Quantitative constructability analysis with a neuro-fuzzy knowledge-based multi-criterion decision support system

Ž .Automation in Construction 8 1999 553–565

Quantitative constructability analysis with a neuro-fuzzyknowledge-based multi-criterion decision support system

Wen-der Yu a,), Miroslaw J. Skibniewski b

a Department of Construction Engineering, Chung-Hua UniÕersity, Hsinchu 300, Taiwanb School of CiÕil Engineering, Purdue UniÕersity, West Lafayette, IN 47907-1294, USA

Accepted 7 September 1998

Abstract

This paper presents a multi-criterion decision model for quantitative constructability analysis based on a neuro-fuzzyknowledge-based system. The traditional constructability definition is modified so that constructability can be quantified,measured, and improved. A multi-layer information aggregation network is proposed to incorporate the manager’s subjectivepreference information. The constructor’s technology management policy can be reflected in the constructability evaluationprocess based on technology implementation preferences. A systematic approach to constructability problem detection andconstructability improvement is developed to improve technology performance. Two examples of constructability analysesfor alternative concrete formwork technologies are given to demonstrate the functions of the proposed methodology. q 1999Elsevier Science B.V. All rights reserved.

Keywords: Quantitative constructability analysis; Constructability improvement; Multi-criterion analysis; Neuro-fuzzy decision supportsystem

1. Introduction

A number of researchers and practitioners haveproposed various definitions of constructability. Two

Ž .of such definitions are quoted here: 1 Con-structability is the optimum use of constructionknowledge and experience in planning, design, pro-curement, and field operations to achieve overall

w x Ž .project objectives 1 ; 2 Constructability is the abil-ity to optimize resources such as manpower, time,quality, environmental conditions of labor and neigh-

w xborhood during construction 2 . The first definitionemphasizes on using construction knowledge learned

) Corresponding author

from past projects throughout the project life cycle.The second, which was defined specifically for theconsideration of construction technologies, providesan operational definition for quantitative analysis ofconstructability. Specifically, the constructability in

Žthis paper is defined as ‘the feasibility or complex-.ity of a considered project to be performed by a

specific technology based on the construction knowl-edge learned from past projects.’ This definition ofconstructability preserves the spirit of the first defini-tion above while adopting the quantitative approachof the second. The feasibility of a project to beconstructed with the use of the considered technol-ogy can be measured by technology performancefactors such as construction time, project cost, re-

0926-5805r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved.Ž .PII: S0926-5805 98 00105-8

( )W.-d. Yu, M.J. SkibniewskirAutomation in Construction 8 1999 553–565554

source requirements, and the constructed productquality. Better performance factor levels reflect bet-ter constructability of the considered project withrespect to the selected technology.

The performance factors can be viewed as projectobjectives which the project participants wish tooptimize, that is, to achieve the shortest projectduration, lowest construction cost, best utilization ofresources, and highest product quality. However,conflicting relationships exist among the project ob-jectives. For example, if the project duration is to beshortened, more resources should be invested, andthe cost is increased. Moreover, multiple constraintsshould be considered such as the project deadline,project budget, company resource availability, etc.Thus, the goal of constructability analysis in con-struction technology selection is to achieve ‘optimal’project objectives while satisfying the constraints.

This paper presents one aspect of a quantitativeconstructability analysis and feedback model which

Ž .consists of two major components: 1 a neuro-fuzzyknowledge-based system for technology performance

Ž .knowledge acquisition; and 2 a multi-layer utilityaggregation network for multi-criterion constructabil-ity analysis. For the first component, a genetic algo-rithm-enhanced neuro-fuzzy knowledge-based con-structability analysis decision support system was

w xdeveloped by Yu 4 to acquire the knowledge oftechnology performance from historic data. This pa-per describes the development of the second compo-nent and the integration of both components to per-form constructability analysis functions. The pro-posed multi-layer information aggregation networkprovides the ability to incorporate the manager’spreference information via different types of utilityfunctions and the weighting of criteria, so that theconstructor’s technology management policy can bebest reflected in the constructability analysis process.

2. Proposed model

As described above, effective constructabilityŽ .analysis consists of two major components: 1 per-

formance knowledge acquisition based on historicalŽ .data; and 2 multi-criterion analysis of the perfor-

mance factors according to the constructor’s internaland external conditions. The historic performance

knowledge can be acquired using neuro-fuzzy net-w xworks as described in Yu 4 . The multi-criterion

analysis of the performance factors is a complexprocess and it should be able to reflect the construc-tor’s technology policies with respect to variousinternal and external conditions. This section pre-sents the development of the multi-criterion decisionmodel for technology constructability analysis.

2.1. A neuro-fuzzy knowledge-based system

The neuro-fuzzy knowledge-based system adoptedhere for computing technology performance was de-

w xveloped by Yu 4 . The neuro-fuzzy knowledge-basedŽ .system is a Fuzzy Logic Decision System FLDS

with self-learning ability. The primary advantage ofan FLDS application to technology evaluation is itsnatural method of knowledge representation. A FLDSrepresents its knowledge in IF–THEN fuzzy rules.Fuzzy IF–THEN rules are expressions of the form‘F x is A, THEN y is B’. Since fuzzy IF–THENrules are intuitive to human, they are suitable tocapture the imprecise modes of reasoning that isessential for human’s ability to make decisions underan uncertain environment. This advantage can bevery useful for technology performance evaluation,since construction operations are usually performedunder an environment which can hardly be expressedprecisely. Thus, FLDS is useful for constructiontechnology evaluation. Unfortunately, the develop-ment of FLDS is not an easy job. It involves deter-mination of membership functions, generation offuzzy rules, and fuzzy partitions of linguistic terms.In the past decade, researchers have developed vari-ous neuro-fuzzy networks to implement functions ofthe traditional FLDS. The advantages of a neuro-fuzzy knowledge-based system over the traditionalFLDS is its ability to automatically construct thefuzzy IF–THEN rule base and memberships requiredfor an FLDS. This is done by the self-learningprocess of the neuro-fuzzy networks. A three-phase

w xlearning process has been proposed by Yu 4 toimprove network convergence while applying theneuro-fuzzy knowledge-based system to con-structability knowledge acquisition. After the learn-ing process, a neuro-fuzzy knowledge-based systemis able to construct the FLDS for technology perfor-mance estimation. The resulting FLDS performs

( )W.-d. Yu, M.J. SkibniewskirAutomation in Construction 8 1999 553–565 555

identically to any classical fuzzy logic decision-mak-ing system. It provides not only the function forconstruction technology performance estimations, butalso the linguistic explanation for the estimationresults. This features a trace-back mechanism forconstructability problem detection and solutionsearching that will be discussed later in this paper.For more details of neuro-fuzzy knowledge-based

w x w xsystems, please refer to Yu 4 , Lin and Lee 5 , andw xJang 6 .

2.2. Basic model

In order to investigate the multi-criterion, multi-attribute constructability analysis problems, let usexpress the general MCDM problem in the followingform:

Optimize Z x ,Z x , . . . , Z x ;� 4Ž . Ž . Ž .1 2 n

subject to xgX , 1Ž .Ž .where Z x is the k th objective, x is vector ofk

solution attributes, and X is the solution space. Herewe assume that there are n objectives to be opti-mized. Assume that the utility functions of all objec-

Žtives are monotonically increasing such as monetary.utility, i.e., more is better . Then, the MCDM prob-

lem becomes:

Max Z x , Z x , . . . ,Z x ;� 4Ž . Ž . .1 2 n

subject to xgX . 2Ž .This formulation is not adequate since for MCDM

problems there usually does not exist a unique solu-tion which optimizes all objectives. Tradeoffs arethus inevitable among the multiple objectives. Apopular approach to solving MCDM problem is sum-ming the weighed objectives to give a scalar value.That is,

Max w Z x ; subject to xgX ,Ž .Ý j j½ 5j

w s1, and w G0; for js1,2, . . . ,n , 3Ž .Ý j jj

where w is the weight for the jth objective. SolutionjŽ .x which gives the maximum value of objective 3 is

considered the optimal solution. However, this ap-proach assumes that a linear additive utility function

exists. The necessary condition for additive utilityfunction is that the criteria be preferentially indepen-

Ž w x.dent Keeney and Raiffa, Ref. 7 . In Keeney andRaiffa’s definition, two objectives are preferentially

Ž .independent PI if and only if that the decisionŽ .maker’s DM’s preference of one objective does not

depend on the value of the other objective. Thisbecomes the essential assumption for the Analytic

Ž .Hierarchy Process AHP method, which was pro-w xposed by Saaty 10 to solve the multi-criterion

weighting problems. Should the PI assumption holdin the MCDM problem, the remaining task is to

Ž .determine the weights in objective 3 . A basic con-cern is that the weights should reflect the DM’sbeliefs in the relative importance of the variousobjectives. The AHP method can be adopted to

Ž .determine weights in objective 3 by pairwise com-parison between each pair of criteria. Each compari-

Žson is transformed into a numerical value see Table.1 . The comparison results are then composed into a

� 4positive reciprocal matrix As a as shown in Fig.i j

1. Comparing matrix A with the pairwise relativeimportance matrix in Fig. 1, we obtain that a swi j i

rw , where w is the weight of the ith objective. Byj jT Žmultiplying A with the transpose of vector w s w ,1

.w , . . . , w , we obtain nw. The problem becomes an2 n

eigenvector problem with the following linear equa-tion:

Awsnw. 4Ž .Using linear algebra, to obtain nontrivial solution for

Ž . Žvector w is to solve AynI ws0, where det Ay.nI s0. This is a well-known eigenvalue problem,

where n is a root of the characteristic equation of A.w x ŽSaaty 8 has shown that A has a unit rank since

.every row is a constant multiple of the first row and

Table 1Numerical values for AHP pairwise comparison

Ž . Ž .Numerical value 1 Linguistic definition 2

1 Equal importance3 Weak importance of one over another5 Essential or strong importance7 Demonstrated importance9 Absolute importance2,4,6,8 Intermediate judgments between

two adjacent judgments


Fig. 1. Pairwise relative importance comparison matrix.

the components of eigenvector corresponding tomaximum eigenvalue of A give the real weights

Ž .associated with the objectives i.e., w , w , . . . ,w .1 2 nŽ .With these weights, we can solve Eq. 3 to obtain

the solution for value x.

2.3. Utility and difficulty index assessments

The basic model in the previous section describesthe method for determining fuzzy weights of variouscriteria in the AHP method. In the original AHPmethod, the relative values of the various alternativesat the bottom layer of AHP are assessed by the sameprocess. That is, the decision-maker determines arelative importance of the alternatives with respect toa specific criterion at the higher layer. This, how-ever, does not reflect a real decision scenario. At thebottom layer, the decision-maker evaluates the alter-natives according to their ‘values’ in his mind forthe considered criterion rather than their relativeimportance. Therefore, the value functions or utilityfunctions are more appropriate for the assessment at

Ž .the bottom layer. The expected utility EU methodcan be useful for this purpose. On the other hand, thenegative influence of a considered alternative withrespect to a specific criterion on the overall evalua-tion should be recorded. This is important for con-structability problem detection and performance im-provement.

The utility functions reflect behaviors of the deci-sion-maker when he makes his decisions. There arethree types of utility functions representing three

Ž . Ž .types of decision-makers: 1 risk averse; 2 riskŽ .neutral; 3 risk seeking. Fig. 2 shows three types of

utility functions associated with the three types ofdecision-makers.

Axis X in Fig. 2 represents the value of a specificless-is-better objective such as construction time,project cost, and resource requirements. Axis Y rep-resents the utility value of the considered objective.The LL on Axis X is defined as the lower limit forthe objective function. It can be viewed as the target

Ž .objective e.g., the planned construction time thatthe construction firm would like to achieve. The ULon Axis X is defined as the upper limit of theobjective function. It can be viewed as the contracted

Ž .objective e.g., contracted price that cannot be ex-ceeded. The concave utility curve in Fig. 2 repre-sents the behavior of risk seeking decision-makers. Arisk-seeking decision-maker increases hisrher utilityvalue with respect to the domain variable morequickly. A small gain in objective function results ina large increase in utility value. That is, hershetends to risk more to improve the objective value.The convex utility curve in Fig. 2 represents thebehavior of risk-averse decision-makers. A risk-averse decision-maker increases hisrher utility valuewith respect to the domain variable more slowly. Alarge gain in objective function can only result in asmall increase in utility value. That is, he tends torisk less to improve the objective value. The linearcurve in Fig. 2 represents the behavior of risk-neutraldecision-makers. The utility increase of a risk-neutraldecision-maker is proportional to the increase ofobjective value. Here we assume that a commonlyused exponential utility function is adopted. Then,the risk-seeking utility function for the less-is-better

Fig. 2. A typical less-is-better utility function.


objective function in Fig. 2 can be described by Eq.Ž .5 as follows:

x s2yeŽ xyLL .lnŽ2.rŽULyLL . , 5Ž . Ž .where LL and UL are the lower limit and upperlimit, respectively. Similarly, the risk-averse utilityfunction for the less-is-better objective function in

Ž .Fig. 2 can be described by Eq. 6 as follows:

x seyŽ xyUL .lnŽ2.rŽULyLL .y1. 6Ž . Ž .The risk-neutral utility function for the less-is-betterobjective function in Fig. 2 can be described by Eq.Ž .7 as follows:

ULyxx s . 7Ž . Ž .

ULyLLŽ .With the utility functions described in Eqs. 5 –

Ž .7 , the utility of a specific alternative with respect toa considered criterion can be assessed based on theobjective estimations.

According to the utility functions described above,the negative influence of a considered alternativewith respect to a specific criterion is defined as the

Ž .difficulty index D and defined as follows:

D x s1yU x . 8Ž . Ž . Ž .The difficulty index can be viewed as an expres-

sion of the difficulty, with respect to a specificcriterion, when applying the considered constructiontechnology to a given project. A higher difficultyindex reflects greater difficulty to implement theconsidered technology. It is therefore an indicator ofthe level of constructability of a given project withthe use of the considered construction technology.Examples of utility and difficulty indexes for domainvariable x are shown in Fig. 2.

2.4. Multi-layer information aggregation network( )MIANet

Based on the basic model and utility assessmentmethod described above, a multi-layer network of

Ž .information aggregation MIANet for constructabil-ity evaluation can be constructed as shown in Fig. 3.

A MIANet consists of four layers which repre-sents the decision structure for constructability anal-ysis. Each layer consists of a single node or severalnodes. Each node is connected to several nodes atthe lower layer and connected to a single node at the

Ž .Fig. 3. Multi-layer information aggregation network MIANet .

higher layer. Connections are represented as weights.Functions of the nodes in each layer are describedbelow layer by layer.

2.4.1. Layer 1The nodes in this layer transmit objective estima-

tions of each alternative into MIANet directly. Thus,the connection weights of Layer 1 are unity. Theobjective estimations are obtained from the neuro-

w xfuzzy networks described by Yu 4 .

2.4.2. Layer 2The nodes in this layer are represented by two

Ž . Ž .different categories: 1 project constraints; 2 com-pany constraints. Project constraints include con-struction time, project cost, and quality requirementset up by the project owner. Thus, they can also beconsidered as owner’s constraints. The second cate-gory includes labor, equipment, and material require-ments, which are constraints representing the con-structor’s abilities. Thus, they can be viewed asconstructor’s constraints. Components in this layercan be added according to project characteristics andthe organizational conditions of the construction firm.The above lists only the essential criteria for effec-tive constructability evaluation.

The first function of nodes in Layer 2 is to assessthe fuzzy utilities of each alternative at Layer 1based on estimations of the objective values. Theassessment results become the connection weights ofLayer 2. The utility assessments are based on Eqs.Ž . Ž .5 – 7 . The second function of the nodes in Layer 2


is to assess the difficulty indexes of the criteria forŽ .each alternative based on Eq. 8 . The third function

of Layer 2 is to transmit the assessed fuzzy utilitiesand difficulty indexes upwards to Layer 3.

2.4.3. Layer 3There are two nodes in Layer 3: the project

Ž .criterion node PC and constructor criterion nodeŽ .CC . The project criterion node connects to theproject constraint nodes and the company criterionnode connects to the constructor constraint nodes inLayer 2. The connection weights of Layer 3 aredetermined based the methodology given earlier inthe description of the basic model.

Ž .Major functions of the nodes in Layer 3 are: 1aggregation of fuzzy utilities from Layer 2 and trans-

Ž .mitting them to Layer 1; 2 recording the difficultyindex and transmitting it upwards to Layer 1. Theaggregation of utilities is a summation process in theAHP method and can be expressed as follows:

33 2x s w U x , 9Ž . Ž . Ž .Ý1 3 i i

is1

and

63 2x s w U x , 10Ž . Ž . Ž .Ý2 3 i i

is4

where the superscripts of utility values indicate thelayer numbers and subscripts indicate the node num-bers. The difficulty indexes are aggregated in adifferent manner from that for utilities. Since thepurpose of difficulty index is identifying the keycriterion at the bottom layer of MIANet causing thelow overall constructability level, the difficulty indexassociated with each criterion is transmitted sepa-rately upwards. The transmission process can bedescribed as follows:

D3 x sw D2 , 11Ž . Ž .i 3 i i

where the superscripts indicate the layer number, andthe subscripts indicate the criterion number at thebottom layer.

2.4.4. Layer 4The node in Layer 4 performs the final con-

structability evaluation of all alternatives. The func-tions of the node in Layer 4 are identical to those in

Layer 3 except that only a single node is there in thislayer. The utility aggregation can be calculated asfollows:

24 3x s w U x . 12Ž . Ž . Ž .Ý3 4 i i

is1

The difficulty indexes are aggregated in a similarmanner as in the previous layer, and can be de-scribed as follows:

D4 x sw D3 , 13Ž . Ž .i 4 i i

After the utility and difficulty index aggregations,the overall constructability evaluation of alternativeconstruction technologies is obtained along with their

Ž .negative influences difficulty indexes with respectto each of the criteria at the bottom layer. Theoverall utility represents the feasibility of applyingthe selected technology to the considered project.The difficulty indexes indicate potential con-structability difficulties which are caused by theassociated criteria at the bottom layer of MIANetwhen the selected technology is applied to the con-sidered project. Therefore, the criterion with thehighest difficulty index is the key criterion for thelow constructability. In search of the solution forconstructability improvement, the key criterionshould be improved first.

3. Incorporating constructor technology policy

According to the neuro-fuzzy knowledge-basedmulti-criterion constructability analysis model pro-posed in the previous section, the constructor’s tech-nology policy can be reflected by one of the follow-

Ž .ing approaches: 1 the assignment of proper weightsfor the various criteria in each layer of MIANet; andŽ .2 the selection of appropriate utility functions inthe criteria for the performance factors at the bottomlayer. The assignment of weights for the variouscriteria in each layer of MIANet reflects the knowl-edge of the construction managers regarding therelative importance of the various considered criteria.The relative importance relationships of the variouscriteria in each layer of MIANet can be determinedby the top managers through a group-discussionprocess. After the assessment process, a set of


Table 2Conditions for various applicable utility functions

Bottom criteria of MIANet Utility function type Conditions for the applicable utility functions

Ž . Ž . Ž .1 Internal condition 2 External condition 3

Project duration risk neutral medium work backlog medium deadline requirementrisk averse high work backlog strict deadline requirementrisk seeking low work backlog slack deadline requirement

Construction cost risk neutral medium work backlog slack marketrisk averse high work backlog prosperous marketrisk seeking low work backlog competitive market

Material requirement risk neutral medium material availability medium market material supplyrisk averse low own material availability market material shortagerisk seeking high own material availability sufficient market material supply

Equipment requirement risk neutral medium equipment availability medium market equipment supplyrisk averse low own equipment availability market equipment shortagerisk seeking high own equipment availability sufficient market equipment supply

Labor requirement risk neutral medium labor availability medium market labor supplyrisk averse low own labor availability market labor shortagerisk seeking high own labor availability sufficient market labor supply

Product quality risk neutral medium skilled labor availability medium quality requirementrisk averse insufficient skilled labor strict quality requirementrisk seeking sufficient skilled labor slack quality requirement

weights for MIANet can be obtained by solving theŽ .eigenvector of Eq. 4 .

Technology policies of a construction companycan be reflected in the proposed model based on theconstructor’s current internal and external conditions.Examples of the constructor’s internal and externalconditions with respect to the associated utility func-tions are listed in Table 2.

Before those utility functions can be used, param-Ž . Ž .eters LL and UL in Eqs. 5 – 7 should be deter-Ž .mined first. The lower limit LL of a domain vari-

able for a less-is-better utility function is the targetŽvalue of the considered criterion e.g., the budgeted

. Ž .project cost . The upper limit UL of a domainvariable for a less-is-better utility function is the

Žmaximum value which cannot be exceeded e.g.,.lump sum contracted price plus profit . The LL and

UL of each criterion at the bottom layer of MIANetshould be determined by the managers based onconstructor’s policy. LL and UL might be identical ifthe managers believe that the project objective candefinitely be achieved by a given construction pro-ject team. The transient range in Fig. 2 becomeswide when the definition of the project objective ishighly uncertain.

By the two approaches described above, the con-structor’s internal and external conditions along withthe associated technology policies can be reflected inthe proposed model. With the functionality providedby the proposed model, the influences of dynamicexternal conditions and constructor’s internal condi-tions can be reflected in the decision making process.Thus, the constructability evaluation of constructiontechnology can be more informative than the otherapproaches which do not consider these factors.

4. Constructability problem detection and im-provement

An important function of constructability analysisconsidering a specific construction technology is todetect potential constructability problems in the earlyphases of a project life cycle and to find a solutionfor the potential constructability problems when thereis no alternative technology can satisfy all projectand company constraints. The earlier the con-structability problems can be detected, the more

w xresulting expenditures can be saved 1 . Key reasonsfor the constructability problem should be identified


in order to achieve project objectives. An effectiveconstructability analysis method should provide ex-plicit explanations of the analysis results and thetrace-back mechanism for the key reasons causingconstructability problems.

The proposed model provides a problem-detectionmechanism by combining the difficulty index ofMIANet with the traceback function of neuro-fuzzynetworks. After aggregating the information, the util-ity value and the difficulty indexes are obtained withrespect to the performance factors at the bottomlayer of MIANet for each alternative. A utility levelof 0.5 can be considered a minimum for a ‘construct-ible’ project. Alternative technologies which canachieve utility levels higher than 0.5 can be consid-ered as feasible alternatives. If there is no alternativetechnology which can achieve a utility level higherthan 0.5 for a considered project, a potential con-structability problem is detected. The performancefactor with the highest difficulty index is identifiedas key reason causing the low utility level and islabeled as an ‘unsatisfactory’ performance factor.Through neuro-fuzzy networks, the key attributescausing the unsatisfactory performance factor can beidentified. A better performance level can be achievedby improving the key attributes. As the performancefactor is improved, the associated technology utility

Ž .is increased. As shown in Eq. 8 , the associateddifficulty index is decreased, thus, the overall con-

structability difficulty is decreased and the projectconstructability is improved.

5. Illustrative examples of the proposed model

The following demonstrates two constructabilityanalysis examples by the proposed multi-criteriondecision model. Performance data generated by asimulation technique developed by Yu and Skib-

w xniewski 3 are used for constructability analysis ofŽ .three formwork technologies: 1 conventional wood

Ž .formwork; 2 equipment-lifted panel form system;Ž .3 stay-in-place precast concrete form system. Formore information about the three formwork tech-

w xnologies, refer to Yu 4 . The project considered inthis example is a concrete frame building with threebays of 6.9 m in one direction and six bays of 8 m inthe other. Columns are 4 m in height. The one-wayslab is supported by beams and girders. Two beamsare supported by the girders in each slab. The taskconsists of rebar arrangements, form setup, and con-crete placement of all columns, girders, beams, andslabs. Before constructability analysis, the neuro-fuzzy networks for each technology are trained withpast technology performance data. The data acquiredin the neuro-fuzzy network serves as the foundationfor the constructability analysis of the consideredtask.

Table 3The selected utility functions

Bottom criterion of MIANet Selected utility function Parameters of utility functions

Ž . Ž . Ž . Ž . Ž .1 LL lower limit 2 UL upper limit 3

Ž .Construction time days risk seeking 12 15Ž .Project cost US$ risk seeking 140,000 160,000

a Ž . Ž .Product quality risk averse 0.5 medium 1 very goodMaterial requirements: risk seeking

2Ž .1. Wood forms m 2500 35002Ž .2. Equipment-lifted forms m 2900 3800

2Ž .3. Precast concrete forms m 2700 3500Ž .Equipment requirement crane risk seeking 3 5

Labor requirements: risk averseŽ .1. Carpenter teams 4 7Ž .2. Iron worker teams 2 3

Ž .3. Concrete worker teams 1 2Ž .4. Crew teams 3 5

a Ž . Ž .Product quality is a more-is-better type utility function which takes index value from 0 very poor to 1 very good . The utility functionsreverse horizontally compared with those shown in Fig. 2.


Table 4The relative importance weighting matrix for Layer 4 of MIANet

Criterion Project criterion Company criterionŽ . Ž . Ž . Ž .PC 1 CC 2

Ž .Project criterion PC 1 5Ž .Company criterion CC 1r5 1

5.1. Constructor’s external and internal conditionsÕs. technology policies

It is assumed that the company is confronting theŽ .following external conditions: 1 construction mar-

Ž .ket is highly competitive; 2 material supply isŽ . Ž .sufficient; 3 skilled labor supply is insufficient; 4

equipment rental market is competitive. The con-structor’s internal conditions can be described as

Ž . Ž .follows: 1 low work backlog; 2 high materialŽ . Ž .inventory; 3 low availability of skilled labor; 4

sufficient availability of equipment. In addition tothe constructor’s internal and external conditions, the

Ž .project characteristics are described as follows: 1Ž .the project duration is strictly constrained; 2 this is

Ž .a lump sum contract; 3 product quality requirementis high.

According to the above constructor’s internal andexternal conditions, project characteristics, and theowner constraints, the appropriate utility functionsfor the criteria at the bottom layer of MIANet areselected as listed in Table 3.

The next step is to determine the relative impor-tance relationships of the various criteria in eachlayer of MIANet. The weighting rules should con-sider the constructor’s current internal and externalconditions as well as the project characteristics. Sincethis is a lump-sum contracted project, the constructorshould control construction cost within the projectbudget. The owner set up a ‘hard’ constraint on theconstruction time, so project duration is strictly con-strained. The owner has a strict quality requirement

Table 6The relative importance weighting matrix for CC at Layer 3 ofMIANet

Criterion Material Equipment LaborŽ . Ž . Ž . Ž . Ž . Ž .C1 1 C2 2 C3 3

Ž .Material C1 1 1r2 1r5Ž .Equipment C2 2 1 1r3

Ž .Labor C3 5 3 1

on this project. On the other hand, constructor’scriteria seem more flexible. The following weightingmatrices are obtained from a group discussion amongthe company’s managers of an international con-

w xstruction corporation 9 . The weighting matrix forLayer 4 of MIANet is concluded as shown in Table

Ž .4. By solving Eq. 4 , the resulted weighting vectorŽ .is shown in Eq. 14 :

0.83334w s 14Ž .0.1667

The relative importance matrix for attributes ofŽ .project criterion PC is assessed through a group

discussion and concluded as shown in Table 5. TheŽ .resulted weighting vector is shown in Eq. 15 :

0.58163w s 15Ž .0.1095PC

0.3090

Similarly, the relative importance matrix for at-Ž .tributes of project criterion PC is assessed through

a group discussion and concluded as shown in Table6. The resulting weighting vector is shown in Eq.Ž .16 :

0.12203w s . 16Ž .0.2297CC

0.6483

w xAccording to Saaty 10 , the consistency ratios of theabove two relative importance weighting matrices

Table 5The relative importance weighting matrix for PC at Layer 3 of MIANet

Ž . Ž . Ž . Ž . Ž . Ž .Criterion Construction time P1 1 Project cost P2 2 Product quality P3 3

Ž .Construction time P1 1 5 2Ž .Project cost P2 1r5 1 1r3

Ž .Product quality P3 1r2 3 1


are 0.0032, which is below the 0.1 requirement.Thus, the results are acceptable. Since there are onlytwo criteria in Layer 4, no inconsistency exist in therelative importance weighting matrix.

With the above utility functions and weightingvectors, various alternative technologies can be eval-uated based on the constructor’s internal and externalconditions. Since the selection of utility functionsand the weighting rules of the various criteria in eachlayer of MIANet can be adjusted according to themost recent constructor’s experience, the proposedmodel provides a flexible and powerful tool forcapturing the constructor’s up-to-date technologypolicy.

5.2. Example I: Formwork technology eÕaluation

Three formwork technologies are evaluated withrespect to the given project scenario. The perfor-mance of the three formwork technologies associatedwith the two sets of resource utilization scenarios,the most favored resource allocation and the maxi-mum resource utilization, is listed in Tables 7 and 8,respectively. The most favored resource allocation isthe scenario that utilizes the same amount of re-sources as planned. The maximum resource utiliza-

Table 7Formwork technology performances with the most favored re-source allocation

Performance factors Formwork technology typea b cŽ . Ž . Ž .I 1 II 2 III 3

Construction time 19.8 13.1 14.2Ž .working days

Ž .Project cost US$ 132,600 157,200 337,900Product quality 0.75 0.9 0.95Material requirements:

2Ž .1. Wood forms m 2450 0 02Ž .2. Equipment-lifted forms m 0 2450 0

2Ž .3. Precast concrete forms m 0 0 2450Ž .Equipment requirement crane 0 3 3

Labor requirements:Ž .1. Carpenter teams 4 0 0Ž .2. Iron worker teams 2 2 2

Ž .3. Concrete worker teams 1 1 1Ž .4. Crew teams 0 3 3

aConventional wood form system.b Equipment-lifted panel form system.cStay-in-place precast concrete form system.

Table 8Formwork technology performances with the maximum resourceutilization

Performance factors Formwork technology typea b cŽ . Ž . Ž .I 1 II 2 III 3

Construction time 8.5 8.1 8.8Ž .working days

Ž .Project cost US$ 131,200 148,100 329,000Product quality 0.75 0.9 0.95Material requirements:

2Ž .1. Wood forms m 2450 0 02Ž .2. Equipment-lifted forms m 0 2450 0

2Ž .3. Precast concrete forms m 0 0 2450Ž .Equipment requirement crane 0 5 5

Labor requirements:Ž .1. Carpenter teams 7 0 0Ž .2. Iron worker teams 5 5 5

Ž .3. Concrete worker teams 2 2 2Ž .4. Crew teams 0 5 5

aConventional wood form system.b Equipment-lifted panel form system.cStay-in-place precast concrete form system.

tion is the scenario that utilizes the maximum amountof resources. Comparing Tables 8 and 9 with Table3, it is apparent that the stay-in-place precast con-crete form system is not feasible for the consideredproject due to an excessively high construction cost.Moreover, the conventional wood form with plannedresource utilization is not feasible due to a longconstruction time. Therefore, there are three feasiblealternatives to be further considered for the given

Ž .project: 1 conventional wood form with maximumŽ .resource utilization; 2 equipment-lifted form with

Ž .planned resource utilization; and 3 equipment-liftedform with maximum resource utilization. If all of thealternatives are not feasible for the considered pro-

Table 9Utility assessments of the alternatives in Example I

Criteria at bottom of MIANet Utility of alternatives

Ž . Ž . Ž .1 2 3

Ž .P1 construction time 1.0 0.7 1.0Ž .P2 project cost 1.0 0.19 0.68Ž .P3 Product quality 0.59 0.85 0.85Ž .C1 material requirements 1.0 1.0 1.0Ž .C2 equipment requirement 1.0 1.0 0.0Ž .C3 labor requirements 0.25 0.75 0.25


ject due to constructor or project constraints, a con-structability problem is detected. Further improve-ment of construction technologies is required for the‘non-constructible’ project. This is discussed in Ex-ample II.

5.2.1. Utility assessmentsThe first step of the constructability analysis by

the proposed model is to assess the utility values ofthe criteria at the bottom layer of MIANet. Eqs.Ž . Ž .5 – 7 are employed for utility assessments. Theutility function parameters can be obtained fromTable 3. The utility assessment results for the abovethree alternatives are listed in Table 9. On the otherhand, the difficulty indexes of the criteria at thebottom layer of MIANet for all alternatives can also

Ž .be calculated by Eq. 8 . The resulting difficultyindexes are shown in Table 10.

5.2.2. MIANet aggregationThe next step in the constructability analysis is

the aggregation of utility and constructability diffi-culty information from the bottom layer to the top

Ž . Ž .layer of MIANet. Eqs. 9 – 13 are employed for theinformation aggregation. The aggregation results arelisted in Table 11. The evaluation results show that

Ž . Žalternative 1 conventional wood form with maxi-. Ž .mum resource utilization and alternative 3

Žequipment-lifted form with maximum resource uti-.lization are better selections under the given project

scenario and constructor’s technology policy. Sinceall utility values of the alternatives are over 0.5, theyare considered to be feasible alternatives. No con-structability improving work is required. However,the difficulty indexes show the direction for furtherconstructability improvements. The performance fac-

Table 10Difficulty index assessments of the alternatives in Example I

Criteria at bottom of MIANet Difficulty index

Ž . Ž . Ž .1 2 3

Ž .P1 construction time 0.0 0.29 0.0Ž .P2 project cost 0.0 0.82 0.33Ž .P3 Product quality 0.41 0.15 0.15Ž .C1 material requirements 0.0 0.0 0.0Ž .C2 equipment requirement 0.0 0.0 1.0Ž .C3 labor requirements 0.75 0.25 0.75

Table 11Aggregated information of Example I

Information type AlternativeŽ . Ž . Ž .1 2 3

Overall utility 0.81 0.72 0.81Difficulty index:

Ž .1. P1 construction time 0.0 0.14 0.0Ž .2. P2 project cost 0.0 0.07 0.03Ž .3. P3 Product quality 0.11 0.04 0.04Ž .4. C1 material requirements 0.0 0.0 0.0Ž .5. C2 equipment requirement 0.0 0.0 0.04Ž .6. C3 labor requirements 0.08 0.03 0.08

tors with the higher difficulty index levels have thehigher potential for constructability improvements.The mechanism will be explained in the followingexample.

5.3. Example II: Technology constructability im-proÕement

In the second example, let’s consider the similarproject with a different scenario given in Table 12. Itis noted that the project construction time has beensignificantly reduced due to the request of the owner.Constructor’s material inventory is low. This hasresulted in a change of the constructor’s materialmanagement strategy from risk seeking to risk-averse.The company plans to earn more from the project.

Ž .Thus, the desired or planned construction cost hasbeen lowered even though the contracted price doesnot change.

5.3.1. Constructability problem detectionAccording to the above project scenario, only two

Ž .alternatives are feasible: 1 conventional wood formŽ .system with maximum resource utilization and 2

equipment-lifted form system with maximum re-source utilization. By the same analysis process, theevaluation results of the two alternatives are shownin Table 13. It is noted that neither of the twoalternatives has a satisfactory overall utility levelover 0.5, which is considered as the minimum re-quirement for feasible alternative. Therefore, a po-tential constructability problem may appear duringthe construction phase. Action should be taken toimprove the constructability. Otherwise, the contrac-


Table 12Project scenario of Example II

Bottom criterion of MIANet Selected utility function Parameters of utility functions

Ž . Ž . Ž . Ž . Ž .1 LL lower limit 2 UL upper limit 3

Ž .Construction time days risk seeking 6 8.5Ž .Project cost US$ risk seeking 120,000 160,000

a Ž . Ž .Product quality risk averse 0.75 good 1 very goodMaterial requirements: risk averse

2Ž .1. Wood forms m 1500 25002Ž .2. Equipment-lifted forms m 1900 2800

2Ž .3. Precast concrete forms m 1700 2500Ž .Equipment requirement crane risk seeking 3 5

Labor requirements: risk averseŽ .1. Carpenter teams 4 7Ž .2. Iron worker teams 2 3

Ž .3. Concrete worker teams 1 2Ž .4. Crew teams 3 5

a Ž . Ž .Product quality is a more-is-better type utility function which takes index value from 0 very poor to 1 very good . The utility functionsreverse horizontally compared with those shown in Fig. 2.

tor’s and the owner’s project objectives cannot befully achieved.

5.3.2. Constructability improÕement with neuro-fuzzydecision systems

The second alternative in Table 13 is consideredmore promising for the considered project, since itachieved a higher overall utility level close to 0.5.Thus, the second alternative is selected for con-structability improvement. It is noted from Table 14that the performance factor causing the highest diffi-culty index is the construction time. By tracing backthrough the neuro-fuzzy decision system, the keyattributes for construction time are the numbers ofcrane and crew for the equipment-lifted formwork

Table 13Evaluation results of Example II

Information type Alternative

Ž . Ž .1 2

Overall utility 0.29 0.43Difficulty index:

Ž .1. P1 construction time 0.48 0.38Ž .2. P2 project cost 0.02 0.06Ž .3. P3 Product quality 0.11 0.04Ž .4. C1 material requirements 0.02 0.01Ž .5. C2 equipment requirement 0.0 0.04Ž .6. C3 labor requirements 0.08 0.08

technology. However, the maximum availability ofthese two resources has been utilized in the consid-ered alternative. The only way to improve the con-struction time is to add extra numbers of cranes,crews, or steelworkers with higher costs. This sug-gests a solution to the managers who are in charge ofthe constructor’s equipment and human resourcemanagement. The managers then find that an extraset of crane and crew can be obtained with 100%additional cost, an extra steelworker may be obtainedfrom the labor market with 50% additional hourly

Table 14Evaluation results of Example II

Performance factors TechnologyŽ .performance 1

Overall utility 0.59Performance factors:1. Construction time 7.02Ž .working days

Ž .2. Project cost US$ 156,2003. Product quality 0.94. Material requirements 2450

Ž .5. Equipment requirement crane 66. Labor requirements:Ž . Ž .a Carpenter teams 0Ž . Ž .b Iron worker teams 7Ž . Ž .c Concrete worker teams 2Ž . Ž .d Crew teams 6


rate for the extra team. Two steelworker teams andone crane and one crew team are included as theadditional resources for the considered project. Thenew evaluation results are shown in Table 14. It isnoted that the construction cost has been increasedby US$8100 or 5.4%. However, the constructiontime is decreased by 1.1 days or 13.5%. The resultedoverall utility is 0.59 which is higher than 0.5. Thus,the new alternative is considered as feasible for thegiven project scenario after constructability improve-ment process.

6. Conclusions and future work

In this paper, a quantitative definition of con-structability is proposed so that constructability canbe quantified, measured, and improved. A multi-criterion decision model has been proposed for con-structability analysis and improvement of construc-tion technologies. The proposed model is based onneuro-fuzzy networks that can acquire constructabil-ity knowledge from historical performance data.In order to incorporate the managers’ knowledgeinto the constructability analysis process, a gene-ric multi-layer information aggregation networkŽ .MIANet has been developed to reflect the construc-tor’s technology management policy. The proposedMIANet can be modified according to the construc-tor’s technology management requirements. In con-trast to the traditional analytical hierarchy processŽ .AHP method, the proposed MIANet is able tomodel the decision-maker’s attitude toward risk withvarious types of utility functions. The constructor’stechnology policy and the managers’ knowledge canbe reflected in the constructability analysis processby the weighting of criteria and selection utilityfunctions in MIANet.

The proposed methodology not only provides auseful tool for technology evaluation but also pro-vides a systematic approach for constructabilityproblem detection and constructability improvement.The performance factor causing the constructabilityproblem is identified by the MIANet. The key at-tributes causing the unsatisfactory performance fac-tor are further traced through the neuro-fuzzy net-work. Thus, performance improvement is achieved

by improving the key attributes. Technology produc-tivity improvement and cost effective constructionare realized via continuous improvement of technol-ogy performance.

Some possible extensions of the proposedŽ .methodology include: 1 definition of more specific

criteria of MIANet for other types of constructionŽ .technologies; 2 develop the specific weighting rule

Ž .knowledge-based system for the constructor; 3 de-velop the comprehensive utility selection knowledgebase to save the time required for developing MI-ANet and also for real-time decision making.

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Quantitative constructability analysis with a neuro-fuzzy knowledge-based multi-criterion decision support system