TECHNOSCIENCE ARTICLE AHP-VIKOR Bridge Structural System ...2)_Ta05.pdf · Malekly (2010) developed...

Published by: National Cave Research and Protection Organization, IndiaVol. 3(2):48-54

Year 2016

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ISSN- 2348 5191 (Print) & 2348 8980 (Electronic)

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Ambient Science, 2016: Vol. 03(2); 48-54DOI:10.21276/ambi.2016.03.2.ta05

The selection of “Structural system” is one of the mostimportant factors in any bridge and infrastructure design.Designers perform the structural calculations for theproject determines the priorities as well as design andperformance criteria. Further analysis of the structuralselection problem and the identif ication of the bridgedesirable capabilities, triggered the consideration ofanalytic hierarchy process (AHP) as a possible basis for thedecision making. The methodology uses the VIKOR toevaluate the alternatives according to the decision criteriaand determine the solution. The methodology wasdeveloped by a group of bridge designers involved in designand management of urban infrastructure projects anddemonstrated using aSteel Girder bridge in an urban areaasanoptimumalternative.

Abstract

Introduction:Bridgesare massive structures thatcarry road (oreven rail)traff ic across which requires large amounts of materialsand construction work. Therefore, the decision regardingthe most convenient construction systems to be usedusually depends on many factors and not limited to theavailable technology and equipment, or the siteconditions. In addition to the tangible costs expressed interms of time, money, and rework, catastrophic bridgefailures such as bridge collapsesduring construction causesignif icant damages to existing transportation networksleading to substantial socioeconomic disruptions for thepublic (Pan, 2008)

The bridge design decision is a complex decision-making process affected by numerous factors includingproject cost and required construction period, traff icvolume (especially in urban environments), type of bridgedeck, passive defense capability, and seismic resistance(Itoh , 2000). Structural and seismic regulation,bridge simulation modeling, and bridge design softwareapplications developed based on the previous case studiesf ixed some standard to the construction method selectionprocess (Arici & Mosalam, 2000). Many studies ormethodologies for facilitating the decision-makingprocess have focused on the decision criteria such as cost,quality, required construction period, safety, and

et al.

structural shape. These criteriacan be furtherdivided intosub-criteria, for instance, direct and indirect costs(McCrea , 2002; Pan, 2006; Pan , 2005;; Ugwu

., 2005; Kerzner, 2001; Ugwu , 2006) . While theearlier researchers have attempted to solve the selectionproblems employing various mathematical tools andtechniques that were affected by the weights assigned tothe considered selection criteria, “Multi-ObjectiveOptimizationon the basisof ratioanalysis” (MOORA) and“Preference Ranking Organization Method forEnrichment Evaluations” are now using successfully forthe grouping and comparing the desired criteria of bridgeselection that would remain unaffected by the criteriaweights and normalization procedure (Choi 2012;Jung & Lee, 2012; Mandal & Sarkar, 2012).

Attempts were also made to integrate differentdecision support systems to prioritize of evaluationcriteria and to rank the bridge design alternatives.Examples include Project Resource Planning, FuzzyAnalytic Hierarchy Process and Analytic Network Process(Vayvay , 2012; Al-Harbi, 2001; Felek , 2002;Basligil, 2005).Malekly (2010) developed an integratedmethodology using “Quality Function Deployment” and“Technique for Order Performance by Similarity to IdealSolution” (TOPSIS) for evaluating conceptual bridge

et al. et al. etal et al.

et al.,

et al. et al.

et al.

AHP-VIKOR Bridge Structural System Selection in Urban AreasTehran: Interchanges Case Study

Ali Akbar Ramezanianpour , Seyyed Alireza

Tabatabaei , Mahyar Pourlak *, Majid

Abareshi

1

2 3

4

1

2

3

4

Department of Civil Engineering, Amirkabir University ofTechnology, Tehran, Iran

Department of Construction Management, Islamic AzadUniversity-SouthTehran Branch, Tehran, Iran

Young Researchers and Elite Club, South Tehran Branch, IslamicAzad University, Tehran, Iran

Department of Industrial Engineering, Iran University of Scienceand Technology, Tehran, Iran

Key words: Analytic Hierarchy Process (AHP),Priority weight.

StudyArea: Tehran, IranCoordinates: 35°41'46”N; 51°25'23”E

TECHNOSCIENCE ARTICLE

http://www.caves.res.in/

design. Along with the availability of more advancedconstruction applications, the selection of appropriateconstruction method becomes vital in bridge engineeringdomain (Skibniewski, 1992; Hastak,1998). However, therehave been relatively few studies that adopted MCDMoptimization and AHP in the f ield of bridge selection(Eshtehardian 2013; Farkas, 2010; Golestanifar &Ahangari, 2011; Wang, 2011). Rashidi & Gibson (2011)proposed a methodology for bridge condition assessment,which used AHP method to evaluate random vectorparameters in the transportationarea.

Analytic Hierarchy Process (AHP) as one of the multicriteria decision making tools, f irstly sets on by Saaty(1980). AHP has been one of the most extensively usedmethods for MCDM and has been extensively studied andref ined since then. It provides a comprehensive andrational framework forstructuring adecision problem, forrepresenting and quantifying its elements, relating theseelements to overall goals, and for evaluating alternativesolutions. AHP has been used to solve MCDM problems ina wide variety of areas such as project selection, budgetallocation (Soh, 2010), and software selection(Štemberger, 2009). It is mainly used to derive the mostadvanced scales of measurement from both discrete andcontinuous paired comparisons in multilevel hierarchicstructures. These comparisons may be taken from actualphysical measurements or from subjective estimates thatreflect the relative strength of preferences of the experts.(Farkas, 2010).

The AHP methodology, as its name implies, requires ahierarchy structure to represent the decision problem, aswell as pairwise comparisons to establish relations withinthe structure. The pairwise comparisons lead todominance matrices. The required number of thesematrices corresponds to the number of weighting factors.Regarding the group participants, it is necessary to f indout how close (or far apart) an individual’s judgment is toothers, so they can be synthesized. Synthesizing thejudgments of decision makers based on the averageweighting factors, will lead to a weighted priority rankingthat indicates the overall preference score for eachdecision alternative (Farkas, 2010). A fuzzy-AHP methodis one of the most appropriate techniques for selecting thesuitable bridge construction method, particularly forsegmental and precast concrete segment bridges. In thisstudy, eight experts (bridge design engineers) were askedto the criteria through pair-wise comparisons. This led tothe development of an AHP model including twohierarchies, three choices, and 5 criteria (Quality, Cost,Safety, Timeand Shape) (Pan, 2008).

VIKOR is an adaptive MADM method that isdeveloped by Opricovic & Tzeng (2007) based on the LP-metric. This method is based on the adaptive planning ofMCDM problems and evaluates problems where decision

et al.,

criteria are inappropriate and inconsistent. The VIKORmethod is well established in situations where thedecision maker has to deal with such criteria and thusinevitably seeks solutions close to the ideal. In thismethod, all decision alternatives are evaluated against thedecision criteria. Moreover, this method is particularlyuseful in cases where the decision maker is not able toidentify the superiorities of a problem upon its startingtime and planning phase. In such cases, the VIKORmethod serves as an effective decision making tool andprovides a maximum group utility value for the majorityand a minimum individual regret for the veto (Opricovic &Tzeng, 2007).

The VIKOR method delivers relative satisfaction ofthe majority of decision criteria in terms of their closenessto the ideal solution and entails minimum levels of regretfor each of the criteria in terms of their closeness to anti-ideal solutions. In other words, minimum regret in havingfailed to choose the ideal solution. Here, the decisionalternativewith the highestrank is theone that isclosest tothe ideal solution; conversely, in methods such as TOPSIS,the highest ranked decision alternative does not alwaysrepresent the closest one to the ideal solution(Valahzaghard & Ferdousnejhad, 2013). The VIKORmethod has been applied to the problems of producermanagement and prioritization in the supply chain (Liou& Chuang, 2010; Liu & Du, 2008; Lixin 2008;Tianchang et al., 2008) optimization of processes (Tong

, 2007), evaluation of banking performances (Wu et al.,2009) and in earthquake and environmental engineering(Opricovic & Tzeng, 2004). This method has also beenused in urban and water resource management (Chang &Hsu, 2009; Opricovic, 2009) . For moreon theapplicationsof the VIKOR method, the interested reader may refer to(Büyüközkan & Ruan, 2008; Chen & Wang, 2009; Chiang,2009; Sanayei 2010).

esigners (usually civil/structural engineers), performing the structuralcalculations for the projectdetermine the prioritiesaswellas design and performance criteria. Depending on theengineer’s opinion, some of the essential criteria orstructural systems may get ignored. This may lead to anincrease in costs and reductions in eff iciency. However,using the step-by-step procedure, such problems could beavoided in theearlystagesof majorbridgeprojects.

this section divides the model into athree-layered hierarchical model, as shown in Figure-1,where the overall objective is placed in level 1, criteria anddecision alternatives are presented in level 2 and 3,respectively.The main objective is to select the mostsuitable bridge structural system (decision made by thedesign engineer). Then, the design criteria includingProject cost, Construction Duration, Traff ic limitation

et al.,et

al.

et al.,

Existing Gap in the Process: d

Proposed Model:

Ambient Science (2016) Vol.-03(2): p. 49

Ambient Science, 2016: Vol. 03(2); 48-54DOI:10.21276/ambi.2016.03.2.ta05TECHNOSCIENCE ARTICLE

(especially in urban zones), Span, Passive defensecapability and Maintenance costs, (level 2) will result inthedesignalternatives (level 3), presented in “Figure-1”.

among all the selection criteria,we only consider Project cost, Construction Duration,Traff ic limitation (especially in urban zones), Span,Passive defense capability and Maintenance costs in thispaper. Thesecriteriaaredescribed in the following:

Definition of Criteria:

Project cost: The structure cost is affected by the projectschedule, resources, and risk. The project cost can be themost important parameter describing a client’s projectrequirements. It should be noted that this study does nottake intoaccountthe mobilizationcost.

Construction Duration: The construction duration arising fromcritical path in which duration for items of work or activityinsequencesorhierarchiescannot bereduced further.

Traff ic Limitation (especially in urban zones): Considering theeffect of construction activities on traff ic flow, the traff icvolume (both vehicles and pedestrians) during theconstruction phase is selected as one of the selectioncriteria.

Deck length between Two Piers: The distance between two piersof a bridge has been considered as a uniform variable in allsystems.

Passive Defense Capability: Capability of a bridge structuralsystem is an inherent characteristic of any structure thatshould beconsidered during thedesignprocess foranycriticsituation.

Maintenance Costs: The maintenance costs of equipment andbridge itself during its lifespan account for a major part oftotal life cycle cost. Performing f ield inspection of thebridge can provide better insight into the detection andcorrection of structural components with serious defects.Maintenance, including tests, measurements, adjustments,and parts replacement, is mainly performed to preventfaults from occurring. "Figure 2" shows the importance ofthe maintenancecosts ina bridgeconstructionproject.

Structure Weight: Theweightof thestructure (Piers, Abutments,and Deck), is dependent on the surface area of the structureand playsa keyrole in the seismiccapabilityof the structure.Earthquake forces are proportional to a structure's mass, soheavy bridgestructuresexperiencegreater forces.

http://www.caves.res.in/Ambient Science (2016) Vol.-03(2): p. 50

Segmental Voided SlabConcrete

BoxGirder

Steel Girder(Steel Beams)

ConcreteGirder

(Concrete Beams)

Suspension&

Cable-stayed

ProjectCost

ConstructionDuration

TrafficLimitation

Deck lengthbetween Two

Piers

PassiveDefense

Capability

MaintenanceCosts

StructureWeight

The BridgeBuilder

FormtravellerEquipments

Bridge Structural System

Figure 1: The Hierarchy for the Consultant Selection Problem

Figure 2: Cost of delaying maintenance

DecisionAlternatives:

Steps in the VIKOR Method:

DeterminationoftheBestand WorstValues

Calculating theVIKORvalueQi

amongdifferent designalternatives,following Tahouni,(2004) the givenBridge StructuralSystems have beenselected for thisstudy; Segmentalbridge, Voided SlabBridge, Box GirderBridge, Steel Girder(Steel Beams)Bridge,

Concrete Girder (Concrete Beams) Bridge, Suspension &Cable-stayedbridge, Bridge Builder Form-travelerEquipments .

Calculation of the Normalized Quantities/ Values-Assume that there are decision alternatives and

decision criteria. The normalized quantities/values arecalculated using the following equation.

The various alternatives, i, are represented as xi. xij isthe value and amount of criteria j. Normalization of thequantities, where xij is the real value of alternative i andthen j, is as follows:

(2)

Where, is thevalueof alternative i forcriterion .

The best and worst values for each criterion are identif iedand called fj*and fj-, respectively.

(3)(4)

Where * is the bestpositive ideal solutionand -is the worst negative ideal solution for criterion .Combining all *, an optimum combination result whichyield the highestrank. Thisalso holds true for .

(5)

(6)

Where is the distance between alternative i and thepositive ideal solution (best combination) and Ri is thedistance between alternative and the negative idealsolution (worst combination). The best and worst ranksare then computed based on the values of and ,respectively. In other words, and are and L01equivalents in the LP-metric technique.

TheVIKORvalue iscalculated forevery i as follows:

m n

xij j

f j f jj

f jf j-

Si

i

S R

S R L1ii i

i i

40%Quality drop

40%Quality drop

Time

would cost$5.00 if

delayed tohere

Each $.00of renovation

here

(Rossow, 1983)

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ij

ij ,...,2,1;,...,2,1,

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f Max f i m

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R Max w f f f f� � ��



Ambient Science (2016) Vol.-03(2): p. 51http://www.caves.res.in/

(7)Where

andand is the maximum group utility or the strategy weightof the majority thatvote in favourof thegivencriteria.

is the distance from alternative i to the negativeideal solution; in other words, this indicatesmajority’svote in favourof thealternative.

is the distance from alternative i to the positiveideal solution; This distance value is themajority’s vote against alternative i. So, when

> 0.5 holds true, leads to a majority agreement/satisfaction, conversely, when < 0.5 holds true,represents the negative view of the majority. Finally, when= 0.5 holds true then this means that a consensus isreached between theevaluationexperts.

In this step, thealternativesare ranked based on thevaluesof Q thatwerecalculated in the previousstepand then thedecisioncan be made.

In this section, an AHP-based selection model for thebridge structure is formulated and then applied to a realcasestudy.

The alternatives are organized and ranked accordingto their values, their ascending rank. Each alternativemustsatisfy the following twoconditions:Condition 1: If alternatives 1 and 2 -in order- are f irst andsecond best alternative in the group and n shows thenumberof alternatives. Then :

Q(A2)- Q(A1) 1n-1

QiQi

Ranking oftheAlternatives Based on Qi

Casestudy

i

>

(1 )i i

i

S S R RQ v v

S S R R

� �

� � � �

� � � ��

� � � �

ii

S MinS� �i

iS Max S� � i

iR Min R� � i

iR Max R� �

v

v

v

v

iS S

S S

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iR R

R R

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Regarding the values and ranks of R, S and Q groups, theselection should be processed towards “Concrete Girder”and “Steel Girder” by checking out two mentionedconditions.

The objective, affected by the selection criteria, isplaced at the top of the hierarchy. These criteria arepresented on the second level and the design alternativesare presented at the bottom of the hierarchy. Thesealternatives are affected by sub-criteria and if there is nosub-criterion, theyareaffected by maincriteria.

After def ining the relative importance of all thedecision criteria via pair-wise comparisons, the result isrepresented in a comparison matrix. The Scales of RelativeImportancearesimply followed "Table-1" rules.

In the f irst step, we interviewed total eight designengineers for obtaining the required informationregarding the mean criteria matrix. Table 2 shows thecomparison matrix for the criteria def ined in this study.This matrix results from the relative weights among all thepossiblecombinationsof theselectioncriteria.

The relative weights are determined after thenormalization of the matrix. This process is performed bydividing the elements of each column with their sum. As a

Q(steel Girder)-Q(concrete Girder) 1 0.0273741030. 1666666677-1

Ratheruniform 1Identical orpartiallyreference 2Relativelyreference 3Moderatelyorstronglyreference 4Stronglyreference 5Strong toverystrong reference 6Verystrong preference 7Areference tothe immensely 8Thesizeof thereference 9

> �

Table -1: Scale of Relative ImportanceThe importanceof pairwisecomparison Numericalvalue

Figures: ( ): Sadr Elevated Expressway, Under Construction (2012), Tehran, IRAN; The Vafadar Bridge, Constructed (2012),Tehran, IRAN; Abbaspour University Box Girder Bridge, Constructed (2012) Tehran, IRAN; Steel Multi-girder bridge usingvariable depth girders Westgate bridge, Gloucester; Sazman Aab Bridge, Constructed (2008), Tehran IRAN; 8- : JavadiehBridge, Constructed (2010), Tehran, IRAN; - Abdoun Bridge, Constructed (2006), Amman, Jordan; Pierre Pflimlin bridgebeing builtoverthe Rhinesouthof Strasbourg

3-10 3- 4-5- 6-

7-9 10-

1

5

22

6

33

77

44

88



result, we compared the decision criteria and calculatetheir relative weights. Although this matrix should fulf illthe client’s needs and requirements, we completed thatbased on the interviewed experts. The experts’ knowledgeand opinion can also demonstrate the difference betweentheirviewpointsand thoseof clients.

The next step is to compare the decision alternativesregarding each decision criterion. This is done by usingseven different tables like “Table 3”, which shows anexample of the comparison matrix with some decisions.Then, theweightof eachalternative iscalculated.

1.00 1.67 1.25 2.67 1.92 1.92 2.670.60 1.00 1.39 1.83 1.83 1.72 1.920.80 0.72 1.00 2.50 1.92 1.83 2.670.38 0.55 0.40 1.00 1.39 0.64 1.170.52 0.55 0.52 0.72 1.00 1.31 1.640.52 0.58 0.55 1.57 0.77 1.00 2.170.38 0.52 0.38 0.86 0.61 0.46 1.00

-Project Cost; -Construction Duration; -Traff ic Limitation;- Deck length; - Passive Defense; - Maintenance Costs; -

StructureWeight

Table 2: Criteria Comparison Matrix; f illed by MCDM Experts

a b cd e f g

a b c d e f gabcdefg

Table 3: Project Cost Comparison Matrix with Decisions

Table 4: The matrix of Decisions-Criteria

hijklmn

h i j k lm n

h i j k l m nhijklmn

h i j k l m n

1.00 0.53 0.75 0.75 0.53 1.63 0.881.89 1.00 1.42 1.42 1.17 2.50 2.001.33 0.71 1.00 1.17 0.97 2.21 1.631.33 0.71 0.86 1.00 0.69 2.24 1.651.89 0.86 1.03 1.44 1.00 2.24 1.900.62 0.40 0.45 0.45 0.45 1.00 0.691.14 0.50 0.62 0.60 0.53 1.44 1.00

Once all matrices are compared and formed, we cannormalize each matrix. Table 4 shows the decision criteriamatrix that is formed based on these thevalues.

0.1087 0.1778 0.1795 0.1694 0.0966 0.1196 0.15090.2097 0.1330 0.1019 0.0958 0.1885 0.2074 0.10100.1631 0.1470 0.1614 0.1063 0.1754 0.1602 0.17700.1495 0.1427 0.1595 0.1110 0.1728 0.1602 0.19300.1878 0.1480 0.1531 0.0814 0.1517 0.1439 0.11740.0742 0.1141 0.1144 0.2325 0.0980 0.0798 0.13780.1037 0.1300 0.1236 0.1875 0.1122 0.1203 0.1174

-Segmental; -Voided Slab ; -Steel Girder ; -Box Girder; -Concrete Girder ; - Suspension & Cable-stayed; - BridgeBuilderForm-travele

Table 5: The matrix of Decisions-Criteria

Criteria Structure Maintenance Passive Deck Construction Traff ic ProjectWeight Costs Defence Length Duration Limitation Costs

Criteria weights (Importance)SegmentalVoided SlabSteel GirderBox GirderConcrete GirderSuspension & Cable-stayedBridge Builder Form-traveler

f *f -

Alternatives Ranking Value (Qi) Value (Vi) Distance from Positive Ideal Distance from PositiveSolution (Ri) Ideal Solution (Si)

SegmentalVoided SlabSteel GirderBox GirderConcrete GirderSuspension & Cable-stayedBridge Builder Form-traveler

0.129 0.07 0.19 0.057 0.02 0.091 0.020.127553388 0.154780231 0.096631358 0.169406642 0.107980281 0.111331152 0.1660004920.19 0.089249888 0.188533065 0.095780022 0.190216063 0.148821968 0.0860328660.11 0.115572398 0.175446833 0.106284896 0.120079488 0.134664752 0.1105659710.1 0.115572398 0.172807515 0.110975135 0.121581415 0.138672467 0.1206890830.16 0.128657183 0.151717799 0.081360889 0.126625949 0.133746197 0.0960579580.14 0.232010364 0.098008617 0.23253168 0.169490316 0.1734502 0.2430308150.16 0.153892077 0.112189039 0.187498131 0.156845803 0.152188897 0.173937749

0.1 0.09 0.19 0.23 0.11 0.11 0.090.19 0.23 0.1 0.08 0.19 0.17 0.24

4 0.555166504 0.5 0.12139812 0.3455467645 0.663255841 0.5 0.190412881 0.4586658281 0.5 0.5 0.076455934 0.2541938662 0.508531816 0.5 0.086208552 0.278015273 0.472625897 0.5 0.091858971 0.3392925667 0.5 0.5 0.244441221 0.8353064856 0.579756231 0.5 0.134076564 0.593271635

As the “Concrete Girder” does not satisfy the abovecondition, it cannot be the best alternative. In the casestudy, “Steel Girder” alternative satisf ied both conditionsand resulted in the best alternative. To analyze theproblem according to the AHP approach, we need tomultiply the matrix shown in Table 4 by the one shown inTable 5. Because the sizes of the matrices are 7×7 and 7×1,

the resulting matrix is 7×1 (Table 6 and Figure 11). Table 7showstheresulting ranking of thealternatives.

Regarding last part, now alternatives should be rankedrelieson R, S, and Qvalues; then:

Results :



0.472625897 Concrete Girder 0.076455934 Steel Girder 0.254193866 Steel Girder0.5 Steel Girder 0.086208552 Box Girder 0.27801527 Box Girder0.5 Suspension & 0.091858971 Concrete Girder 0.339292566 Steel Girder

Cable-stayed0.508531816 Box Girder 0.12139812 Segmental 0.345546764 Segmental0.579756231 Bridge Builder 0.134076564 Bridge Builder 0.458665828 Voided Slab

Form-traveler Eqp. Form-traveler Eqp.0.555166504 Segmental 0.190412881 Voided Slab 0.593271635 Bridge Builder

Form-traveler Eqp.0.663255841 Voided Slab 0.244441221 Suspension & 0.835306485 Suspension &Concrete Girder Cable-stayed Cable-stayed

Rely on Q value Rely on R value Rely on Q value

Ambient Science (2016) Vol.-03(2): p. 53http://www.caves.res.in/

Table 6: Result Matrix

Table 7: Ranked Result Matrix

Segmental 0.1412Voided Slab 0.1512Steel Girder 0.1540Box Girder 0.1510Concrete Girder 0.1472Suspension & Cable-stayed 0.0293Bridge Builder Form-traveler Eqp. 0.1219

1 Steel Girder 0.1542 Voided Slab 0.15123 Box Girder 0.15104 Concrete Girder 0.14725 Segmental 0.14126 The Bridge Builder Form-traveler Eqp. 0.12197 Suspension & Cable-stayed 0.0293

Bridge construction decisions during the design andconstruction stages of a project became more complex asnew construction methods have been developed. Thediversity and complexity of the construction methodsdemonstrate the need for using a uniform and systematicway to select the best decision alternative. The MCDMapproaches are the ones that quantify the decision criteriaand alternatives.

In this paper, we used AHP and VIKOR techniques forevaluating f ive different bridge structural systems; SteelGirder, Voided Slab, Box Girder, Concrete Girder,Segmental, Bridge Builder Form-traveler Equipment andSuspension & Cable- stayed. Also, the experts’ opinionswere utilized for the evaluation of each alternative and itsrelative weight. Through a case study, the application ofthe method was presented and “Steel Girder” system wasselected as the bestalternative.

We wish to thank Mr. Shapour Tahouni,Assistant Professor in department of civil engineering AmirkabirUniversity of Technology for his assistance and consultant in thisresearch.

Conclusion:

Acknowledgements:

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