060 0046 0053 0053 0053 0048 0043 0050 0053 00381198629

0048 0055 0058 0058 0038 0060 0055 0060 0000 0060 0041 0053 0041 0050 0055 0046 0043 0038 0041 003611986210

0048 0041 0041 0046 0043 0055 0053 0053 0043 0000 0048 0034 0043 0058 0048 0046 0041 0043 0048 003811986211

0050 0055 0046 0053 0048 0048 0050 0055 0034 0055 0000 0050 0046 0060 0060 0050 0053 0053 0055 004611986212

0034 0053 0046 0050 0046 0041 0043 0053 0043 0048 0055 0000 0041 0048 0060 0046 0046 0046 0046 004111986213

0041 0053 0043 0046 0048 0046 0043 0043 0038 0046 0048 0055 0000 0060 0048 0060 0050 0048 0050 004111986214

0036 0038 0050 0053 0041 0048 0038 0050 0043 0043 0048 0041 0038 0000 0053 0036 0036 0038 0038 003811986215

0055 0058 0050 0055 0048 0043 0043 0048 0036 0048 0055 0046 0043 0058 0000 0046 0036 0048 0043 003811986216

0050 0043 0046 0043 0050 0046 0048 0043 0048 0050 0053 0043 0036 0053 0053 0000 0058 0046 0055 003811986217

0055 0050 0046 0050 0046 0046 0041 0055 0036 0046 0048 0046 0043 0048 0050 0055 0000 0048 0046 004311986218

0058 0055 0050 0060 0053 0050 0048 0053 0041 0050 0055 0043 0046 0053 0058 0050 0055 0000 0055 003811986219

0053 0043 0050 0048 0053 0041 0041 0055 0031 0046 0060 0038 0050 0046 0058 0050 0050 0062 0000 004811986220

0041 0048 0050 0043 0041 0036 0036 0041 0031 0041 0046 0038 0038 0043 0048 0041 0038 0043 0050 0000




T(T119862) 1198621

1198622

1198623

1198624

1198625

1198626

1198627

1198628

1198629

11986210

11986211

11986212

11986213

11986214

11986215

11986216

11986217

11986218

11986219

11986220

1198621

0379 0414 0419 0450 0416 0441 0415 0459 0369 0431 0438 0377 0411 0472 0475 0425 0412 0429 0418 03651198622

0416 0361 0416 0450 0405 0437 0418 0459 0361 0435 0427 0366 0389 0454 0465 0414 0403 0422 0413 03551198623

0351 0335 0307 0361 0345 0357 0341 0380 0300 0362 0367 0321 0328 0383 0388 0345 0347 0359 0347 03031198624

0410 0386 0388 0376 0384 0424 0403 0445 0357 0411 0412 0360 0377 0442 0447 0404 0400 0414 0401 03441198625

0395 0377 0386 0405 0338 0398 0367 0427 0335 0405 0413 0350 0368 0436 0441 0396 0384 0398 0400 03491198626

0432 0412 0424 0443 0415 0394 0424 0467 0371 0450 0453 0395 0407 0476 0479 0433 0424 0434 0425 03761198627

0354 0345 0349 0375 0339 0376 0309 0397 0316 0374 0372 0328 0331 0387 0391 0350 0343 0351 0350 03051198628

0418 0401 0405 0433 0403 0437 0413 0404 0359 0431 0445 0380 0398 0458 0464 0417 0404 0422 0420 03571198629

0423 0418 0426 0449 0401 0444 0421 0467 0324 0445 0432 0391 0392 0461 0471 0419 0408 0416 0414 035911986210

0398 0381 0386 0411 0382 0414 0393 0432 0344 0362 0413 0351 0370 0440 0437 0394 0382 0395 0395 034011986211

0438 0431 0427 0458 0423 0446 0428 0476 0367 0453 0407 0400 0408 0484 0490 0436 0429 0442 0440 037911986212

0390 0398 0396 0422 0389 0406 0390 0439 0348 0414 0425 0323 0373 0438 0454 0400 0392 0403 0399 034711986213

0406 0406 0402 0427 0400 0420 0399 0440 0352 0421 0428 0383 0342 0459 0453 0422 0405 0415 0413 035511986214

0363 0356 0371 0393 0357 0383 0357 0405 0323 0379 0388 0336 0344 0360 0415 0362 0354 0368 0363 031911986215

0415 0407 0405 0432 0397 0414 0396 0440 0347 0419 0431 0371 0381 0453 0404 0405 0388 0411 0402 034911986216

0413 0396 0403 0423 0401 0418 0402 0438 0359 0424 0431 0371 0376 0450 0456 0364 0410 0411 0415 035111986217

0416 0401 0401 0428 0395 0417 0394 0447 0347 0418 0425 0372 0381 0444 0452 0415 0354 0412 0405 035411986218

0447 0433 0434 0467 0430 0451 0428 0476 0376 0452 0461 0395 0410 0480 0491 0439 0434 0395 0442 037411986219

0424 0405 0416 0437 0412 0423 0404 0458 0351 0428 0447 0375 0398 0454 0470 0421 0412 0435 0372 036711986220

0362 0359 0366 0379 0351 0366 0349 0390 0307 0371 0380 0328 0339 0395 0404 0361 0351 0366 0369 0278T119863

1198631

1198632

1198633

1198634

1198631

0387 0397 0404 03861198632

0401 0399 0413 03891198633

0404 0403 0406 03921198634

0408 0404 0415 0388Note where 119905119901

119894119895and 119905119901minus1119894119895


119894=1sum119899

119895=1(|119905119901

119894119895minus 119905119901minus1

119894119895|119905119901






1





119894 and the



119894+









2) the imple-




119894minus 119888119894)





W120572 1198621

1198622

1198623

1198624

1198625

1198626

1198627

1198628

1198629

11986210

11986211

11986212

11986213

11986214

11986215

11986216

11986217

11986218

11986219

11986220

1198621

0045 0050 0051 0052 0051 0051 0050 0051 0050 0051 0051 0049 0050 0050 0051 0051 0051 0051 0051 00501198622

0049 0043 0049 0049 0049 0049 0049 0049 0049 0049 0050 0050 0050 0049 0050 0049 0050 0049 0049 00501198623

0049 0050 0044 0049 0050 0050 0050 0049 0050 0049 0049 0050 0050 0051 0050 0050 0050 0050 0050 00511198624

0053 0054 0052 0047 0052 0052 0053 0053 0053 0053 0053 0053 0053 0054 0053 0052 0053 0053 0053 00531198625

0049 0049 0050 0049 0044 0049 0048 0049 0047 0049 0049 0049 0049 0049 0049 0050 0049 0049 0050 00491198626

0053 0052 0052 0052 0052 0047 0053 0053 0053 0053 0052 0051 0052 0052 0052 0051 0052 0052 0051 00511198627

0050 0050 0049 0050 0048 0050 0043 0050 0050 0050 0049 0049 0049 0049 0049 0049 0049 0049 0049 00491198628

0055 0055 0055 0055 0056 0055 0056 0049 0055 0055 0055 0055 0054 0055 0055 0054 0055 0055 0055 00551198629

0044 0043 0044 0044 0044 0044 0044 0044 0038 0044 0042 0044 0043 0044 0043 0044 0043 0043 0043 004311986210

0051 0052 0053 0051 0053 0053 0053 0053 0053 0046 0052 0052 0052 0052 0052 0052 0052 0052 0052 005211986211

0052 0052 0053 0052 0053 0053 0053 0053 0052 0053 0047 0053 0052 0053 0053 0053 0053 0053 0054 005311986212

0045 0045 0046 0045 0045 0046 0047 0046 0047 0045 0046 0041 0047 0046 0046 0046 0046 0045 0045 004611986213

0049 0048 0047 0048 0047 0047 0047 0048 0047 0047 0047 0047 0042 0047 0047 0046 0047 0047 0048 004711986214

0056 0055 0055 0056 0056 0055 0055 0055 0055 0056 0056 0055 0056 0049 0056 0056 0055 0055 0054 005511986215

0056 0057 0056 0056 0056 0056 0056 0056 0057 0056 0057 0057 0056 0057 0050 0056 0056 0056 0056 005611986216

0051 0051 0050 0050 0050 0050 0050 0050 0051 0050 0050 0050 0051 0050 0051 0045 0051 0051 0050 005011986217

0049 0049 0050 0050 0049 0049 0049 0049 0049 0049 0049 0049 0049 0049 0048 0050 0044 0050 0049 004911986218

0051 0052 0052 0052 0051 0050 0050 0051 0050 0050 0051 0051 0050 0051 0051 0051 0051 0046 0052 005111986219

0050 0050 0050 0050 0051 0049 0050 0051 0050 0050 0051 0050 0050 0050 0050 0051 0050 0051 0045 005111986220

0044 0043 0044 0043 0044 0044 0044 0043 0043 0043 0044 0044 0043 0044 0044 0043 0044 0043 0044 0039








4)



4) is



1) is 0408







4) and



3) to




2until


1and 119880


follows 1198801 1198634(0518) ≻ 119863

3(0488) ≻ 119863

1(0408) ≻

1198632(0395) and 119880

2 1198634(0753) ≻ 119863

1(0653) ≻

1198633(0633) ≻ 119863



Table6Th

einfl

uentialw

eightsob

tained

throug

hDANP

Influ

entia


imensio

ns(119863119895)

Factors

1198621

1198622

1198623

1198624

1198625

1198626

1198627

1198628

1198629

11986210

11986211

11986212

11986213

11986214

11986215

11986216

11986217

11986218

11986219

11986220

0050

0049

0050

0053

0049

0052

0049

0055

0043

0052

0053

0045

0047

0055

0056

0050

0049

0051

0050

0043

Dim

ensio

ns1198631

1198632

1198633

1198634

0250

0251

0256

0243













1198802

1198801

1198802

EVM users (1198631) 0250 0408 0653

Experience (1198621) 0201 0050 3350 1944 0413 0764

Training (1198622) 0196 0049 3750 2667 0313 0583




EVM methodology (1198632) 0251 0395 0600

WBS (1198626) 0206 0052 4000 2833 0250 0542

CPM (1198627) 0196 0049 3500 1722 0375 0819

IPT (1198628) 0218 0055 3300 2889 0425 0528

Computer system (1198629) 0173 0043 3100 3056 0475 0486











17) 0201 0049 2900 2278 0525 0681

Risk free (11986218) 0208 0051 2800 1833 0550 0792

Culture (11986219) 0206 0050 2750 2389 0563 0653

Regulations (11986220) 0178 0043 3200 1722 0450 0819








4)




(15913 0241) being risk free11986218

(16817 0616) culture 11986219

(16310 0305) and regula-tions 119862










119888119894

119903119894+ 119888119894

119903119894minus 119888119894

EVM users (1198631) 1574 1600 3174 minus0025

Experience (1198621) 8416 8046 16463 0370

Training (1198622) 8265 7821 16086 0445





WBS (1198626) 8532 8265 16796 0267

CPM (1198627) 7040 7850 14890 minus0810

IPT (1198628) 8269 8745 17014 minus0476

Computer system (1198629) 8382 6914 15296 1467











Risk free (11986218) 8716 8101 16817 0616

Culture (11986219) 8308 8003 16310 0305

Regulations (11986220) 7170 6925 14095 0245



1) in the


12) in the






15) an integrated







D4 (3171 0060)Gaps

U1 0518U2 0753

minus004

minus002

000

002

004

006

316

INRM_dimensions


U1 0408U2 0653


U1 0395U2 0600


U1 0488U2 0633

317 318 319 320 321 322 323 324 325

riminusc i

ri + ci

(a)

INRM_factors in D1





minus104

minus074

minus044

minus014

016

046

1450 1500 1550 1600 1650 1700

C2 (16086 0445)Gaps

U1 0313U2 0583


U1 0450U2 0556


U1 0343U2 0569

C1 (16463 0370)Gaps

U1 0413U2 0764


U1 0500U2 0792

riminusc i ri + ci

(b)

riminusc i

ri + ci

INRM_factors in D2

WBS ( )C6

CPM ( )C7

IPT (C8)


minus090

minus040

010

060

110

160

147 152 157 162 167 172

C9 (15296 1467)Gaps

U1 0475U2 0468

C6 (16796 0267)Gaps

U1 0250U2 0542


U1 0450U2 0625


U1 0374U2 0819


U1 0425U2 0528

(c)

riminusc i ri + ci

070

1510 1560 1610 1660 1710


U1 0413U2 0625

C12 (15218 0674)Gaps

U1 0513U2 0736


U1 0588U2 0681

C13 (15671 0625)Gaps

U1 0425U2 0639

C11 (17503 0266)Gaps

U1 0500U2 0486

minus180

minus130

minus080

minus030

020

INRM_factors in D3





(d)

riminusc i

ri + ci

INRM_factors in D4

Risk free (C18)



C18 (16817 0616)Gaps

U1 0550U2 0792

C19 (16310 0305)Gaps

U1 0563U2 0653

C15 (16132 0091)Gaps

U1 0500U2 0819

C17 (15913 0241)Gaps

U1 0525U2 0681

C20 (14095 0245)Gaps

U1 0450U2 0819

1390 1440 1490 1540 1590 1640 1690

000

030

060

(e)

Figure 3 The INRM




5 Conclusions





Competing Interests


References















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Goal

Dimensions

Criteria(factors)

Alternatives

Gaps


Opencommunication


Top-down approach



Unit 2

EVM users

Experience

Training




EVMmethodology

WBS

CPM

IPT

Computersystem

Integratedproject

management

Unit 1

Projectenvironment



project managers

Risk free

Culture

Regulations


D1

D2 D3D4

C1

C2

C3

C4

C5

C6

C7

C8

C9

C10

C11

C12

C13

C14

C15

C16

C17

C18

C19

C20

U3 Uz

Unit 3 Unit zU1 U2

D1 D2

D3D4

C1 C2 C3

C4 C5

C6 C7 C8

C9 C10

C11 C12

C13

C14 C15

C16 C17

C18

C19 C20














1and 119880




119894119895]20times20



D =A119904

= [119889119894119895]119899times119899

(1)


sum119899

119895=1119886119894119895max1le119895le119899

sum119899

119894=1119886119894119895)






D119906 = [0]119899times119899 (2)


0 le 119889119894119895

lt 1 0 lt

sum119899

119895=1119889119894119895

le 1 0 lt sum119899

119894=1119889119894119895


119906rarrinfinD119906 = [0]

119899times119899



119862and T

119863obtained


119863 and then









2were



119895= 1



119903119897119895=

(10038161003816100381610038161003816119891lowast119895

minus 119891119897119895

10038161003816100381610038161003816)

(10038161003816100381610038161003816119891lowast119895


10038161003816100381610038161003816) (3)

119878119897=

119899

sum119895=1

119908119895119903119897119895 119897 = 1 2 119898 (4)


119876119897= max119895

119903119897119895| 119895 = 1 2 119899 119897 = 1 2 119898 (5)

119877119897= V (119878

119897) + (1 minus V) (119876

119897) (6)



A 1198621

1198622

1198623

1198624

1198625

1198626

1198627

1198628

1198629

11986210

11986211

11986212

11986213

11986214

11986215

11986216

11986217

11986218

11986219

11986220

1198621

0000 2857 2857 3429 3143 3286 2857 3000 2714 2571 2714 2143 3571 3571 3429 3000 2714 3000 2571 24291198622

2714 0000 3143 3857 2857 3429 3429 3429 2571 3286 2429 1857 2571 2857 3286 2714 2571 3000 2714 21431198623

2429 2000 0000 2143 2714 2286 2286 2571 2000 2571 2571 2429 2286 2571 2571 2143 2714 2857 2286 21431198624

3143 2286 2143 0000 2286 3429 3286 3429 3000 2571 2286 2143 2571 3000 3000 2857 3143 3286 2714 21431198625

2857 2286 2571 2429 0000 2429 1571 3000 2143 2857 3000 2143 2571 3286 3286 3000 2714 2857 3286 30001198626

3000 2429 2857 2571 2714 0000 3143 3143 2571 3429 3286 3000 3000 3429 3286 3143 3143 3000 2714 28571198627

2286 2286 2286 2714 2000 3143 0000 3286 2714 3000 2571 2571 2143 2429 2429 2143 2143 2000 2143 20001198628

2857 2429 2429 2714 2714 3429 3143 0000 2429 3000 3571 2714 3143 3143 3143 2857 2571 3000 3143 22861198629

2857 3286 3429 3429 2286 3571 3286 3571 0000 3571 2429 3143 2429 3000 3286 2714 2571 2286 2429 214311986210

2857 2429 2429 2714 2571 3286 3143 3143 2571 0000 2857 2000 2571 3429 2857 2714 2429 2571 2857 228611986211

3000 3286 2714 3143 2857 2857 3000 3286 2000 3286 0000 3000 2714 3571 3571 3000 3143 3143 3286 271411986212

2000 3143 2714 3000 2714 2429 2571 3143 2571 2857 3286 0000 2429 2857 3571 2714 2714 2714 2714 242911986213

2429 3143 2571 2714 2857 2714 2571 2571 2286 2714 2857 3286 0000 3571 2857 3571 3000 2857 3000 242911986214

2143 2286 3000 3143 2429 2857 2286 3000 2571 2571 2857 2429 2286 0000 3143 2143 2143 2286 2286 228611986215

3286 3429 3000 3286 2857 2571 2571 2857 2143 2857 3286 2714 2571 3429 0000 2714 2143 2857 2571 228611986216

3000 2571 2714 2571 3000 2714 2857 2571 2857 3000 3143 2571 2143 3143 3143 0000 3429 2714 3286 228611986217

3286 3000 2714 3000 2714 2714 2429 3286 2143 2714 2857 2714 2571 2857 3000 3286 0000 2857 2714 257111986218

3429 3286 3000 3571 3143 3000 2857 3143 2429 3000 3286 2571 2714 3143 3429 3000 3286 0000 3286 228611986219

3143 2571 3000 2857 3143 2429 2429 3286 1857 2714 3571 2286 3000 2714 3429 3000 3000 3714 0000 285711986220

2429 2857 3000 2571 2429 2143 2143 2429 1857 2429 2714 2286 2286 2571 2857 2429 2286 2571 3000 0000


D 1198621

1198622

1198623

1198624

1198625

1198626

1198627

1198628

1198629

11986210

11986211

11986212

11986213

11986214

11986215

11986216

11986217

11986218

11986219

11986220

1198621

0000 0048 0048 0058 0053 0055 0048 0050 0046 0043 0046 0036 0060 0060 0058 0050 0046 0050 0043 00411198622

0046 0000 0053 0065 0048 0058 0058 0058 0043 0055 0041 0031 0043 0048 0055 0046 0043 0050 0046 00361198623

0041 0034 0000 0036 0046 0038 0038 0043 0034 0043 0043 0041 0038 0043 0043 0036 0046 0048 0038 00361198624

0053 0038 0036 0000 0038 0058 0055 0058 0050 0043 0038 0036 0043 0050 0050 0048 0053 0055 0046 00361198625

0048 0038 0043 0041 0000 0041 0026 0050 0036 0048 0050 0036 0043 0055 0055 0050 0046 0048 0055 00501198626

0050 0041 0048 0043 0046 0000 0053 0053 0043 0058 0055 0050 0050 0058 0055 0053 0053 0050 0046 00481198627

0038 0038 0038 0046 0034 0053 0000 0055 0046 0050 0043 0043 0036 0041 0041 0036 0036 0034 0036 00341198628

0048 0041 0041 0046 0046 0058 0053 0000 0041 0050 0060 0046 0053 0053 0053 0048 0043 0050 0053 00381198629

0048 0055 0058 0058 0038 0060 0055 0060 0000 0060 0041 0053 0041 0050 0055 0046 0043 0038 0041 003611986210

0048 0041 0041 0046 0043 0055 0053 0053 0043 0000 0048 0034 0043 0058 0048 0046 0041 0043 0048 003811986211

0050 0055 0046 0053 0048 0048 0050 0055 0034 0055 0000 0050 0046 0060 0060 0050 0053 0053 0055 004611986212

0034 0053 0046 0050 0046 0041 0043 0053 0043 0048 0055 0000 0041 0048 0060 0046 0046 0046 0046 004111986213

0041 0053 0043 0046 0048 0046 0043 0043 0038 0046 0048 0055 0000 0060 0048 0060 0050 0048 0050 004111986214

0036 0038 0050 0053 0041 0048 0038 0050 0043 0043 0048 0041 0038 0000 0053 0036 0036 0038 0038 003811986215

0055 0058 0050 0055 0048 0043 0043 0048 0036 0048 0055 0046 0043 0058 0000 0046 0036 0048 0043 003811986216

0050 0043 0046 0043 0050 0046 0048 0043 0048 0050 0053 0043 0036 0053 0053 0000 0058 0046 0055 003811986217

0055 0050 0046 0050 0046 0046 0041 0055 0036 0046 0048 0046 0043 0048 0050 0055 0000 0048 0046 004311986218

0058 0055 0050 0060 0053 0050 0048 0053 0041 0050 0055 0043 0046 0053 0058 0050 0055 0000 0055 003811986219

0053 0043 0050 0048 0053 0041 0041 0055 0031 0046 0060 0038 0050 0046 0058 0050 0050 0062 0000 004811986220

0041 0048 0050 0043 0041 0036 0036 0041 0031 0041 0046 0038 0038 0043 0048 0041 0038 0043 0050 0000




T(T119862) 1198621

1198622

1198623

1198624

1198625

1198626

1198627

1198628

1198629

11986210

11986211

11986212

11986213

11986214

11986215

11986216

11986217

11986218

11986219

11986220

1198621

0379 0414 0419 0450 0416 0441 0415 0459 0369 0431 0438 0377 0411 0472 0475 0425 0412 0429 0418 03651198622

0416 0361 0416 0450 0405 0437 0418 0459 0361 0435 0427 0366 0389 0454 0465 0414 0403 0422 0413 03551198623

0351 0335 0307 0361 0345 0357 0341 0380 0300 0362 0367 0321 0328 0383 0388 0345 0347 0359 0347 03031198624

0410 0386 0388 0376 0384 0424 0403 0445 0357 0411 0412 0360 0377 0442 0447 0404 0400 0414 0401 03441198625

0395 0377 0386 0405 0338 0398 0367 0427 0335 0405 0413 0350 0368 0436 0441 0396 0384 0398 0400 03491198626

0432 0412 0424 0443 0415 0394 0424 0467 0371 0450 0453 0395 0407 0476 0479 0433 0424 0434 0425 03761198627

0354 0345 0349 0375 0339 0376 0309 0397 0316 0374 0372 0328 0331 0387 0391 0350 0343 0351 0350 03051198628

0418 0401 0405 0433 0403 0437 0413 0404 0359 0431 0445 0380 0398 0458 0464 0417 0404 0422 0420 03571198629

0423 0418 0426 0449 0401 0444 0421 0467 0324 0445 0432 0391 0392 0461 0471 0419 0408 0416 0414 035911986210

0398 0381 0386 0411 0382 0414 0393 0432 0344 0362 0413 0351 0370 0440 0437 0394 0382 0395 0395 034011986211

0438 0431 0427 0458 0423 0446 0428 0476 0367 0453 0407 0400 0408 0484 0490 0436 0429 0442 0440 037911986212

0390 0398 0396 0422 0389 0406 0390 0439 0348 0414 0425 0323 0373 0438 0454 0400 0392 0403 0399 034711986213

0406 0406 0402 0427 0400 0420 0399 0440 0352 0421 0428 0383 0342 0459 0453 0422 0405 0415 0413 035511986214

0363 0356 0371 0393 0357 0383 0357 0405 0323 0379 0388 0336 0344 0360 0415 0362 0354 0368 0363 031911986215

0415 0407 0405 0432 0397 0414 0396 0440 0347 0419 0431 0371 0381 0453 0404 0405 0388 0411 0402 034911986216

0413 0396 0403 0423 0401 0418 0402 0438 0359 0424 0431 0371 0376 0450 0456 0364 0410 0411 0415 035111986217

0416 0401 0401 0428 0395 0417 0394 0447 0347 0418 0425 0372 0381 0444 0452 0415 0354 0412 0405 035411986218

0447 0433 0434 0467 0430 0451 0428 0476 0376 0452 0461 0395 0410 0480 0491 0439 0434 0395 0442 037411986219

0424 0405 0416 0437 0412 0423 0404 0458 0351 0428 0447 0375 0398 0454 0470 0421 0412 0435 0372 036711986220

0362 0359 0366 0379 0351 0366 0349 0390 0307 0371 0380 0328 0339 0395 0404 0361 0351 0366 0369 0278T119863

1198631

1198632

1198633

1198634

1198631

0387 0397 0404 03861198632

0401 0399 0413 03891198633

0404 0403 0406 03921198634

0408 0404 0415 0388Note where 119905119901

119894119895and 119905119901minus1119894119895


119894=1sum119899

119895=1(|119905119901

119894119895minus 119905119901minus1

119894119895|119905119901






1





119894 and the



119894+









2) the imple-




119894minus 119888119894)





W120572 1198621

1198622

1198623

1198624

1198625

1198626

1198627

1198628

1198629

11986210

11986211

11986212

11986213

11986214

11986215

11986216

11986217

11986218

11986219

11986220

1198621

0045 0050 0051 0052 0051 0051 0050 0051 0050 0051 0051 0049 0050 0050 0051 0051 0051 0051 0051 00501198622

0049 0043 0049 0049 0049 0049 0049 0049 0049 0049 0050 0050 0050 0049 0050 0049 0050 0049 0049 00501198623

0049 0050 0044 0049 0050 0050 0050 0049 0050 0049 0049 0050 0050 0051 0050 0050 0050 0050 0050 00511198624

0053 0054 0052 0047 0052 0052 0053 0053 0053 0053 0053 0053 0053 0054 0053 0052 0053 0053 0053 00531198625

0049 0049 0050 0049 0044 0049 0048 0049 0047 0049 0049 0049 0049 0049 0049 0050 0049 0049 0050 00491198626

0053 0052 0052 0052 0052 0047 0053 0053 0053 0053 0052 0051 0052 0052 0052 0051 0052 0052 0051 00511198627

0050 0050 0049 0050 0048 0050 0043 0050 0050 0050 0049 0049 0049 0049 0049 0049 0049 0049 0049 00491198628

0055 0055 0055 0055 0056 0055 0056 0049 0055 0055 0055 0055 0054 0055 0055 0054 0055 0055 0055 00551198629

0044 0043 0044 0044 0044 0044 0044 0044 0038 0044 0042 0044 0043 0044 0043 0044 0043 0043 0043 004311986210

0051 0052 0053 0051 0053 0053 0053 0053 0053 0046 0052 0052 0052 0052 0052 0052 0052 0052 0052 005211986211

0052 0052 0053 0052 0053 0053 0053 0053 0052 0053 0047 0053 0052 0053 0053 0053 0053 0053 0054 005311986212

0045 0045 0046 0045 0045 0046 0047 0046 0047 0045 0046 0041 0047 0046 0046 0046 0046 0045 0045 004611986213

0049 0048 0047 0048 0047 0047 0047 0048 0047 0047 0047 0047 0042 0047 0047 0046 0047 0047 0048 004711986214

0056 0055 0055 0056 0056 0055 0055 0055 0055 0056 0056 0055 0056 0049 0056 0056 0055 0055 0054 005511986215

0056 0057 0056 0056 0056 0056 0056 0056 0057 0056 0057 0057 0056 0057 0050 0056 0056 0056 0056 005611986216

0051 0051 0050 0050 0050 0050 0050 0050 0051 0050 0050 0050 0051 0050 0051 0045 0051 0051 0050 005011986217

0049 0049 0050 0050 0049 0049 0049 0049 0049 0049 0049 0049 0049 0049 0048 0050 0044 0050 0049 004911986218

0051 0052 0052 0052 0051 0050 0050 0051 0050 0050 0051 0051 0050 0051 0051 0051 0051 0046 0052 005111986219

0050 0050 0050 0050 0051 0049 0050 0051 0050 0050 0051 0050 0050 0050 0050 0051 0050 0051 0045 005111986220

0044 0043 0044 0043 0044 0044 0044 0043 0043 0043 0044 0044 0043 0044 0044 0043 0044 0043 0044 0039








4)



4) is



1) is 0408







4) and



3) to




2until


1and 119880


follows 1198801 1198634(0518) ≻ 119863

3(0488) ≻ 119863

1(0408) ≻

1198632(0395) and 119880

2 1198634(0753) ≻ 119863

1(0653) ≻

1198633(0633) ≻ 119863



Table6Th

einfl

uentialw

eightsob

tained

throug

hDANP

Influ

entia


imensio

ns(119863119895)

Factors

1198621

1198622

1198623

1198624

1198625

1198626

1198627

1198628

1198629

11986210

11986211

11986212

11986213

11986214

11986215

11986216

11986217

11986218

11986219

11986220

0050

0049

0050

0053

0049

0052

0049

0055

0043

0052

0053

0045

0047

0055

0056

0050

0049

0051

0050

0043

Dim

ensio

ns1198631

1198632

1198633

1198634

0250

0251

0256

0243













1198802

1198801

1198802

EVM users (1198631) 0250 0408 0653

Experience (1198621) 0201 0050 3350 1944 0413 0764

Training (1198622) 0196 0049 3750 2667 0313 0583




EVM methodology (1198632) 0251 0395 0600

WBS (1198626) 0206 0052 4000 2833 0250 0542

CPM (1198627) 0196 0049 3500 1722 0375 0819

IPT (1198628) 0218 0055 3300 2889 0425 0528

Computer system (1198629) 0173 0043 3100 3056 0475 0486











17) 0201 0049 2900 2278 0525 0681

Risk free (11986218) 0208 0051 2800 1833 0550 0792

Culture (11986219) 0206 0050 2750 2389 0563 0653

Regulations (11986220) 0178 0043 3200 1722 0450 0819








4)




(15913 0241) being risk free11986218

(16817 0616) culture 11986219

(16310 0305) and regula-tions 119862










119888119894

119903119894+ 119888119894

119903119894minus 119888119894

EVM users (1198631) 1574 1600 3174 minus0025

Experience (1198621) 8416 8046 16463 0370

Training (1198622) 8265 7821 16086 0445





WBS (1198626) 8532 8265 16796 0267

CPM (1198627) 7040 7850 14890 minus0810

IPT (1198628) 8269 8745 17014 minus0476

Computer system (1198629) 8382 6914 15296 1467











Risk free (11986218) 8716 8101 16817 0616

Culture (11986219) 8308 8003 16310 0305

Regulations (11986220) 7170 6925 14095 0245



1) in the


12) in the






15) an integrated







D4 (3171 0060)Gaps

U1 0518U2 0753

minus004

minus002

000

002

004

006

316

INRM_dimensions


U1 0408U2 0653


U1 0395U2 0600


U1 0488U2 0633

317 318 319 320 321 322 323 324 325

riminusc i

ri + ci

(a)

INRM_factors in D1





minus104

minus074

minus044

minus014

016

046

1450 1500 1550 1600 1650 1700

C2 (16086 0445)Gaps

U1 0313U2 0583


U1 0450U2 0556


U1 0343U2 0569

C1 (16463 0370)Gaps

U1 0413U2 0764


U1 0500U2 0792

riminusc i ri + ci

(b)

riminusc i

ri + ci

INRM_factors in D2

WBS ( )C6

CPM ( )C7

IPT (C8)


minus090

minus040

010

060

110

160

147 152 157 162 167 172

C9 (15296 1467)Gaps

U1 0475U2 0468

C6 (16796 0267)Gaps

U1 0250U2 0542


U1 0450U2 0625


U1 0374U2 0819


U1 0425U2 0528

(c)

riminusc i ri + ci

070

1510 1560 1610 1660 1710


U1 0413U2 0625

C12 (15218 0674)Gaps

U1 0513U2 0736


U1 0588U2 0681

C13 (15671 0625)Gaps

U1 0425U2 0639

C11 (17503 0266)Gaps

U1 0500U2 0486

minus180

minus130

minus080

minus030

020

INRM_factors in D3





(d)

riminusc i

ri + ci

INRM_factors in D4

Risk free (C18)



C18 (16817 0616)Gaps

U1 0550U2 0792

C19 (16310 0305)Gaps

U1 0563U2 0653

C15 (16132 0091)Gaps

U1 0500U2 0819

C17 (15913 0241)Gaps

U1 0525U2 0681

C20 (14095 0245)Gaps

U1 0450U2 0819

1390 1440 1490 1540 1590 1640 1690

000

030

060

(e)

Figure 3 The INRM




5 Conclusions





Competing Interests


References















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra















1and 119880




119894119895]20times20



D =A119904

= [119889119894119895]119899times119899

(1)


sum119899

119895=1119886119894119895max1le119895le119899

sum119899

119894=1119886119894119895)






D119906 = [0]119899times119899 (2)


0 le 119889119894119895

lt 1 0 lt

sum119899

119895=1119889119894119895

le 1 0 lt sum119899

119894=1119889119894119895


119906rarrinfinD119906 = [0]

119899times119899



119862and T

119863obtained


119863 and then









2were



119895= 1



119903119897119895=

(10038161003816100381610038161003816119891lowast119895

minus 119891119897119895

10038161003816100381610038161003816)

(10038161003816100381610038161003816119891lowast119895


10038161003816100381610038161003816) (3)

119878119897=

119899

sum119895=1

119908119895119903119897119895 119897 = 1 2 119898 (4)


119876119897= max119895

119903119897119895| 119895 = 1 2 119899 119897 = 1 2 119898 (5)

119877119897= V (119878

119897) + (1 minus V) (119876

119897) (6)



A 1198621

1198622

1198623

1198624

1198625

1198626

1198627

1198628

1198629

11986210

11986211

11986212

11986213

11986214

11986215

11986216

11986217

11986218

11986219

11986220

1198621

0000 2857 2857 3429 3143 3286 2857 3000 2714 2571 2714 2143 3571 3571 3429 3000 2714 3000 2571 24291198622

2714 0000 3143 3857 2857 3429 3429 3429 2571 3286 2429 1857 2571 2857 3286 2714 2571 3000 2714 21431198623

2429 2000 0000 2143 2714 2286 2286 2571 2000 2571 2571 2429 2286 2571 2571 2143 2714 2857 2286 21431198624

3143 2286 2143 0000 2286 3429 3286 3429 3000 2571 2286 2143 2571 3000 3000 2857 3143 3286 2714 21431198625

2857 2286 2571 2429 0000 2429 1571 3000 2143 2857 3000 2143 2571 3286 3286 3000 2714 2857 3286 30001198626

3000 2429 2857 2571 2714 0000 3143 3143 2571 3429 3286 3000 3000 3429 3286 3143 3143 3000 2714 28571198627

2286 2286 2286 2714 2000 3143 0000 3286 2714 3000 2571 2571 2143 2429 2429 2143 2143 2000 2143 20001198628

2857 2429 2429 2714 2714 3429 3143 0000 2429 3000 3571 2714 3143 3143 3143 2857 2571 3000 3143 22861198629

2857 3286 3429 3429 2286 3571 3286 3571 0000 3571 2429 3143 2429 3000 3286 2714 2571 2286 2429 214311986210

2857 2429 2429 2714 2571 3286 3143 3143 2571 0000 2857 2000 2571 3429 2857 2714 2429 2571 2857 228611986211

3000 3286 2714 3143 2857 2857 3000 3286 2000 3286 0000 3000 2714 3571 3571 3000 3143 3143 3286 271411986212

2000 3143 2714 3000 2714 2429 2571 3143 2571 2857 3286 0000 2429 2857 3571 2714 2714 2714 2714 242911986213

2429 3143 2571 2714 2857 2714 2571 2571 2286 2714 2857 3286 0000 3571 2857 3571 3000 2857 3000 242911986214

2143 2286 3000 3143 2429 2857 2286 3000 2571 2571 2857 2429 2286 0000 3143 2143 2143 2286 2286 228611986215

3286 3429 3000 3286 2857 2571 2571 2857 2143 2857 3286 2714 2571 3429 0000 2714 2143 2857 2571 228611986216

3000 2571 2714 2571 3000 2714 2857 2571 2857 3000 3143 2571 2143 3143 3143 0000 3429 2714 3286 228611986217

3286 3000 2714 3000 2714 2714 2429 3286 2143 2714 2857 2714 2571 2857 3000 3286 0000 2857 2714 257111986218

3429 3286 3000 3571 3143 3000 2857 3143 2429 3000 3286 2571 2714 3143 3429 3000 3286 0000 3286 228611986219

3143 2571 3000 2857 3143 2429 2429 3286 1857 2714 3571 2286 3000 2714 3429 3000 3000 3714 0000 285711986220

2429 2857 3000 2571 2429 2143 2143 2429 1857 2429 2714 2286 2286 2571 2857 2429 2286 2571 3000 0000


D 1198621

1198622

1198623

1198624

1198625

1198626

1198627

1198628

1198629

11986210

11986211

11986212

11986213

11986214

11986215

11986216

11986217

11986218

11986219

11986220

1198621

0000 0048 0048 0058 0053 0055 0048 0050 0046 0043 0046 0036 0060 0060 0058 0050 0046 0050 0043 00411198622

0046 0000 0053 0065 0048 0058 0058 0058 0043 0055 0041 0031 0043 0048 0055 0046 0043 0050 0046 00361198623

0041 0034 0000 0036 0046 0038 0038 0043 0034 0043 0043 0041 0038 0043 0043 0036 0046 0048 0038 00361198624

0053 0038 0036 0000 0038 0058 0055 0058 0050 0043 0038 0036 0043 0050 0050 0048 0053 0055 0046 00361198625

0048 0038 0043 0041 0000 0041 0026 0050 0036 0048 0050 0036 0043 0055 0055 0050 0046 0048 0055 00501198626

0050 0041 0048 0043 0046 0000 0053 0053 0043 0058 0055 0050 0050 0058 0055 0053 0053 0050 0046 00481198627

0038 0038 0038 0046 0034 0053 0000 0055 0046 0050 0043 0043 0036 0041 0041 0036 0036 0034 0036 00341198628

0048 0041 0041 0046 0046 0058 0053 0000 0041 0050 0060 0046 0053 0053 0053 0048 0043 0050 0053 00381198629

0048 0055 0058 0058 0038 0060 0055 0060 0000 0060 0041 0053 0041 0050 0055 0046 0043 0038 0041 003611986210

0048 0041 0041 0046 0043 0055 0053 0053 0043 0000 0048 0034 0043 0058 0048 0046 0041 0043 0048 003811986211

0050 0055 0046 0053 0048 0048 0050 0055 0034 0055 0000 0050 0046 0060 0060 0050 0053 0053 0055 004611986212

0034 0053 0046 0050 0046 0041 0043 0053 0043 0048 0055 0000 0041 0048 0060 0046 0046 0046 0046 004111986213

0041 0053 0043 0046 0048 0046 0043 0043 0038 0046 0048 0055 0000 0060 0048 0060 0050 0048 0050 004111986214

0036 0038 0050 0053 0041 0048 0038 0050 0043 0043 0048 0041 0038 0000 0053 0036 0036 0038 0038 003811986215

0055 0058 0050 0055 0048 0043 0043 0048 0036 0048 0055 0046 0043 0058 0000 0046 0036 0048 0043 003811986216

0050 0043 0046 0043 0050 0046 0048 0043 0048 0050 0053 0043 0036 0053 0053 0000 0058 0046 0055 003811986217

0055 0050 0046 0050 0046 0046 0041 0055 0036 0046 0048 0046 0043 0048 0050 0055 0000 0048 0046 004311986218

0058 0055 0050 0060 0053 0050 0048 0053 0041 0050 0055 0043 0046 0053 0058 0050 0055 0000 0055 003811986219

0053 0043 0050 0048 0053 0041 0041 0055 0031 0046 0060 0038 0050 0046 0058 0050 0050 0062 0000 004811986220

0041 0048 0050 0043 0041 0036 0036 0041 0031 0041 0046 0038 0038 0043 0048 0041 0038 0043 0050 0000




T(T119862) 1198621

1198622

1198623

1198624

1198625

1198626

1198627

1198628

1198629

11986210

11986211

11986212

11986213

11986214

11986215

11986216

11986217

11986218

11986219

11986220

1198621

0379 0414 0419 0450 0416 0441 0415 0459 0369 0431 0438 0377 0411 0472 0475 0425 0412 0429 0418 03651198622

0416 0361 0416 0450 0405 0437 0418 0459 0361 0435 0427 0366 0389 0454 0465 0414 0403 0422 0413 03551198623

0351 0335 0307 0361 0345 0357 0341 0380 0300 0362 0367 0321 0328 0383 0388 0345 0347 0359 0347 03031198624

0410 0386 0388 0376 0384 0424 0403 0445 0357 0411 0412 0360 0377 0442 0447 0404 0400 0414 0401 03441198625

0395 0377 0386 0405 0338 0398 0367 0427 0335 0405 0413 0350 0368 0436 0441 0396 0384 0398 0400 03491198626

0432 0412 0424 0443 0415 0394 0424 0467 0371 0450 0453 0395 0407 0476 0479 0433 0424 0434 0425 03761198627

0354 0345 0349 0375 0339 0376 0309 0397 0316 0374 0372 0328 0331 0387 0391 0350 0343 0351 0350 03051198628

0418 0401 0405 0433 0403 0437 0413 0404 0359 0431 0445 0380 0398 0458 0464 0417 0404 0422 0420 03571198629

0423 0418 0426 0449 0401 0444 0421 0467 0324 0445 0432 0391 0392 0461 0471 0419 0408 0416 0414 035911986210

0398 0381 0386 0411 0382 0414 0393 0432 0344 0362 0413 0351 0370 0440 0437 0394 0382 0395 0395 034011986211

0438 0431 0427 0458 0423 0446 0428 0476 0367 0453 0407 0400 0408 0484 0490 0436 0429 0442 0440 037911986212

0390 0398 0396 0422 0389 0406 0390 0439 0348 0414 0425 0323 0373 0438 0454 0400 0392 0403 0399 034711986213

0406 0406 0402 0427 0400 0420 0399 0440 0352 0421 0428 0383 0342 0459 0453 0422 0405 0415 0413 035511986214

0363 0356 0371 0393 0357 0383 0357 0405 0323 0379 0388 0336 0344 0360 0415 0362 0354 0368 0363 031911986215

0415 0407 0405 0432 0397 0414 0396 0440 0347 0419 0431 0371 0381 0453 0404 0405 0388 0411 0402 034911986216

0413 0396 0403 0423 0401 0418 0402 0438 0359 0424 0431 0371 0376 0450 0456 0364 0410 0411 0415 035111986217

0416 0401 0401 0428 0395 0417 0394 0447 0347 0418 0425 0372 0381 0444 0452 0415 0354 0412 0405 035411986218

0447 0433 0434 0467 0430 0451 0428 0476 0376 0452 0461 0395 0410 0480 0491 0439 0434 0395 0442 037411986219

0424 0405 0416 0437 0412 0423 0404 0458 0351 0428 0447 0375 0398 0454 0470 0421 0412 0435 0372 036711986220

0362 0359 0366 0379 0351 0366 0349 0390 0307 0371 0380 0328 0339 0395 0404 0361 0351 0366 0369 0278T119863

1198631

1198632

1198633

1198634

1198631

0387 0397 0404 03861198632

0401 0399 0413 03891198633

0404 0403 0406 03921198634

0408 0404 0415 0388Note where 119905119901

119894119895and 119905119901minus1119894119895


119894=1sum119899

119895=1(|119905119901

119894119895minus 119905119901minus1

119894119895|119905119901






1





119894 and the



119894+









2) the imple-




119894minus 119888119894)





W120572 1198621

1198622

1198623

1198624

1198625

1198626

1198627

1198628

1198629

11986210

11986211

11986212

11986213

11986214

11986215

11986216

11986217

11986218

11986219

11986220

1198621

0045 0050 0051 0052 0051 0051 0050 0051 0050 0051 0051 0049 0050 0050 0051 0051 0051 0051 0051 00501198622

0049 0043 0049 0049 0049 0049 0049 0049 0049 0049 0050 0050 0050 0049 0050 0049 0050 0049 0049 00501198623

0049 0050 0044 0049 0050 0050 0050 0049 0050 0049 0049 0050 0050 0051 0050 0050 0050 0050 0050 00511198624

0053 0054 0052 0047 0052 0052 0053 0053 0053 0053 0053 0053 0053 0054 0053 0052 0053 0053 0053 00531198625

0049 0049 0050 0049 0044 0049 0048 0049 0047 0049 0049 0049 0049 0049 0049 0050 0049 0049 0050 00491198626

0053 0052 0052 0052 0052 0047 0053 0053 0053 0053 0052 0051 0052 0052 0052 0051 0052 0052 0051 00511198627

0050 0050 0049 0050 0048 0050 0043 0050 0050 0050 0049 0049 0049 0049 0049 0049 0049 0049 0049 00491198628

0055 0055 0055 0055 0056 0055 0056 0049 0055 0055 0055 0055 0054 0055 0055 0054 0055 0055 0055 00551198629

0044 0043 0044 0044 0044 0044 0044 0044 0038 0044 0042 0044 0043 0044 0043 0044 0043 0043 0043 004311986210

0051 0052 0053 0051 0053 0053 0053 0053 0053 0046 0052 0052 0052 0052 0052 0052 0052 0052 0052 005211986211

0052 0052 0053 0052 0053 0053 0053 0053 0052 0053 0047 0053 0052 0053 0053 0053 0053 0053 0054 005311986212

0045 0045 0046 0045 0045 0046 0047 0046 0047 0045 0046 0041 0047 0046 0046 0046 0046 0045 0045 004611986213

0049 0048 0047 0048 0047 0047 0047 0048 0047 0047 0047 0047 0042 0047 0047 0046 0047 0047 0048 004711986214

0056 0055 0055 0056 0056 0055 0055 0055 0055 0056 0056 0055 0056 0049 0056 0056 0055 0055 0054 005511986215

0056 0057 0056 0056 0056 0056 0056 0056 0057 0056 0057 0057 0056 0057 0050 0056 0056 0056 0056 005611986216

0051 0051 0050 0050 0050 0050 0050 0050 0051 0050 0050 0050 0051 0050 0051 0045 0051 0051 0050 005011986217

0049 0049 0050 0050 0049 0049 0049 0049 0049 0049 0049 0049 0049 0049 0048 0050 0044 0050 0049 004911986218

0051 0052 0052 0052 0051 0050 0050 0051 0050 0050 0051 0051 0050 0051 0051 0051 0051 0046 0052 005111986219

0050 0050 0050 0050 0051 0049 0050 0051 0050 0050 0051 0050 0050 0050 0050 0051 0050 0051 0045 005111986220

0044 0043 0044 0043 0044 0044 0044 0043 0043 0043 0044 0044 0043 0044 0044 0043 0044 0043 0044 0039








4)



4) is



1) is 0408







4) and



3) to




2until


1and 119880


follows 1198801 1198634(0518) ≻ 119863

3(0488) ≻ 119863

1(0408) ≻

1198632(0395) and 119880

2 1198634(0753) ≻ 119863

1(0653) ≻

1198633(0633) ≻ 119863



Table6Th

einfl

uentialw

eightsob

tained

throug

hDANP

Influ

entia


imensio

ns(119863119895)

Factors

1198621

1198622

1198623

1198624

1198625

1198626

1198627

1198628

1198629

11986210

11986211

11986212

11986213

11986214

11986215

11986216

11986217

11986218

11986219

11986220

0050

0049

0050

0053

0049

0052

0049

0055

0043

0052

0053

0045

0047

0055

0056

0050

0049

0051

0050

0043

Dim

ensio

ns1198631

1198632

1198633

1198634

0250

0251

0256

0243













1198802

1198801

1198802

EVM users (1198631) 0250 0408 0653

Experience (1198621) 0201 0050 3350 1944 0413 0764

Training (1198622) 0196 0049 3750 2667 0313 0583




EVM methodology (1198632) 0251 0395 0600

WBS (1198626) 0206 0052 4000 2833 0250 0542

CPM (1198627) 0196 0049 3500 1722 0375 0819

IPT (1198628) 0218 0055 3300 2889 0425 0528

Computer system (1198629) 0173 0043 3100 3056 0475 0486











17) 0201 0049 2900 2278 0525 0681

Risk free (11986218) 0208 0051 2800 1833 0550 0792

Culture (11986219) 0206 0050 2750 2389 0563 0653

Regulations (11986220) 0178 0043 3200 1722 0450 0819








4)




(15913 0241) being risk free11986218

(16817 0616) culture 11986219

(16310 0305) and regula-tions 119862










119888119894

119903119894+ 119888119894

119903119894minus 119888119894

EVM users (1198631) 1574 1600 3174 minus0025

Experience (1198621) 8416 8046 16463 0370

Training (1198622) 8265 7821 16086 0445





WBS (1198626) 8532 8265 16796 0267

CPM (1198627) 7040 7850 14890 minus0810

IPT (1198628) 8269 8745 17014 minus0476

Computer system (1198629) 8382 6914 15296 1467











Risk free (11986218) 8716 8101 16817 0616

Culture (11986219) 8308 8003 16310 0305

Regulations (11986220) 7170 6925 14095 0245



1) in the


12) in the






15) an integrated







D4 (3171 0060)Gaps

U1 0518U2 0753

minus004

minus002

000

002

004

006

316

INRM_dimensions


U1 0408U2 0653


U1 0395U2 0600


U1 0488U2 0633

317 318 319 320 321 322 323 324 325

riminusc i

ri + ci

(a)

INRM_factors in D1





minus104

minus074

minus044

minus014

016

046

1450 1500 1550 1600 1650 1700

C2 (16086 0445)Gaps

U1 0313U2 0583


U1 0450U2 0556


U1 0343U2 0569

C1 (16463 0370)Gaps

U1 0413U2 0764


U1 0500U2 0792

riminusc i ri + ci

(b)

riminusc i

ri + ci

INRM_factors in D2

WBS ( )C6

CPM ( )C7

IPT (C8)


minus090

minus040

010

060

110

160

147 152 157 162 167 172

C9 (15296 1467)Gaps

U1 0475U2 0468

C6 (16796 0267)Gaps

U1 0250U2 0542


U1 0450U2 0625


U1 0374U2 0819


U1 0425U2 0528

(c)

riminusc i ri + ci

070

1510 1560 1610 1660 1710


U1 0413U2 0625

C12 (15218 0674)Gaps

U1 0513U2 0736


U1 0588U2 0681

C13 (15671 0625)Gaps

U1 0425U2 0639

C11 (17503 0266)Gaps

U1 0500U2 0486

minus180

minus130

minus080

minus030

020

INRM_factors in D3





(d)

riminusc i

ri + ci

INRM_factors in D4

Risk free (C18)



C18 (16817 0616)Gaps

U1 0550U2 0792

C19 (16310 0305)Gaps

U1 0563U2 0653

C15 (16132 0091)Gaps

U1 0500U2 0819

C17 (15913 0241)Gaps

U1 0525U2 0681

C20 (14095 0245)Gaps

U1 0450U2 0819

1390 1440 1490 1540 1590 1640 1690

000

030

060

(e)

Figure 3 The INRM




5 Conclusions





Competing Interests


References















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











A 1198621

1198622

1198623

1198624

1198625

1198626

1198627

1198628

1198629

11986210

11986211

11986212

11986213

11986214

11986215

11986216

11986217

11986218

11986219

11986220

1198621

0000 2857 2857 3429 3143 3286 2857 3000 2714 2571 2714 2143 3571 3571 3429 3000 2714 3000 2571 24291198622

2714 0000 3143 3857 2857 3429 3429 3429 2571 3286 2429 1857 2571 2857 3286 2714 2571 3000 2714 21431198623

2429 2000 0000 2143 2714 2286 2286 2571 2000 2571 2571 2429 2286 2571 2571 2143 2714 2857 2286 21431198624

3143 2286 2143 0000 2286 3429 3286 3429 3000 2571 2286 2143 2571 3000 3000 2857 3143 3286 2714 21431198625

2857 2286 2571 2429 0000 2429 1571 3000 2143 2857 3000 2143 2571 3286 3286 3000 2714 2857 3286 30001198626

3000 2429 2857 2571 2714 0000 3143 3143 2571 3429 3286 3000 3000 3429 3286 3143 3143 3000 2714 28571198627

2286 2286 2286 2714 2000 3143 0000 3286 2714 3000 2571 2571 2143 2429 2429 2143 2143 2000 2143 20001198628

2857 2429 2429 2714 2714 3429 3143 0000 2429 3000 3571 2714 3143 3143 3143 2857 2571 3000 3143 22861198629

2857 3286 3429 3429 2286 3571 3286 3571 0000 3571 2429 3143 2429 3000 3286 2714 2571 2286 2429 214311986210

2857 2429 2429 2714 2571 3286 3143 3143 2571 0000 2857 2000 2571 3429 2857 2714 2429 2571 2857 228611986211

3000 3286 2714 3143 2857 2857 3000 3286 2000 3286 0000 3000 2714 3571 3571 3000 3143 3143 3286 271411986212

2000 3143 2714 3000 2714 2429 2571 3143 2571 2857 3286 0000 2429 2857 3571 2714 2714 2714 2714 242911986213

2429 3143 2571 2714 2857 2714 2571 2571 2286 2714 2857 3286 0000 3571 2857 3571 3000 2857 3000 242911986214

2143 2286 3000 3143 2429 2857 2286 3000 2571 2571 2857 2429 2286 0000 3143 2143 2143 2286 2286 228611986215

3286 3429 3000 3286 2857 2571 2571 2857 2143 2857 3286 2714 2571 3429 0000 2714 2143 2857 2571 228611986216

3000 2571 2714 2571 3000 2714 2857 2571 2857 3000 3143 2571 2143 3143 3143 0000 3429 2714 3286 228611986217

3286 3000 2714 3000 2714 2714 2429 3286 2143 2714 2857 2714 2571 2857 3000 3286 0000 2857 2714 257111986218

3429 3286 3000 3571 3143 3000 2857 3143 2429 3000 3286 2571 2714 3143 3429 3000 3286 0000 3286 228611986219

3143 2571 3000 2857 3143 2429 2429 3286 1857 2714 3571 2286 3000 2714 3429 3000 3000 3714 0000 285711986220

2429 2857 3000 2571 2429 2143 2143 2429 1857 2429 2714 2286 2286 2571 2857 2429 2286 2571 3000 0000


D 1198621

1198622

1198623

1198624

1198625

1198626

1198627

1198628

1198629

11986210

11986211

11986212

11986213

11986214

11986215

11986216

11986217

11986218

11986219

11986220

1198621

0000 0048 0048 0058 0053 0055 0048 0050 0046 0043 0046 0036 0060 0060 0058 0050 0046 0050 0043 00411198622

0046 0000 0053 0065 0048 0058 0058 0058 0043 0055 0041 0031 0043 0048 0055 0046 0043 0050 0046 00361198623

0041 0034 0000 0036 0046 0038 0038 0043 0034 0043 0043 0041 0038 0043 0043 0036 0046 0048 0038 00361198624

0053 0038 0036 0000 0038 0058 0055 0058 0050 0043 0038 0036 0043 0050 0050 0048 0053 0055 0046 00361198625

0048 0038 0043 0041 0000 0041 0026 0050 0036 0048 0050 0036 0043 0055 0055 0050 0046 0048 0055 00501198626

0050 0041 0048 0043 0046 0000 0053 0053 0043 0058 0055 0050 0050 0058 0055 0053 0053 0050 0046 00481198627

0038 0038 0038 0046 0034 0053 0000 0055 0046 0050 0043 0043 0036 0041 0041 0036 0036 0034 0036 00341198628

0048 0041 0041 0046 0046 0058 0053 0000 0041 0050 0060 0046 0053 0053 0053 0048 0043 0050 0053 00381198629

0048 0055 0058 0058 0038 0060 0055 0060 0000 0060 0041 0053 0041 0050 0055 0046 0043 0038 0041 003611986210

0048 0041 0041 0046 0043 0055 0053 0053 0043 0000 0048 0034 0043 0058 0048 0046 0041 0043 0048 003811986211

0050 0055 0046 0053 0048 0048 0050 0055 0034 0055 0000 0050 0046 0060 0060 0050 0053 0053 0055 004611986212

0034 0053 0046 0050 0046 0041 0043 0053 0043 0048 0055 0000 0041 0048 0060 0046 0046 0046 0046 004111986213

0041 0053 0043 0046 0048 0046 0043 0043 0038 0046 0048 0055 0000 0060 0048 0060 0050 0048 0050 004111986214

0036 0038 0050 0053 0041 0048 0038 0050 0043 0043 0048 0041 0038 0000 0053 0036 0036 0038 0038 003811986215

0055 0058 0050 0055 0048 0043 0043 0048 0036 0048 0055 0046 0043 0058 0000 0046 0036 0048 0043 003811986216

0050 0043 0046 0043 0050 0046 0048 0043 0048 0050 0053 0043 0036 0053 0053 0000 0058 0046 0055 003811986217

0055 0050 0046 0050 0046 0046 0041 0055 0036 0046 0048 0046 0043 0048 0050 0055 0000 0048 0046 004311986218

0058 0055 0050 0060 0053 0050 0048 0053 0041 0050 0055 0043 0046 0053 0058 0050 0055 0000 0055 003811986219

0053 0043 0050 0048 0053 0041 0041 0055 0031 0046 0060 0038 0050 0046 0058 0050 0050 0062 0000 004811986220

0041 0048 0050 0043 0041 0036 0036 0041 0031 0041 0046 0038 0038 0043 0048 0041 0038 0043 0050 0000




T(T119862) 1198621

1198622

1198623

1198624

1198625

1198626

1198627

1198628

1198629

11986210

11986211

11986212

11986213

11986214

11986215

11986216

11986217

11986218

11986219

11986220

1198621

0379 0414 0419 0450 0416 0441 0415 0459 0369 0431 0438 0377 0411 0472 0475 0425 0412 0429 0418 03651198622

0416 0361 0416 0450 0405 0437 0418 0459 0361 0435 0427 0366 0389 0454 0465 0414 0403 0422 0413 03551198623

0351 0335 0307 0361 0345 0357 0341 0380 0300 0362 0367 0321 0328 0383 0388 0345 0347 0359 0347 03031198624

0410 0386 0388 0376 0384 0424 0403 0445 0357 0411 0412 0360 0377 0442 0447 0404 0400 0414 0401 03441198625

0395 0377 0386 0405 0338 0398 0367 0427 0335 0405 0413 0350 0368 0436 0441 0396 0384 0398 0400 03491198626

0432 0412 0424 0443 0415 0394 0424 0467 0371 0450 0453 0395 0407 0476 0479 0433 0424 0434 0425 03761198627

0354 0345 0349 0375 0339 0376 0309 0397 0316 0374 0372 0328 0331 0387 0391 0350 0343 0351 0350 03051198628

0418 0401 0405 0433 0403 0437 0413 0404 0359 0431 0445 0380 0398 0458 0464 0417 0404 0422 0420 03571198629

0423 0418 0426 0449 0401 0444 0421 0467 0324 0445 0432 0391 0392 0461 0471 0419 0408 0416 0414 035911986210

0398 0381 0386 0411 0382 0414 0393 0432 0344 0362 0413 0351 0370 0440 0437 0394 0382 0395 0395 034011986211

0438 0431 0427 0458 0423 0446 0428 0476 0367 0453 0407 0400 0408 0484 0490 0436 0429 0442 0440 037911986212

0390 0398 0396 0422 0389 0406 0390 0439 0348 0414 0425 0323 0373 0438 0454 0400 0392 0403 0399 034711986213

0406 0406 0402 0427 0400 0420 0399 0440 0352 0421 0428 0383 0342 0459 0453 0422 0405 0415 0413 035511986214

0363 0356 0371 0393 0357 0383 0357 0405 0323 0379 0388 0336 0344 0360 0415 0362 0354 0368 0363 031911986215

0415 0407 0405 0432 0397 0414 0396 0440 0347 0419 0431 0371 0381 0453 0404 0405 0388 0411 0402 034911986216

0413 0396 0403 0423 0401 0418 0402 0438 0359 0424 0431 0371 0376 0450 0456 0364 0410 0411 0415 035111986217

0416 0401 0401 0428 0395 0417 0394 0447 0347 0418 0425 0372 0381 0444 0452 0415 0354 0412 0405 035411986218

0447 0433 0434 0467 0430 0451 0428 0476 0376 0452 0461 0395 0410 0480 0491 0439 0434 0395 0442 037411986219

0424 0405 0416 0437 0412 0423 0404 0458 0351 0428 0447 0375 0398 0454 0470 0421 0412 0435 0372 036711986220

0362 0359 0366 0379 0351 0366 0349 0390 0307 0371 0380 0328 0339 0395 0404 0361 0351 0366 0369 0278T119863

1198631

1198632

1198633

1198634

1198631

0387 0397 0404 03861198632

0401 0399 0413 03891198633

0404 0403 0406 03921198634

0408 0404 0415 0388Note where 119905119901

119894119895and 119905119901minus1119894119895


119894=1sum119899

119895=1(|119905119901

119894119895minus 119905119901minus1

119894119895|119905119901






1





119894 and the



119894+









2) the imple-




119894minus 119888119894)





W120572 1198621

1198622

1198623

1198624

1198625

1198626

1198627

1198628

1198629

11986210

11986211

11986212

11986213

11986214

11986215

11986216

11986217

11986218

11986219

11986220

1198621

0045 0050 0051 0052 0051 0051 0050 0051 0050 0051 0051 0049 0050 0050 0051 0051 0051 0051 0051 00501198622

0049 0043 0049 0049 0049 0049 0049 0049 0049 0049 0050 0050 0050 0049 0050 0049 0050 0049 0049 00501198623

0049 0050 0044 0049 0050 0050 0050 0049 0050 0049 0049 0050 0050 0051 0050 0050 0050 0050 0050 00511198624

0053 0054 0052 0047 0052 0052 0053 0053 0053 0053 0053 0053 0053 0054 0053 0052 0053 0053 0053 00531198625

0049 0049 0050 0049 0044 0049 0048 0049 0047 0049 0049 0049 0049 0049 0049 0050 0049 0049 0050 00491198626

0053 0052 0052 0052 0052 0047 0053 0053 0053 0053 0052 0051 0052 0052 0052 0051 0052 0052 0051 00511198627

0050 0050 0049 0050 0048 0050 0043 0050 0050 0050 0049 0049 0049 0049 0049 0049 0049 0049 0049 00491198628

0055 0055 0055 0055 0056 0055 0056 0049 0055 0055 0055 0055 0054 0055 0055 0054 0055 0055 0055 00551198629

0044 0043 0044 0044 0044 0044 0044 0044 0038 0044 0042 0044 0043 0044 0043 0044 0043 0043 0043 004311986210

0051 0052 0053 0051 0053 0053 0053 0053 0053 0046 0052 0052 0052 0052 0052 0052 0052 0052 0052 005211986211

0052 0052 0053 0052 0053 0053 0053 0053 0052 0053 0047 0053 0052 0053 0053 0053 0053 0053 0054 005311986212

0045 0045 0046 0045 0045 0046 0047 0046 0047 0045 0046 0041 0047 0046 0046 0046 0046 0045 0045 004611986213

0049 0048 0047 0048 0047 0047 0047 0048 0047 0047 0047 0047 0042 0047 0047 0046 0047 0047 0048 004711986214

0056 0055 0055 0056 0056 0055 0055 0055 0055 0056 0056 0055 0056 0049 0056 0056 0055 0055 0054 005511986215

0056 0057 0056 0056 0056 0056 0056 0056 0057 0056 0057 0057 0056 0057 0050 0056 0056 0056 0056 005611986216

0051 0051 0050 0050 0050 0050 0050 0050 0051 0050 0050 0050 0051 0050 0051 0045 0051 0051 0050 005011986217

0049 0049 0050 0050 0049 0049 0049 0049 0049 0049 0049 0049 0049 0049 0048 0050 0044 0050 0049 004911986218

0051 0052 0052 0052 0051 0050 0050 0051 0050 0050 0051 0051 0050 0051 0051 0051 0051 0046 0052 005111986219

0050 0050 0050 0050 0051 0049 0050 0051 0050 0050 0051 0050 0050 0050 0050 0051 0050 0051 0045 005111986220

0044 0043 0044 0043 0044 0044 0044 0043 0043 0043 0044 0044 0043 0044 0044 0043 0044 0043 0044 0039








4)



4) is



1) is 0408







4) and



3) to




2until


1and 119880


follows 1198801 1198634(0518) ≻ 119863

3(0488) ≻ 119863

1(0408) ≻

1198632(0395) and 119880

2 1198634(0753) ≻ 119863

1(0653) ≻

1198633(0633) ≻ 119863



Table6Th

einfl

uentialw

eightsob

tained

throug

hDANP

Influ

entia


imensio

ns(119863119895)

Factors

1198621

1198622

1198623

1198624

1198625

1198626

1198627

1198628

1198629

11986210

11986211

11986212

11986213

11986214

11986215

11986216

11986217

11986218

11986219

11986220

0050

0049

0050

0053

0049

0052

0049

0055

0043

0052

0053

0045

0047

0055

0056

0050

0049

0051

0050

0043

Dim

ensio

ns1198631

1198632

1198633

1198634

0250

0251

0256

0243













1198802

1198801

1198802

EVM users (1198631) 0250 0408 0653

Experience (1198621) 0201 0050 3350 1944 0413 0764

Training (1198622) 0196 0049 3750 2667 0313 0583




EVM methodology (1198632) 0251 0395 0600

WBS (1198626) 0206 0052 4000 2833 0250 0542

CPM (1198627) 0196 0049 3500 1722 0375 0819

IPT (1198628) 0218 0055 3300 2889 0425 0528

Computer system (1198629) 0173 0043 3100 3056 0475 0486











17) 0201 0049 2900 2278 0525 0681

Risk free (11986218) 0208 0051 2800 1833 0550 0792

Culture (11986219) 0206 0050 2750 2389 0563 0653

Regulations (11986220) 0178 0043 3200 1722 0450 0819








4)




(15913 0241) being risk free11986218

(16817 0616) culture 11986219

(16310 0305) and regula-tions 119862










119888119894

119903119894+ 119888119894

119903119894minus 119888119894

EVM users (1198631) 1574 1600 3174 minus0025

Experience (1198621) 8416 8046 16463 0370

Training (1198622) 8265 7821 16086 0445





WBS (1198626) 8532 8265 16796 0267

CPM (1198627) 7040 7850 14890 minus0810

IPT (1198628) 8269 8745 17014 minus0476

Computer system (1198629) 8382 6914 15296 1467











Risk free (11986218) 8716 8101 16817 0616

Culture (11986219) 8308 8003 16310 0305

Regulations (11986220) 7170 6925 14095 0245



1) in the


12) in the






15) an integrated







D4 (3171 0060)Gaps

U1 0518U2 0753

minus004

minus002

000

002

004

006

316

INRM_dimensions


U1 0408U2 0653


U1 0395U2 0600


U1 0488U2 0633

317 318 319 320 321 322 323 324 325

riminusc i

ri + ci

(a)

INRM_factors in D1





minus104

minus074

minus044

minus014

016

046

1450 1500 1550 1600 1650 1700

C2 (16086 0445)Gaps

U1 0313U2 0583


U1 0450U2 0556


U1 0343U2 0569

C1 (16463 0370)Gaps

U1 0413U2 0764


U1 0500U2 0792

riminusc i ri + ci

(b)

riminusc i

ri + ci

INRM_factors in D2

WBS ( )C6

CPM ( )C7

IPT (C8)


minus090

minus040

010

060

110

160

147 152 157 162 167 172

C9 (15296 1467)Gaps

U1 0475U2 0468

C6 (16796 0267)Gaps

U1 0250U2 0542


U1 0450U2 0625


U1 0374U2 0819


U1 0425U2 0528

(c)

riminusc i ri + ci

070

1510 1560 1610 1660 1710


U1 0413U2 0625

C12 (15218 0674)Gaps

U1 0513U2 0736


U1 0588U2 0681

C13 (15671 0625)Gaps

U1 0425U2 0639

C11 (17503 0266)Gaps

U1 0500U2 0486

minus180

minus130

minus080

minus030

020

INRM_factors in D3





(d)

riminusc i

ri + ci

INRM_factors in D4

Risk free (C18)



C18 (16817 0616)Gaps

U1 0550U2 0792

C19 (16310 0305)Gaps

U1 0563U2 0653

C15 (16132 0091)Gaps

U1 0500U2 0819

C17 (15913 0241)Gaps

U1 0525U2 0681

C20 (14095 0245)Gaps

U1 0450U2 0819

1390 1440 1490 1540 1590 1640 1690

000

030

060

(e)

Figure 3 The INRM




5 Conclusions





Competing Interests


References















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












T(T119862) 1198621

1198622

1198623

1198624

1198625

1198626

1198627

1198628

1198629

11986210

11986211

11986212

11986213

11986214

11986215

11986216

11986217

11986218

11986219

11986220

1198621

0379 0414 0419 0450 0416 0441 0415 0459 0369 0431 0438 0377 0411 0472 0475 0425 0412 0429 0418 03651198622

0416 0361 0416 0450 0405 0437 0418 0459 0361 0435 0427 0366 0389 0454 0465 0414 0403 0422 0413 03551198623

0351 0335 0307 0361 0345 0357 0341 0380 0300 0362 0367 0321 0328 0383 0388 0345 0347 0359 0347 03031198624

0410 0386 0388 0376 0384 0424 0403 0445 0357 0411 0412 0360 0377 0442 0447 0404 0400 0414 0401 03441198625

0395 0377 0386 0405 0338 0398 0367 0427 0335 0405 0413 0350 0368 0436 0441 0396 0384 0398 0400 03491198626

0432 0412 0424 0443 0415 0394 0424 0467 0371 0450 0453 0395 0407 0476 0479 0433 0424 0434 0425 03761198627

0354 0345 0349 0375 0339 0376 0309 0397 0316 0374 0372 0328 0331 0387 0391 0350 0343 0351 0350 03051198628

0418 0401 0405 0433 0403 0437 0413 0404 0359 0431 0445 0380 0398 0458 0464 0417 0404 0422 0420 03571198629

0423 0418 0426 0449 0401 0444 0421 0467 0324 0445 0432 0391 0392 0461 0471 0419 0408 0416 0414 035911986210

0398 0381 0386 0411 0382 0414 0393 0432 0344 0362 0413 0351 0370 0440 0437 0394 0382 0395 0395 034011986211

0438 0431 0427 0458 0423 0446 0428 0476 0367 0453 0407 0400 0408 0484 0490 0436 0429 0442 0440 037911986212

0390 0398 0396 0422 0389 0406 0390 0439 0348 0414 0425 0323 0373 0438 0454 0400 0392 0403 0399 034711986213

0406 0406 0402 0427 0400 0420 0399 0440 0352 0421 0428 0383 0342 0459 0453 0422 0405 0415 0413 035511986214

0363 0356 0371 0393 0357 0383 0357 0405 0323 0379 0388 0336 0344 0360 0415 0362 0354 0368 0363 031911986215

0415 0407 0405 0432 0397 0414 0396 0440 0347 0419 0431 0371 0381 0453 0404 0405 0388 0411 0402 034911986216

0413 0396 0403 0423 0401 0418 0402 0438 0359 0424 0431 0371 0376 0450 0456 0364 0410 0411 0415 035111986217

0416 0401 0401 0428 0395 0417 0394 0447 0347 0418 0425 0372 0381 0444 0452 0415 0354 0412 0405 035411986218

0447 0433 0434 0467 0430 0451 0428 0476 0376 0452 0461 0395 0410 0480 0491 0439 0434 0395 0442 037411986219

0424 0405 0416 0437 0412 0423 0404 0458 0351 0428 0447 0375 0398 0454 0470 0421 0412 0435 0372 036711986220

0362 0359 0366 0379 0351 0366 0349 0390 0307 0371 0380 0328 0339 0395 0404 0361 0351 0366 0369 0278T119863

1198631

1198632

1198633

1198634

1198631

0387 0397 0404 03861198632

0401 0399 0413 03891198633

0404 0403 0406 03921198634

0408 0404 0415 0388Note where 119905119901

119894119895and 119905119901minus1119894119895


119894=1sum119899

119895=1(|119905119901

119894119895minus 119905119901minus1

119894119895|119905119901






1





119894 and the



119894+









2) the imple-




119894minus 119888119894)





W120572 1198621

1198622

1198623

1198624

1198625

1198626

1198627

1198628

1198629

11986210

11986211

11986212

11986213

11986214

11986215

11986216

11986217

11986218

11986219

11986220

1198621

0045 0050 0051 0052 0051 0051 0050 0051 0050 0051 0051 0049 0050 0050 0051 0051 0051 0051 0051 00501198622

0049 0043 0049 0049 0049 0049 0049 0049 0049 0049 0050 0050 0050 0049 0050 0049 0050 0049 0049 00501198623

0049 0050 0044 0049 0050 0050 0050 0049 0050 0049 0049 0050 0050 0051 0050 0050 0050 0050 0050 00511198624

0053 0054 0052 0047 0052 0052 0053 0053 0053 0053 0053 0053 0053 0054 0053 0052 0053 0053 0053 00531198625

0049 0049 0050 0049 0044 0049 0048 0049 0047 0049 0049 0049 0049 0049 0049 0050 0049 0049 0050 00491198626

0053 0052 0052 0052 0052 0047 0053 0053 0053 0053 0052 0051 0052 0052 0052 0051 0052 0052 0051 00511198627

0050 0050 0049 0050 0048 0050 0043 0050 0050 0050 0049 0049 0049 0049 0049 0049 0049 0049 0049 00491198628

0055 0055 0055 0055 0056 0055 0056 0049 0055 0055 0055 0055 0054 0055 0055 0054 0055 0055 0055 00551198629

0044 0043 0044 0044 0044 0044 0044 0044 0038 0044 0042 0044 0043 0044 0043 0044 0043 0043 0043 004311986210

0051 0052 0053 0051 0053 0053 0053 0053 0053 0046 0052 0052 0052 0052 0052 0052 0052 0052 0052 005211986211

0052 0052 0053 0052 0053 0053 0053 0053 0052 0053 0047 0053 0052 0053 0053 0053 0053 0053 0054 005311986212

0045 0045 0046 0045 0045 0046 0047 0046 0047 0045 0046 0041 0047 0046 0046 0046 0046 0045 0045 004611986213

0049 0048 0047 0048 0047 0047 0047 0048 0047 0047 0047 0047 0042 0047 0047 0046 0047 0047 0048 004711986214

0056 0055 0055 0056 0056 0055 0055 0055 0055 0056 0056 0055 0056 0049 0056 0056 0055 0055 0054 005511986215

0056 0057 0056 0056 0056 0056 0056 0056 0057 0056 0057 0057 0056 0057 0050 0056 0056 0056 0056 005611986216

0051 0051 0050 0050 0050 0050 0050 0050 0051 0050 0050 0050 0051 0050 0051 0045 0051 0051 0050 005011986217

0049 0049 0050 0050 0049 0049 0049 0049 0049 0049 0049 0049 0049 0049 0048 0050 0044 0050 0049 004911986218

0051 0052 0052 0052 0051 0050 0050 0051 0050 0050 0051 0051 0050 0051 0051 0051 0051 0046 0052 005111986219

0050 0050 0050 0050 0051 0049 0050 0051 0050 0050 0051 0050 0050 0050 0050 0051 0050 0051 0045 005111986220

0044 0043 0044 0043 0044 0044 0044 0043 0043 0043 0044 0044 0043 0044 0044 0043 0044 0043 0044 0039








4)



4) is



1) is 0408







4) and



3) to




2until


1and 119880


follows 1198801 1198634(0518) ≻ 119863

3(0488) ≻ 119863

1(0408) ≻

1198632(0395) and 119880

2 1198634(0753) ≻ 119863

1(0653) ≻

1198633(0633) ≻ 119863



Table6Th

einfl

uentialw

eightsob

tained

throug

hDANP

Influ

entia


imensio

ns(119863119895)

Factors

1198621

1198622

1198623

1198624

1198625

1198626

1198627

1198628

1198629

11986210

11986211

11986212

11986213

11986214

11986215

11986216

11986217

11986218

11986219

11986220

0050

0049

0050

0053

0049

0052

0049

0055

0043

0052

0053

0045

0047

0055

0056

0050

0049

0051

0050

0043

Dim

ensio

ns1198631

1198632

1198633

1198634

0250

0251

0256

0243













1198802

1198801

1198802

EVM users (1198631) 0250 0408 0653

Experience (1198621) 0201 0050 3350 1944 0413 0764

Training (1198622) 0196 0049 3750 2667 0313 0583




EVM methodology (1198632) 0251 0395 0600

WBS (1198626) 0206 0052 4000 2833 0250 0542

CPM (1198627) 0196 0049 3500 1722 0375 0819

IPT (1198628) 0218 0055 3300 2889 0425 0528

Computer system (1198629) 0173 0043 3100 3056 0475 0486











17) 0201 0049 2900 2278 0525 0681

Risk free (11986218) 0208 0051 2800 1833 0550 0792

Culture (11986219) 0206 0050 2750 2389 0563 0653

Regulations (11986220) 0178 0043 3200 1722 0450 0819








4)




(15913 0241) being risk free11986218

(16817 0616) culture 11986219

(16310 0305) and regula-tions 119862










119888119894

119903119894+ 119888119894

119903119894minus 119888119894

EVM users (1198631) 1574 1600 3174 minus0025

Experience (1198621) 8416 8046 16463 0370

Training (1198622) 8265 7821 16086 0445





WBS (1198626) 8532 8265 16796 0267

CPM (1198627) 7040 7850 14890 minus0810

IPT (1198628) 8269 8745 17014 minus0476

Computer system (1198629) 8382 6914 15296 1467











Risk free (11986218) 8716 8101 16817 0616

Culture (11986219) 8308 8003 16310 0305

Regulations (11986220) 7170 6925 14095 0245



1) in the


12) in the






15) an integrated







D4 (3171 0060)Gaps

U1 0518U2 0753

minus004

minus002

000

002

004

006

316

INRM_dimensions


U1 0408U2 0653


U1 0395U2 0600


U1 0488U2 0633

317 318 319 320 321 322 323 324 325

riminusc i

ri + ci

(a)

INRM_factors in D1





minus104

minus074

minus044

minus014

016

046

1450 1500 1550 1600 1650 1700

C2 (16086 0445)Gaps

U1 0313U2 0583


U1 0450U2 0556


U1 0343U2 0569

C1 (16463 0370)Gaps

U1 0413U2 0764


U1 0500U2 0792

riminusc i ri + ci

(b)

riminusc i

ri + ci

INRM_factors in D2

WBS ( )C6

CPM ( )C7

IPT (C8)


minus090

minus040

010

060

110

160

147 152 157 162 167 172

C9 (15296 1467)Gaps

U1 0475U2 0468

C6 (16796 0267)Gaps

U1 0250U2 0542


U1 0450U2 0625


U1 0374U2 0819


U1 0425U2 0528

(c)

riminusc i ri + ci

070

1510 1560 1610 1660 1710


U1 0413U2 0625

C12 (15218 0674)Gaps

U1 0513U2 0736


U1 0588U2 0681

C13 (15671 0625)Gaps

U1 0425U2 0639

C11 (17503 0266)Gaps

U1 0500U2 0486

minus180

minus130

minus080

minus030

020

INRM_factors in D3





(d)

riminusc i

ri + ci

INRM_factors in D4

Risk free (C18)



C18 (16817 0616)Gaps

U1 0550U2 0792

C19 (16310 0305)Gaps

U1 0563U2 0653

C15 (16132 0091)Gaps

U1 0500U2 0819

C17 (15913 0241)Gaps

U1 0525U2 0681

C20 (14095 0245)Gaps

U1 0450U2 0819

1390 1440 1490 1540 1590 1640 1690

000

030

060

(e)

Figure 3 The INRM




5 Conclusions





Competing Interests


References















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











W120572 1198621

1198622

1198623

1198624

1198625

1198626

1198627

1198628

1198629

11986210

11986211

11986212

11986213

11986214

11986215

11986216

11986217

11986218

11986219

11986220

1198621

0045 0050 0051 0052 0051 0051 0050 0051 0050 0051 0051 0049 0050 0050 0051 0051 0051 0051 0051 00501198622

0049 0043 0049 0049 0049 0049 0049 0049 0049 0049 0050 0050 0050 0049 0050 0049 0050 0049 0049 00501198623

0049 0050 0044 0049 0050 0050 0050 0049 0050 0049 0049 0050 0050 0051 0050 0050 0050 0050 0050 00511198624

0053 0054 0052 0047 0052 0052 0053 0053 0053 0053 0053 0053 0053 0054 0053 0052 0053 0053 0053 00531198625

0049 0049 0050 0049 0044 0049 0048 0049 0047 0049 0049 0049 0049 0049 0049 0050 0049 0049 0050 00491198626

0053 0052 0052 0052 0052 0047 0053 0053 0053 0053 0052 0051 0052 0052 0052 0051 0052 0052 0051 00511198627

0050 0050 0049 0050 0048 0050 0043 0050 0050 0050 0049 0049 0049 0049 0049 0049 0049 0049 0049 00491198628

0055 0055 0055 0055 0056 0055 0056 0049 0055 0055 0055 0055 0054 0055 0055 0054 0055 0055 0055 00551198629

0044 0043 0044 0044 0044 0044 0044 0044 0038 0044 0042 0044 0043 0044 0043 0044 0043 0043 0043 004311986210

0051 0052 0053 0051 0053 0053 0053 0053 0053 0046 0052 0052 0052 0052 0052 0052 0052 0052 0052 005211986211

0052 0052 0053 0052 0053 0053 0053 0053 0052 0053 0047 0053 0052 0053 0053 0053 0053 0053 0054 005311986212

0045 0045 0046 0045 0045 0046 0047 0046 0047 0045 0046 0041 0047 0046 0046 0046 0046 0045 0045 004611986213

0049 0048 0047 0048 0047 0047 0047 0048 0047 0047 0047 0047 0042 0047 0047 0046 0047 0047 0048 004711986214

0056 0055 0055 0056 0056 0055 0055 0055 0055 0056 0056 0055 0056 0049 0056 0056 0055 0055 0054 005511986215

0056 0057 0056 0056 0056 0056 0056 0056 0057 0056 0057 0057 0056 0057 0050 0056 0056 0056 0056 005611986216

0051 0051 0050 0050 0050 0050 0050 0050 0051 0050 0050 0050 0051 0050 0051 0045 0051 0051 0050 005011986217

0049 0049 0050 0050 0049 0049 0049 0049 0049 0049 0049 0049 0049 0049 0048 0050 0044 0050 0049 004911986218

0051 0052 0052 0052 0051 0050 0050 0051 0050 0050 0051 0051 0050 0051 0051 0051 0051 0046 0052 005111986219

0050 0050 0050 0050 0051 0049 0050 0051 0050 0050 0051 0050 0050 0050 0050 0051 0050 0051 0045 005111986220

0044 0043 0044 0043 0044 0044 0044 0043 0043 0043 0044 0044 0043 0044 0044 0043 0044 0043 0044 0039








4)



4) is



1) is 0408







4) and



3) to




2until


1and 119880


follows 1198801 1198634(0518) ≻ 119863

3(0488) ≻ 119863

1(0408) ≻

1198632(0395) and 119880

2 1198634(0753) ≻ 119863

1(0653) ≻

1198633(0633) ≻ 119863



Table6Th

einfl

uentialw

eightsob

tained

throug

hDANP

Influ

entia


imensio

ns(119863119895)

Factors

1198621

1198622

1198623

1198624

1198625

1198626

1198627

1198628

1198629

11986210

11986211

11986212

11986213

11986214

11986215

11986216

11986217

11986218

11986219

11986220

0050

0049

0050

0053

0049

0052

0049

0055

0043

0052

0053

0045

0047

0055

0056

0050

0049

0051

0050

0043

Dim

ensio

ns1198631

1198632

1198633

1198634

0250

0251

0256

0243













1198802

1198801

1198802

EVM users (1198631) 0250 0408 0653

Experience (1198621) 0201 0050 3350 1944 0413 0764

Training (1198622) 0196 0049 3750 2667 0313 0583




EVM methodology (1198632) 0251 0395 0600

WBS (1198626) 0206 0052 4000 2833 0250 0542

CPM (1198627) 0196 0049 3500 1722 0375 0819

IPT (1198628) 0218 0055 3300 2889 0425 0528

Computer system (1198629) 0173 0043 3100 3056 0475 0486











17) 0201 0049 2900 2278 0525 0681

Risk free (11986218) 0208 0051 2800 1833 0550 0792

Culture (11986219) 0206 0050 2750 2389 0563 0653

Regulations (11986220) 0178 0043 3200 1722 0450 0819








4)




(15913 0241) being risk free11986218

(16817 0616) culture 11986219

(16310 0305) and regula-tions 119862










119888119894

119903119894+ 119888119894

119903119894minus 119888119894

EVM users (1198631) 1574 1600 3174 minus0025

Experience (1198621) 8416 8046 16463 0370

Training (1198622) 8265 7821 16086 0445





WBS (1198626) 8532 8265 16796 0267

CPM (1198627) 7040 7850 14890 minus0810

IPT (1198628) 8269 8745 17014 minus0476

Computer system (1198629) 8382 6914 15296 1467











Risk free (11986218) 8716 8101 16817 0616

Culture (11986219) 8308 8003 16310 0305

Regulations (11986220) 7170 6925 14095 0245



1) in the


12) in the






15) an integrated







D4 (3171 0060)Gaps

U1 0518U2 0753

minus004

minus002

000

002

004

006

316

INRM_dimensions


U1 0408U2 0653


U1 0395U2 0600


U1 0488U2 0633

317 318 319 320 321 322 323 324 325

riminusc i

ri + ci

(a)

INRM_factors in D1





minus104

minus074

minus044

minus014

016

046

1450 1500 1550 1600 1650 1700

C2 (16086 0445)Gaps

U1 0313U2 0583


U1 0450U2 0556


U1 0343U2 0569

C1 (16463 0370)Gaps

U1 0413U2 0764


U1 0500U2 0792

riminusc i ri + ci

(b)

riminusc i

ri + ci

INRM_factors in D2

WBS ( )C6

CPM ( )C7

IPT (C8)


minus090

minus040

010

060

110

160

147 152 157 162 167 172

C9 (15296 1467)Gaps

U1 0475U2 0468

C6 (16796 0267)Gaps

U1 0250U2 0542


U1 0450U2 0625


U1 0374U2 0819


U1 0425U2 0528

(c)

riminusc i ri + ci

070

1510 1560 1610 1660 1710


U1 0413U2 0625

C12 (15218 0674)Gaps

U1 0513U2 0736


U1 0588U2 0681

C13 (15671 0625)Gaps

U1 0425U2 0639

C11 (17503 0266)Gaps

U1 0500U2 0486

minus180

minus130

minus080

minus030

020

INRM_factors in D3





(d)

riminusc i

ri + ci

INRM_factors in D4

Risk free (C18)



C18 (16817 0616)Gaps

U1 0550U2 0792

C19 (16310 0305)Gaps

U1 0563U2 0653

C15 (16132 0091)Gaps

U1 0500U2 0819

C17 (15913 0241)Gaps

U1 0525U2 0681

C20 (14095 0245)Gaps

U1 0450U2 0819

1390 1440 1490 1540 1590 1640 1690

000

030

060

(e)

Figure 3 The INRM




5 Conclusions





Competing Interests


References















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Table6Th

einfl

uentialw

eightsob

tained

throug

hDANP

Influ

entia


imensio

ns(119863119895)

Factors

1198621

1198622

1198623

1198624

1198625

1198626

1198627

1198628

1198629

11986210

11986211

11986212

11986213

11986214

11986215

11986216

11986217

11986218

11986219

11986220

0050

0049

0050

0053

0049

0052

0049

0055

0043

0052

0053

0045

0047

0055

0056

0050

0049

0051

0050

0043

Dim

ensio

ns1198631

1198632

1198633

1198634

0250

0251

0256

0243













1198802

1198801

1198802

EVM users (1198631) 0250 0408 0653

Experience (1198621) 0201 0050 3350 1944 0413 0764

Training (1198622) 0196 0049 3750 2667 0313 0583




EVM methodology (1198632) 0251 0395 0600

WBS (1198626) 0206 0052 4000 2833 0250 0542

CPM (1198627) 0196 0049 3500 1722 0375 0819

IPT (1198628) 0218 0055 3300 2889 0425 0528

Computer system (1198629) 0173 0043 3100 3056 0475 0486











17) 0201 0049 2900 2278 0525 0681

Risk free (11986218) 0208 0051 2800 1833 0550 0792

Culture (11986219) 0206 0050 2750 2389 0563 0653

Regulations (11986220) 0178 0043 3200 1722 0450 0819








4)




(15913 0241) being risk free11986218

(16817 0616) culture 11986219

(16310 0305) and regula-tions 119862










119888119894

119903119894+ 119888119894

119903119894minus 119888119894

EVM users (1198631) 1574 1600 3174 minus0025

Experience (1198621) 8416 8046 16463 0370

Training (1198622) 8265 7821 16086 0445





WBS (1198626) 8532 8265 16796 0267

CPM (1198627) 7040 7850 14890 minus0810

IPT (1198628) 8269 8745 17014 minus0476

Computer system (1198629) 8382 6914 15296 1467











Risk free (11986218) 8716 8101 16817 0616

Culture (11986219) 8308 8003 16310 0305

Regulations (11986220) 7170 6925 14095 0245



1) in the


12) in the






15) an integrated







D4 (3171 0060)Gaps

U1 0518U2 0753

minus004

minus002

000

002

004

006

316

INRM_dimensions


U1 0408U2 0653


U1 0395U2 0600


U1 0488U2 0633

317 318 319 320 321 322 323 324 325

riminusc i

ri + ci

(a)

INRM_factors in D1





minus104

minus074

minus044

minus014

016

046

1450 1500 1550 1600 1650 1700

C2 (16086 0445)Gaps

U1 0313U2 0583


U1 0450U2 0556


U1 0343U2 0569

C1 (16463 0370)Gaps

U1 0413U2 0764


U1 0500U2 0792

riminusc i ri + ci

(b)

riminusc i

ri + ci

INRM_factors in D2

WBS ( )C6

CPM ( )C7

IPT (C8)


minus090

minus040

010

060

110

160

147 152 157 162 167 172

C9 (15296 1467)Gaps

U1 0475U2 0468

C6 (16796 0267)Gaps

U1 0250U2 0542


U1 0450U2 0625


U1 0374U2 0819


U1 0425U2 0528

(c)

riminusc i ri + ci

070

1510 1560 1610 1660 1710


U1 0413U2 0625

C12 (15218 0674)Gaps

U1 0513U2 0736


U1 0588U2 0681

C13 (15671 0625)Gaps

U1 0425U2 0639

C11 (17503 0266)Gaps

U1 0500U2 0486

minus180

minus130

minus080

minus030

020

INRM_factors in D3





(d)

riminusc i

ri + ci

INRM_factors in D4

Risk free (C18)



C18 (16817 0616)Gaps

U1 0550U2 0792

C19 (16310 0305)Gaps

U1 0563U2 0653

C15 (16132 0091)Gaps

U1 0500U2 0819

C17 (15913 0241)Gaps

U1 0525U2 0681

C20 (14095 0245)Gaps

U1 0450U2 0819

1390 1440 1490 1540 1590 1640 1690

000

030

060

(e)

Figure 3 The INRM




5 Conclusions





Competing Interests


References















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





















1198802

1198801

1198802

EVM users (1198631) 0250 0408 0653

Experience (1198621) 0201 0050 3350 1944 0413 0764

Training (1198622) 0196 0049 3750 2667 0313 0583




EVM methodology (1198632) 0251 0395 0600

WBS (1198626) 0206 0052 4000 2833 0250 0542

CPM (1198627) 0196 0049 3500 1722 0375 0819

IPT (1198628) 0218 0055 3300 2889 0425 0528

Computer system (1198629) 0173 0043 3100 3056 0475 0486











17) 0201 0049 2900 2278 0525 0681

Risk free (11986218) 0208 0051 2800 1833 0550 0792

Culture (11986219) 0206 0050 2750 2389 0563 0653

Regulations (11986220) 0178 0043 3200 1722 0450 0819








4)




(15913 0241) being risk free11986218

(16817 0616) culture 11986219

(16310 0305) and regula-tions 119862










119888119894

119903119894+ 119888119894

119903119894minus 119888119894

EVM users (1198631) 1574 1600 3174 minus0025

Experience (1198621) 8416 8046 16463 0370

Training (1198622) 8265 7821 16086 0445





WBS (1198626) 8532 8265 16796 0267

CPM (1198627) 7040 7850 14890 minus0810

IPT (1198628) 8269 8745 17014 minus0476

Computer system (1198629) 8382 6914 15296 1467











Risk free (11986218) 8716 8101 16817 0616

Culture (11986219) 8308 8003 16310 0305

Regulations (11986220) 7170 6925 14095 0245



1) in the


12) in the






15) an integrated







D4 (3171 0060)Gaps

U1 0518U2 0753

minus004

minus002

000

002

004

006

316

INRM_dimensions


U1 0408U2 0653


U1 0395U2 0600


U1 0488U2 0633

317 318 319 320 321 322 323 324 325

riminusc i

ri + ci

(a)

INRM_factors in D1





minus104

minus074

minus044

minus014

016

046

1450 1500 1550 1600 1650 1700

C2 (16086 0445)Gaps

U1 0313U2 0583


U1 0450U2 0556


U1 0343U2 0569

C1 (16463 0370)Gaps

U1 0413U2 0764


U1 0500U2 0792

riminusc i ri + ci

(b)

riminusc i

ri + ci

INRM_factors in D2

WBS ( )C6

CPM ( )C7

IPT (C8)


minus090

minus040

010

060

110

160

147 152 157 162 167 172

C9 (15296 1467)Gaps

U1 0475U2 0468

C6 (16796 0267)Gaps

U1 0250U2 0542


U1 0450U2 0625


U1 0374U2 0819


U1 0425U2 0528

(c)

riminusc i ri + ci

070

1510 1560 1610 1660 1710


U1 0413U2 0625

C12 (15218 0674)Gaps

U1 0513U2 0736


U1 0588U2 0681

C13 (15671 0625)Gaps

U1 0425U2 0639

C11 (17503 0266)Gaps

U1 0500U2 0486

minus180

minus130

minus080

minus030

020

INRM_factors in D3





(d)

riminusc i

ri + ci

INRM_factors in D4

Risk free (C18)



C18 (16817 0616)Gaps

U1 0550U2 0792

C19 (16310 0305)Gaps

U1 0563U2 0653

C15 (16132 0091)Gaps

U1 0500U2 0819

C17 (15913 0241)Gaps

U1 0525U2 0681

C20 (14095 0245)Gaps

U1 0450U2 0819

1390 1440 1490 1540 1590 1640 1690

000

030

060

(e)

Figure 3 The INRM




5 Conclusions





Competing Interests


References















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












119888119894

119903119894+ 119888119894

119903119894minus 119888119894

EVM users (1198631) 1574 1600 3174 minus0025

Experience (1198621) 8416 8046 16463 0370

Training (1198622) 8265 7821 16086 0445





WBS (1198626) 8532 8265 16796 0267

CPM (1198627) 7040 7850 14890 minus0810

IPT (1198628) 8269 8745 17014 minus0476

Computer system (1198629) 8382 6914 15296 1467











Risk free (11986218) 8716 8101 16817 0616

Culture (11986219) 8308 8003 16310 0305

Regulations (11986220) 7170 6925 14095 0245



1) in the


12) in the






15) an integrated







D4 (3171 0060)Gaps

U1 0518U2 0753

minus004

minus002

000

002

004

006

316

INRM_dimensions


U1 0408U2 0653


U1 0395U2 0600


U1 0488U2 0633

317 318 319 320 321 322 323 324 325

riminusc i

ri + ci

(a)

INRM_factors in D1





minus104

minus074

minus044

minus014

016

046

1450 1500 1550 1600 1650 1700

C2 (16086 0445)Gaps

U1 0313U2 0583


U1 0450U2 0556


U1 0343U2 0569

C1 (16463 0370)Gaps

U1 0413U2 0764


U1 0500U2 0792

riminusc i ri + ci

(b)

riminusc i

ri + ci

INRM_factors in D2

WBS ( )C6

CPM ( )C7

IPT (C8)


minus090

minus040

010

060

110

160

147 152 157 162 167 172

C9 (15296 1467)Gaps

U1 0475U2 0468

C6 (16796 0267)Gaps

U1 0250U2 0542


U1 0450U2 0625


U1 0374U2 0819


U1 0425U2 0528

(c)

riminusc i ri + ci

070

1510 1560 1610 1660 1710


U1 0413U2 0625

C12 (15218 0674)Gaps

U1 0513U2 0736


U1 0588U2 0681

C13 (15671 0625)Gaps

U1 0425U2 0639

C11 (17503 0266)Gaps

U1 0500U2 0486

minus180

minus130

minus080

minus030

020

INRM_factors in D3





(d)

riminusc i

ri + ci

INRM_factors in D4

Risk free (C18)



C18 (16817 0616)Gaps

U1 0550U2 0792

C19 (16310 0305)Gaps

U1 0563U2 0653

C15 (16132 0091)Gaps

U1 0500U2 0819

C17 (15913 0241)Gaps

U1 0525U2 0681

C20 (14095 0245)Gaps

U1 0450U2 0819

1390 1440 1490 1540 1590 1640 1690

000

030

060

(e)

Figure 3 The INRM




5 Conclusions





Competing Interests


References















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












D4 (3171 0060)Gaps

U1 0518U2 0753

minus004

minus002

000

002

004

006

316

INRM_dimensions


U1 0408U2 0653


U1 0395U2 0600


U1 0488U2 0633

317 318 319 320 321 322 323 324 325

riminusc i

ri + ci

(a)

INRM_factors in D1





minus104

minus074

minus044

minus014

016

046

1450 1500 1550 1600 1650 1700

C2 (16086 0445)Gaps

U1 0313U2 0583


U1 0450U2 0556


U1 0343U2 0569

C1 (16463 0370)Gaps

U1 0413U2 0764


U1 0500U2 0792

riminusc i ri + ci

(b)

riminusc i

ri + ci

INRM_factors in D2

WBS ( )C6

CPM ( )C7

IPT (C8)


minus090

minus040

010

060

110

160

147 152 157 162 167 172

C9 (15296 1467)Gaps

U1 0475U2 0468

C6 (16796 0267)Gaps

U1 0250U2 0542


U1 0450U2 0625


U1 0374U2 0819


U1 0425U2 0528

(c)

riminusc i ri + ci

070

1510 1560 1610 1660 1710


U1 0413U2 0625

C12 (15218 0674)Gaps

U1 0513U2 0736


U1 0588U2 0681

C13 (15671 0625)Gaps

U1 0425U2 0639

C11 (17503 0266)Gaps

U1 0500U2 0486

minus180

minus130

minus080

minus030

020

INRM_factors in D3





(d)

riminusc i

ri + ci

INRM_factors in D4

Risk free (C18)



C18 (16817 0616)Gaps

U1 0550U2 0792

C19 (16310 0305)Gaps

U1 0563U2 0653

C15 (16132 0091)Gaps

U1 0500U2 0819

C17 (15913 0241)Gaps

U1 0525U2 0681

C20 (14095 0245)Gaps

U1 0450U2 0819

1390 1440 1490 1540 1590 1640 1690

000

030

060

(e)

Figure 3 The INRM




5 Conclusions





Competing Interests


References















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












5 Conclusions





Competing Interests


References















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra









Research Article A Novel Hybrid MCDM Procedure...

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