Role of Statistics and Engineering Judgment in DevelopingOptimized Time-Cost Relationship Models

Vitor Sousa1; Nuno Marques Almeida2; and Luís Alves Dias3

Abstract: When estimating the duration of the construction stage during the design stages of construction projects, empirical models areoften used as a substitute for more accurate estimates based on detailed scheduling. These models, traditionally designated as time-costrelationships (TCR), derive from regressions relating the duration of concluded construction projects with characteristics that can be easilyforeseen during the planning and design stages—both quantitative (e.g., cost, gross floor area, number of floors) and qualitative (e.g., type ofcontract). This paper reviews the approaches that have been adopted to develop the TCR models and discusses the complementary roles thatstatistics and engineering judgment can play towards their optimization and enhanced accuracy. This discussion includes the statistical andpractical implications of (1) the quantitative independent variables used, (2) the qualitative independent variables used, and (3) the math-ematical structure used. The paper aims at demonstrating the importance of sound statistics and highlights some of the most common mis-takes. Additionally, it provides illustrative examples to show the complementary role that engineering judgment should have in the process ofdeveloping more robust, reliable, and accurate statistical-based TCR. DOI: 10.1061/(ASCE)CO.1943-7862.0000874. © 2014 AmericanSociety of Civil Engineers.

Author keywords: Construction project scheduling; Time-cost relationship; Regression; Statistics; Engineering judgment; Cost andschedule.

Introduction

The most accurate duration estimate of a construction projects isusually determined based on the detailed schedule, either usingdeterministic [e.g., critical path method (CPM)] or probabilistic[e.g., program evaluation and review technique (PERT), probabi-listic network evaluation technique (PNET), Monte Carlo simula-tion (MCS)] methods. In practice, the scheduling is done bydividing and subdividing the project into smaller and more man-ageable components, creating a work breakdown structure and pro-viding a hierarchical decomposition of the work that needs to becompleted [ISO 21500 (ISO 2012)]. In most cases, the detailedwork breakdown structures delivered during the design stage aredeveloped for cost estimating purposes and do not include the nec-essary information for time estimation, namely: (1) the estimate ofthe duration of each activity; (2) the definition of the sequence ofexecution of the activities; and (3) the activities constrains. This canonly be done accurately by the contractors, taking into considera-tion not only the project characteristics, but also the resources theyplan to allocate and the productivity of the teams that willeffectively be involved in the construction stage of the project. Even

in this case, the duration estimate will still rely on the estimators’experience and judgment to correctly interpret project and site in-formation and make the best possible decisions (Alfred 1988).

However, there is a need for estimating project durations in asimplified but reliable way. Designers and clients frequently needto estimate durations in order to set deadlines for the constructionstage. On the other hand, contractors need to validate the estimatesduring the bidding process, because the time available is notenough, in most cases, to develop a schedule with a level of detaildeemed necessary for high confidence in the project duration fore-cast (Skitmore and Ng 2003).

Several simplified models for predicting project durations havebeen developed using varied approaches. The statistical approacheshave been the most used, despite the growing trend in recent yearsfor using artificial intelligence tools, particularly neural networks(e.g., Hegazy and Ayed 1998; Chen and Huang 2006; Holaand Schabowicz 2010; Le-Hoai et al. 2013; Shehab and Farooq2013). Most authors following the statistical approach developedparametric models by regression analysis of data from completedprojects of a specific type (e.g., buildings, roads, sewer networks,water networks). In these regressions, several mathematical struc-tures and independent variables were used, depending on theinformation available and the type of project. These models arecharacterized by their simplicity and ease of development, com-bined with the flexibility to accommodate different situations withacceptable results. Furthermore, contrary to the artificial intelli-gence models, the comprehension of the relation between the in-dependent variables and the project time is explicit and easy tointerpret. Consequently, they are the most used in practice andare important tools for estimating the duration of the constructionstage in the early stages of the project’s development.

The Bromilow time cost (BTC) model proposed by Bromilow(1969), based on a power law with the cost as the only independentvariable, is referenced as the precursor of the parametric modelsand has the following mathematical form:

1Assistant Professor, ICIST, DECivil, Instituto Superior Técnico,Universidade de Lisboa, Av. Rovisco Pais 1, Lisbon 1049-001, Portugal(corresponding author). E-mail: vitor.sousa@ist.utl.pt

2Assistant Professor, ICIST, DECivil, Instituto Superior Técnico,Universidade de Lisboa, Av. Rovisco Pais 1, Lisbon 1049-001, Portugal.E-mail: nunomarquesalmeida@ist.utl.pt

3Professor, ICIST, DECivil, Instituto Superior Técnico, Universidade deLisboa, Av. Rovisco Pais 1, Lisbon 1049-001, Portugal. E-mail: luis.alves.dias@ist.utl.pt

Note. This manuscript was submitted on November 18, 2013; approvedon March 26, 2014; published online on May 12, 2014. Discussion periodopen until October 12, 2014; separate discussions must be submitted forindividual papers. This paper is part of the Journal of Construction En-gineering and Management, © ASCE, ISSN 0733-9364/04014034(10)/$25.00.

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T ¼ K × CB ð1Þwhere T is the duration of the construction stage of the project intime units (usually days or weeks); C is the estimated cost for theconstruction stage of the project in monetary units (usually thou-sands or millions); K is a constant describing the general level oftime performance for a unit cost construction project; and B is aconstant describing the variation of the time performance withthe project size as measured by cost. Following this pioneer work,several authors have developed parametric models to estimate aconstruction project’s time by (1) using different quantitative inde-pendent variables; (2) including dummy variables to representqualitative independent variables; and (3) adopting different math-ematical structures for the regression curve. These parametric mod-els are usually known as time-cost relationships (TCR). The presentpaper evaluates the statistical and practical implications of variousalternatives that have been proposed using the original TCR model(BTC) as a basis of comparison. It also includes a discussion aboutsome of the most relevant limitations of TCR models in generalwith the aim of clarifying their statistical and practical implicationsand the particular restrictions for the use of TCR models in con-struction projects. The role that engineering judgment can playas a (necessary) complement to sound statistics when developinga TCR model is illustrated with examples. It is the authors’ beliefthat engineering judgment has not yet been sufficiently explored asa complement to sound statistics to ensure the development ofrobust, reliable, and accurate TCR models, as well as their correctuse. This paper is intended to contribute towards this goal byfocusing on parametric models developed for buildings, whichare the most numerous in the literature, although the argumentspresented are generally applicable to TCR models for any typeof construction project.

Statistical and Practical Balance of Time-CostRelationships

General Issues

The reasons underlying the time performance of construction proj-ects have been and still are a topic of research (e.g., Hegab andSmith 2007; Sweis et al. 2008; Toor and Ogunlana 2008; Song et al.2009; Nguyen et al. 2010; Meng 2012). Chan (1998) organized thefactors affecting construction time performance of building projectsinto scope (cost, gross floor area, number of stories, building type,contract procurement systems, variations), complexity (client’sattributes, site conditions/access issues, buildability of projectdesign, quality of design coordination, quality management), envi-ronment (physical, economic, socio-political, relationships), andmanagement (client/design and construction team managementattributes, communication management, organizational structureand human resources management, productivity) related. However,several of the factors affecting the time performance of theconstruction stage cannot be accurately predicted (e.g., weather,unforeseen site conditions, design and construction errors) or therequired information is not available in the early stages of theproject development (e.g., construction team-related issues).Nevertheless, there is a need for estimating the time in the designstage of construction projects in an easy yet roughly accurate way.In this regard, the TCR models are still the option that present oneof the most favorable relations between the difficulty in developing/using and the accuracy of the estimates.

Parametric TCR models are an extreme simplification of thetime performance of a construction project. Nevertheless, consid-ering the original TCR model (BTC), the fact is noted that so many

authors have obtained high correlations between the cost and thetime for varied types of construction projects, in different countriesand in different periods. Based on this fact, it will be assumed thatthe cost (as well as the alternative variables used by different au-thors) can explain a significant part of the time performance of con-struction projects and the TCR models can be used for estimationpurposes in the early stages of the construction projects develop-ment. Before addressing the restrictions of different TCR models,the following discussion will focus in three general limitationsaffecting any TCR model: (1) nature, (2) space, and (3) time.

If, on the one hand, the applicability of a TCR model depends onthe nature of the projects used in its development, on the other hand,the validity of a TCR model also depends on the nature of theprojects used in its development. The first issue reflects the fact thatTCR models do not account for changes affecting the time perfor-mance of the construction industry in general, such as technology(e.g., equipment, methods) or process (e.g., procurement, contract,management) changes. However, the construction industry ischaracterized by a slow evolution of the technology and processes,which enables the use of parametric TCR models for, at least, aperiod of time. The applicability of the TCR models to projects withsignificant features substantially distinct from the projects that wereused in their development may incur in considerable estimate error.This is an obvious limitation of these models, as opposed to the sec-ond issue. The characteristics of the sample of projects used in thedevelopment of TCR models may induce nature-related bias. Themost common is the unbalanced distribution of projects by cost, usu-ally because the number of projects in the data samples decreaseswith the project cost. Consequently, in most cases, the TCR modelsare defined by a small number of large projects, which may not be agood statistical representation of the projects’ time performance inthat cost range. Other scope-related biases may also exist in the sam-ple of projects (e.g., unbalanced sample of buildings with and with-out underground floors, unbalanced sample of buildings in regard tothe number of floors, unbalanced sample of buildings in regard to thetype of contractual arrangement).

Most authors use a wide spatial resolution for collecting theirproject’s data, usually considering a national or regional scale.Given the sample size used in most studies (usually less than150 projects), this approach may induce a substantial space biasif significant differences exist between the construction market ofeach location (e.g., workers’ availability and wages, material andequipment availability and price, level of competition, weather andother environmental constraints, type of clients). The bias may re-sult from the reduced sample representing each location and/or theunbalanced distribution of the projects from each location, both interms the number of projects or/and the size of the projects. Anextreme situation of spatial bias would be the use of a sampleof projects mostly composed of (large) projects from a big citymixed with (small) projects from several other smaller cities, inparticular if the locations have significantly different market con-ditions. To avoid this source of bias, larger data samples should beused (e.g., Kaka and Price 1991; BCIS 2004, 2005; Hoffman 2005;Hoffman et al. 2007) or local specific TCR models should bedeveloped (e.g., Yousef and Baccarini 2001).

The last general source of bias is the time frame used to collectthe project sample. The first issue in this regard stems from theprice variations. Fortunately, the existence of construction price in-dexes makes it possible to overcome the variation of prices withtime and ensures that the costs of projects from different yearsare comparable. The second issue is related to the fact that theremay be distinct time performance of the projects between construc-tion recession and construction boom periods. During recessionperiods, the time performance of the construction projects may

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be limited by the monetary flux available. When the economy isgrowing, the productivity and the availability of construction re-sources (manpower, material, and equipment) are the most limitingfactors. Developments on the construction technology or processesthat have impacts on the time performance globally were accountedfor in the nature-related bias discussion.

In order to reduce the influence of the limitations highlighted inthe TCR model results, special care should be taken when (1) se-lecting the projects to include in the sample used to develop theTCR models, and (2) evaluating the applicability of a TCR modelto estimate the time of a given construction project. Regarding theformer, an effort should be made to collect a database of projectswithout outliers and that reduces as much as possible the diversityof factors affecting the time performance. The reduction of thediversity of factors affecting the time performance can be achievedby selecting projects that are similar in nature (e.g., avoid mixingcommercial with residential buildings or new building projectswith rehabilitation/refurbishment projects) and carried out in sim-ilar contexts (e.g., market competition characteristics, procurementand contracting practices). For instance, Sousa et al. (2014) devel-oped TCR models for sanitation projects and restricted the projectsin the sample to a specific time frame in Chicago. The authors alsoexplore the statistical differences of the TCR models for water andsewer projects. This ensured a high uniformity of the context inwhich the projects were carried out (e.g., promoter, designers, con-tractors and other interested party practices; project characteristics)and made it possible to assume that the variability of the time per-formance not explained by the TCR models developed is mostlyproject related.

Quantitative Independent Variables

Walker (1994) considers that C in Eq. (1) should be interpreted asthe project scope, defined as a measure of the project size. Theproject size can be described not only by the construction costsbut also by parameters such as the gross floor area, the numberof stories, the building type, the procurement method, or thecontractual arrangement. Some authors (e.g., Love et al. 2005)argue that the cost is not a good predictor of the project time be-cause it is not known accurately at the outset of the constructionstage, mainly due to the possibility of significant cost deviations.Following this reasoning, several authors developed TCR modelsusing other quantitative predictors. For buildings, the total grossfloor area (TA) and the number of stories (S) have been the mostused (e.g., Chan and Kumaraswamy 1995; Love et al. 2005; Chenand Huang 2006).

However, most, if not all, of the alternative quantitative variablesthat have been included in the TCR models are similar to those usedin parametric models for estimating the cost (e.g., Kim et al. 2004;Sonmez 2004, 2008; Chen and Huang 2006; Lowe et al. 2006; Yehet al. 2008; Chou 2009; Gunduz et al. 2011) or cost deviation(e.g., Thal et al. 2010) of construction projects. In fact, almost threedecades ago, Karshenas (1984) obtained a power equation with thetypical floor area and the number of stories as the best parametricmodel for estimating the cost of multistory buildings in the UnitedStates. Considering the results obtained by Karshenas (1984), onemay argue that the cost and the total gross floor area (and, indi-rectly, the typical floor area and the number of stories) are equiv-alent indicators of the project scope for TCR models for multistorybuildings. Additionally, if cost variations may affect the estimatesof conventional TCR models, there are also substantial differencesin construction projects affecting their time performance that arenot reflected in variables such as the total gross floor area or thenumber of stories but are accounted for in the cost (e.g., type

and/or quality of construction; space configuration). Therefore,although this is contested by some authors (e.g., Love et al.2005), it seems that cost is also a suitable independent variableto use in the development of TCR models.

When using alternative quantitative independent variables, thefollowing two situations must be considered: (1) using each predic-tor alone, and (2) using a combination of predictors. The former isequivalent to the discussion presented earlier regarding which is thebest quantitative predictor for estimating the time performance ofbuilding projects. To demonstrate this issue further, the raw data on37 public building projects collected by Chan (1998) were used todevelop TCRmodels (Fig. 1). The TCRmodels and their respectiveregression coefficients are all statistically significant (p-value ¼0.000 for the TCR model using the cost and the gross floor areaand p-value ¼ 0.004 for the TCR model using the number of sto-ries), with the cost providing a higher correlation than the totalgross floor area or the number of stories. In this case, the costproved to be the predictor providing the best explanation of the timeperformance of public buildings in Hong Kong. It should be notedthat among the 37 public building projects, only 21 had informationregarding the number of stories, which explains the difference ofdata points between Figs. 1(a, b, and c).

Using a combination of independent quantitative variables isa valid option if the variables are complementary in explainingthe variability of the dependent variable. However, most of thequantitative variables used in combination in TCR models arenot independent, leading to multicollinearity issues. In statisticalterms, the consequences are large standard errors and large confi-dence intervals associated with the estimated regression coeffi-cients. In the limit, the overall model may by highly significantwhereas none or only few of the individual predictors are. Froma practical perspective, the implications of multicollinearity arisewhen estimating the time of a project with a combination ofindependent variables substantially different from the data usedto develop the TCR model. For instance, using the model devel-oped by Love et al. (2005) for demonstration purposes only, thetime estimate to build a six-story building with a total gross floorarea of 8,000 m2 (363 days) is roughly the same as building anuncommon 20,000 m2 building with just one story (362 days).In this extreme example, one may question if the fact of havingto build in height (six stories) overcompensates the time necessaryto build more than the double the total gross floor area.

To provide additional detail regarding the combination ofindependent variables, four TCR models were developed usingvarious combinations of quantitative predictors based on the Chan(1998) sample of public building projects. The results are presentedin Table 1 and it is noticeable that (1) comparing with the best TCRmodel using the independent variables individually [Fig. 1(a)],there is only a slight increase of the coefficient of determination(R2) by using a combination of independent variables; and(2) despite all regressions being statistically significant, most ofthe regression coefficients are not statistically significant. Whena regression coefficient is not statistically significant, in principlethe corresponding independent variables should not be included inthe model because it is not a predictor of the dependent variable.

All the independent variables in the first and the last models inTable 1 are not significant (i.e., none of the independent variables isa predictor) while the model is significant (i.e., at least one inde-pendent variable is a predictor). These apparently contradictory re-sults are a consequence of the high correlation between C and TA.This can be concluded from the fact that the variance inflation fac-tor (VIF) is higher than 5 and the tolerance less than 0.2 in bothcases. The number of stories is never a predictor of the time whenused in combination with any of the other independent variables.

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Independent of the quantitative independent variables used, aslong as the underlying specification is correct, multicollinearitydoes not actually bias the results. When there are other problemsthat introduce bias (e.g., omitted variables), multicollinearity can

multiply (by orders of magnitude) the effects of that bias. Moreimportantly, when applying a TCR model to estimate the durationof a project where the pattern of multicollinearity differs from thatin the sample of projects that was used for its development, such

Fig. 1. TCRmodels for public buildings in Honk Kong using (a) the cost, (b) the total gross floor area, and (c) the number of stories as predictors [datafrom Chan (1998)]

Fig. 2. Hypothetical sample of projects created from the TCR models of Bromilow et al. (1988) and the alternative TCR models obtained

Table 1. TCR Models for Public Buildings in Hong Kong Using Various Combinations of Quantitative Independent Variables [Data from Chan (1998)]

TCR R2 F (significance)

Regression coefficients (significance)

K B M N

T ¼ K × Cb × TAM 0.637 29.8(0.000a) 151.01 (0.000a) 0.171 (0.055) 0.073 (0.310) —T ¼ K × Cb × SN 0.659 17.4(0.000a) 189.23 (0.000a) 0.213 (0.001b) — 0.161 (0.052)T ¼ K × TAM × SN 0.632 15.4(0.000a) 56.36 (0.000a) — 0.251 (0.002b) 0.040 (0.699)T ¼ K × Cb × TAM × SN 0.664 11.2(0.000a) 128.23 (0.000a) 0.159 (0.218) 0.075 (0.630) 0.119 (0.324)aStatistically significant p-value < 0.001.bStatistically significant p-value < 0.010.

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extrapolation may introduce large errors in the predictions. There-fore, when multicollinearity exists it is preferable to use alternativeregression models, such as ridge regression or LASSO regression.

It is the authors’ belief that engineering judgment plays an im-portant role when selecting the best set of predictors for each spe-cific context. In the example presented, the cost and the total grossfloor area individually are very similar predictors in statisticalterms; therefore, the selection would benefit from an engineeringjudgment (e.g., if cost deviations are frequent and large, the totalgross floor area may be a more robust predictor; if the time is highlyvariable depending on the level of luxury, the cost may be a morerobust predictor). Regarding the quantitative variables, engineeringjudgment should also be used to evaluate if (1) the characteristics ofa project for which a time is to be estimated are compatible with thesample of projects used to develop the TCR model and/or, (2) asample of projects available is representative of the possible com-binations between quantitative variables and decide whether to de-velop a TCR model with a combination of quantitative variable isthe best option.

Qualitative Independent Variables

The time performance of construction projects has been found todepend not only on quantitative predictors but also on qualitativepredictors. A very wide range of qualitative independent variables(e.g., use of information technology by the management team, in-dustrial relations environment, procurement method) has been in-cluded in TCR models by various authors (e.g., Walker 1994; Blyth1995; Khosrowshahi and Kaka 1996; MacKenzie 1996; Love et al.2005; Hoffman 2005; Hoffman et al. 2007).

The type of project (e.g., buildings, roads) is one of the mostused qualitative independent variables. For this particular predictor,the majority of the authors opted to develop separate TCR modelsfor each type of project. However, for other qualitative predictors(e.g., type of owner, type of contractual arrangement, type of build-ing), it is possible to find separate TCR models for each class ofqualitative independent variable as well as TCR models includingdummy variables representing the qualitative predictors. If the for-mer approach has no serious statistical or practical implications,because each TCR is independent from the remaining, the lattermay have significant statistical and practical implications.

The inclusion of a dummy variable may seem, in theory, an ex-cellent option because (1) it makes it possible for a larger data sam-ple to be used, even if the samples of projects for all or some of theclasses of the qualitative independent variables individually aresmall, (2) it enables the inclusion of additional relevant informationin the TCR model, and (3) it may lead to higher correlations. How-ever, each TCR model in particular may present several limitations.Considering the TCR models from past studies with independentqualitative variables, most were derived from reduced projectsamples [Walker (1994), 33 projects; Blyth (1995), 15 projects;Khosrowshahi and Kaka (1996), 54 projects; MacKenzie (1996),17 projects]. Given the number of projects and the number of in-dependent predictors, the use of the TCR models proposed by theseauthors should take into consideration that probably (1) the numberof projects used for developing the TCR model in each class of thequalitative predictors is very small, (2) there are several possiblecombinations of the qualitative predictors that were not representedin the projects used for developing the TCR model, and (3) therange of the quantitative predictors in each class may be very differ-ent. Even if the size of the sample is not an issue, two situations thatneed to be addressed when including qualitative predictors may bepointed out: (1) a masking effect may occur when one of the classesis clearly more prevalent in the sample of projects used to develop

the TCR model; and (2) the implicit assumption of equal slopes ofthe quantitative predictor between the classes of projects defined byqualitative predictors may be incorrect.

When the data set is not uniformly distributed throughout thevarious classes of projects defined by the dummy variable, eitherin terms of the number of projects in each class or in terms of theirdistribution over the range of the quantitative predictors, and theprojects of one of the classes of the dummy variable dominatethe sample, the regression coefficients will be dictated by that class.Whereas, in statistical terms, the resulting TCR model and the re-gression coefficients may be significant, in practical terms, a TCRmodel with qualitative predictors developed in these conditionsmay represent correctly the dominating class of projects but notthe remaining.

Given that a dummy variable assumes arbitrary discrete valuesto represent each class, in statistical terms it is simply a constantdifferentiating the mean time performance of each class of projects.Considering the simple case of a linear regression with one quan-titative predictor and one qualitative predictor, the dummy variablewill differentiate the intercept of the regression for each class ofprojects defined by the qualitative variable. Implicitly, such aTCR model assumes that the slope of the quantitative predictoris the same for all the classes defined by the independent qualitativevariable. This is a very strong assumption that needs to be checked,which for a two-class dummy variable can be easily done byevaluating the significance of the interaction between classes inan analysis of covariance. In statistical terms, the TCR modeland all regression coefficients may be significant, independentlyif the assumption of equal slopes is true or false. However, in prac-tical terms, if the assumption of equal slopes for each project classis not valid, a TCR model with a dummy variable is less accurate inrepresenting the time performance of each project class than thealternative of developing individual TCR for each project class.

To illustrate these implications, two examples are presented. Inthe first example, the TCR models developed by Bromilow et al.(1988) for buildings are used. Based on those models, a hypotheti-cal sample of projects was created by randomly generating projectcosts between 0.01 and 10 million AUD and estimating the corre-sponding time. An artificial error was also introduced by randomlymultiplying the estimated time by a value between 0.95 and 1.05.The original TCR models and the TCR models developed from thehypothetical sample of projects are presented in Table 2.

Defining a dummy variable to account for the building projecttype (P), with P ¼ 10 for public buildings and P ¼ 1 for privatebuildings, the following TCR model was obtained:

T ¼ 165.8 × C0.363 × P0.138 ð2Þ

All TCR models and the corresponding regression coefficientswere found to be significant (p-value ¼ 0.000), both for the TCRmodels in Table 2 and Eq. (2), which might induce the wrongassumption that all models are equally valid. The hypothetical

Table 2. TCR Models Derived from the Hypothetical Sample of ProjectsCreated from the TCR Models of Bromilow et al. (1988)

Buildingproject

Bromilowet al. (1988)original TCR

models

Hypothetical sample of projects

Number ofprojects TCR model

developedGenerated Used

All T ¼ 219 × C0.37 — 300 T ¼ 218 × C0.355

Public T ¼ 222 × C0.38 250 250 T ¼ 223.4 × C0.377

Private T ¼ 189 × C0.28 50 50 T ¼ 187.1 × C0.283

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sample of projects and the TCR models derived from it are pre-sented in Fig. 2, demonstrating that a TCR model with all projectsor with a qualitative independent variable would not provide goodtime estimates for the private building projects.

The result of aggregating all projects is a TCR model dictated bythe dominant class of building projects in the hypothetical sampleof projects (the public building projects) that does not representcorrectly the time performance of the private building projects.TCR models developed separately for each class of building projecttype and a single TCR model developed with a dummy variableyield substantially different results. This is due to the incorrectassumption of equal slopes of the relation between the time andthe cost for public and private buildings implicit in the latter[Eq. (2)]. The assumption of equal slopes was tested by performingan analysis of covariance considering the interaction between thecost and the project type because the dummy variable has only twoclasses. In this case, the interaction was found to be significant(p-value ¼ 0.000), indicating that the regression coefficient asso-ciated with the cost (the slope) is statistically different for each classof building project type. Consequently, a valid option for develop-ing a TCR model with a dummy variable would require the inter-action between the quantitative and the qualitative variables to beconsidered, resulting in

T ¼ 187.1 × C0.283 × P0.077 × 100.094×logC×logP ð3Þ

The comparison of Eq. (3) and the TCR model developed foreach type of building project separately (Table 2) is presented inFig. 3. In practical terms, both approaches seem similar, but froma statistical point of view, Eq. (3) is more robust because it consid-ers the errors of all the classes defined by the dummy variable in-stead of using just the variability of each class individually in theprocess of finding the regression coefficients. The choice of the bestapproach requires an engineering judgment to decide whether therelation between the classes of projects represented by the qualita-tive independent variable is strong, in which case the best option isto consider a TCR model with a dummy variable and consideringinteraction, or weak, in which case developing separate TCR mod-els would be the best option. More specifically, Eq. (3) would bethe best TCR model if the causes underlying the variability of thetime performance of public and private buildings not explained bythe cost are the same and have equivalent effects. Otherwise, de-veloping separate TCR models is the correct option.

The second example uses the TCR models developed byKumaraswamy and Chan (1995) for residential and nonresidential

private buildings, based on final cost values. Similarly to the pre-vious example, a hypothetical data set was created by randomlygenerating project costs between 0.01 and 10 million HKD. Anartificial error was also introduced by randomly multiplying theestimated time by a value between 0.95 and 1.05. The originalTCR models and the TCR models developed from the hypotheticaldata set are presented in Table 3.

Defining a dummy variable to account for the building projecttype (P), with P ¼ 10 for residential buildings and P ¼ 1 for non-residential buildings, the following TCR was obtained:

T ¼ 313.3 × C0.199 × P−0.107 ð4Þ

All TCR models and the corresponding regression coefficientswere found to be significant (p-value ¼ 0.000), both for the TCRin Table 3 and Eq. (4). As in the previous example, this may lead tothe mistaken conclusion that all models are equally valid. Thehypothetical sample of projects and the TCR models derived fromit are presented in Fig. 4, in order to show that a TCRmodel with allprojects would not provide good time estimates for the nonresiden-tial projects.

As in the first example, the result of aggregating all projects isa TCR model dictated by the dominant class of building projectsin the hypothetical sample of projects (the residential buildingprojects) that does not represent correctly the time performanceof the nonresidential building projects. Contrary to the previousexample, separate TCR models for each class of building projecttype and a single TCR model with a dummy variable yield similarresults. Performing an analysis of covariance, the interaction be-tween the cost and the project type was found to be not significant(p-value ¼ 0.314), confirming that the slope of the regression co-efficient associated with the cost is statistically the same for eachclass of building project type. In practical terms, the approachesseem similar, but from a statistical point of view, Eq. (4) is more

Fig. 3. Comparison of separate and dummy variable with interactionTCR model derived from the hypothetical sample of projects createdfrom the TCR models of Bromilow et al. (1988)

Table 3. TCR Models Derived from the Hypothetical Sample of ProjectsCreated from the TCR Models of Kumaraswamy and Chan (1995)

Buildingproject

Kumaraswamyand Chan(1995)original

TCR models

Hypothetical sample of projects

Number ofprojects

TCR modeldevelopedGenerated Used

All T ¼ 250.9 × C0.215 — 300 T ¼ 254.7 × C0.202

Residential T ¼ 245.0 × C0.202 250 250 T ¼ 244.9 × C0.200

Nonresidential T ¼ 315.5 × C0.197 50 50 T ¼ 315.5 × C0.196

Fig. 4. TCR models derived from the hypothetical sample of projectscreated from the TCR models of Kumaraswamy and Chan (1995)

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robust because it considers the errors of all the classes definedby the dummy variable. The choice of the best approach requiresan engineering judgment to decide whether the relation betweenthe classes of projects represented by the qualitative independentvariable is strong, in which case the best option is to considera TCR with a dummy variable, or weak, in which case developingseparate TCRwould be the best option. As in the previous example,if the causes underlying the variability of the time performanceof residential and nonresidential buildings not explained by thecost are the same and have equivalent effects, Eq. (4) would providethe best fit; otherwise, developing separate TCR models is thecorrect option.

Mathematical Structure

The power law has been the most used mathematical structure inthe development of TCR models. Along with the good fits that havebeen obtained by several authors in a diversified range of cases(e.g., project types, countries and regions, scope range), this math-ematical structure presents the following intrinsic advantages: (1) ittends to zero with the quantitative predictors; (2) it has no localmaxima or minima; and (3) it enables for an infinite range ofregression curve forms depending if the power of the quantitativepredictors is higher than one (exponential type), one (straight line),or less than one (logarithmic type). Despite the good results thathave been obtained, the intrinsic properties, the simplicity, andthe possibility of obtaining a linear form of the power law justby using the logarithm of the variables, some authors have exploredother mathematical structures to develop TCR models. The use ofpolynomial mathematical structures has been the most commonalternative (Chan and Kumaraswamy 1999a; Chen and Huang2006; Odabaşi 2009), but there are also examples of TCR modelsusing exponential and logarithms (e.g., Walker 1994; Chan andKumaraswamy 1999b; Chan and Chan 2004; Martin et al. 2006).

If the regression is correctly performed and valid, the alternativemathematical structures have no statistical implications differentfrom those previously addressed regarding the predictors used.However, some have specific practical implications, in particularthe fact that they do not tend to zero with the quantitative predictors.For some alternative mathematical structures, the TCR modelscan even estimate negative project duration estimates when thepredictors tend to zero. For others, local maxima may exist. In thesesituations, the validity limitations for extrapolating the time rela-tionships beyond the range/scope of the projects in the sample usedfor their development are further aggravated by logical limits.All TCR models show limited validity when extrapolating beyond

the range of the predictors or the scope of the projects from whichthey were developed. For example, when estimating the time of a$10 million project using a TCR model derived from a samplewhere $4 million was the maximum project cost, a question ariseswhether the TCR model is valid or not. If the TCR model mayestimate negative project durations or have a local maximum, thereis also the doubt regarding when the estimates start to be illogical.

Other Issues

Some authors (e.g., Nkado 1992; Ming 1998; Chan andKumaraswamy 1999a, b) developed specific TCR models forkey construction operations, from which time performance isestimated taking into consideration specific details of each buildingproject. The TCR models of this type show some limitations froma statistical perspective because, looking more carefully at the finalrules for estimating the total duration of the project, they were de-veloped with a large number of predictors (some with over 20qualitative and quantitative independent variables) that have beenobtained from reduced samples of projects (e.g., Nkado 1992, 29projects; Ming 1998, 71 projects; Chan and Kumaraswamy 1999b,56 projects; Chan and Kumaraswamy 1999a, 15 projects). Also,given that the independent variables are used repeatedly in the timerelationships for each construction operation, there may be unde-sirable interactions affecting the overall result. In practical terms,the use of these TCR models to estimate the time of each individualconstruction operations is straightforward and simple. However,because of the reasons previously mentioned, their use for estimat-ing the total time of a project should be made with due care.

Irfan et al. (2011) proposed an innovative approach, developingWeibull and Log-logistic TCR models for highway projects withthe following general form:

T ¼ eβ0þβ1×Cþβ2×CT ð5Þ

where CT is the contract type (1 for fixed deadline and 0 for fixedavailable days); and β0, β1, and β2 are regression coefficients. Theauthors developed separate TCR models for road maintenance,road construction, road resurfacing, traffic, and bridge constructionprojects, which are represented in Fig. 5.

These authors also suggest the use of the survival functions ofthe Weibull and Log-logistic TCR models, SðtÞ, to determine theprobability of a project duration being greater or equal than a speci-fied time, t

SðtÞ ¼ Prob½T ≥ t� ¼ e−ðλtÞp ð6Þ

Fig. 5. TCR models developed by Irfan et al. (2011) for (a) fixed deadline; (b) fixed available days contracts

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where T is a random time variable; t is some specified time; λ ¼e−β , where β is the parameter estimate of the covariate; andp ¼ 1=σ, where σ is the ancillary parameter of survival. Relatingthe estimated time with the cost using Eq. (5), Fig. 6 presents thesurvival functions relating the probability of exceeding the esti-mated duration with the project cost.

Considering the details provided in Irfan et al. (2011), theapproach seems to be statistically correct. However, its practicalapplication seems limited when estimating the project time orthe probability of the project time estimate being exceeded. Furtherdetails would be necessary to explain why the exponential growthof the project time with the project cost represented in Fig. 5 contra-dicts the other studied TCR models and the logarithm trend ofthe preliminary plots of projects time and cost presented by Irfanet al. (2011). Furthermore, Fig. 6 indicates that the probability ofexceeding the estimated time in any project over $3 million forfixed deadline contract, or $4 million for fixed available dayscontract, is nearly 0. On the other end, any low-cost project hasalmost 100% probability of being exceeded. This result is notconfirmed or is even contradictory to several quantitative (e.g., Al-Momani 2000; Aibinu and Jagboro 2002; Aibinu and Odeyinka2006) and qualitative (e.g., Odeh and Battaineh 2002; Sambasivanand Soon 2007; Sweis et al. 2008) studies on the causes ofproject delays.

Discussion

In reality, construction projects do not present a time performanceas uniform as the hypothetical samples of projects developed forsome of the examples presented in this paper. In order to use datafrom real projects, the information of public and private buildingsand of civil engineering projects provided by Chan (1998) wasused to develop TCR models (original TCR models). The authorsdeveloped four TCR models and compared two pairs of time per-formance results: (1) building projects against civil engineeringprojects (Fig. 7), and (2) public building projects against privatebuilding projects (Fig. 8). All regressions and regression coeffi-cients were found to be significant (p-value ¼ 0.000). TCR modelswith a qualitative independent variable were also developed (notpresented herein), but the regression coefficients of the dummy var-iable were nonsignificant (p-value ¼ 0.094 for the case comparingbuilding projects against civil engineering projects and p-value ¼0.668 for the case comparing public building projects againstprivate building projects).

In statistical terms, developing a single TCR model may be con-sidered a valid option in both cases. In practical terms, engineering

judgment must also be taken into account. In this example, it wouldbe recommended to consult experts familiar with the constructionof buildings in Hong Kong to decide whether it is reasonable toconsider a similar time performance for public and private buildingprojects. On the other hand, and according to the approach adoptedby Chan (1998), it does not seem reasonable to consider an uniqueTCR model for building and civil engineering projects given theirintrinsic and extrinsic differences affecting their time performance(e.g., type of construction operations involved, construction tech-nologies used, constrains, procurement and contracting practices).

(a) (b)

Fig. 6. Survival functions developed by Irfan et al. (2011) for (a) fixed deadline; (b) fixed available days contracts

Fig. 7. TCR models comparing building and civil engineering projectsof Chan (1998) data set

Fig. 8. TCR models comparing the public and private building projectsof Chan (1998) data set

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Based on the reasoning presented in the section “MathematicalStructure”, the power law or equivalent mathematical structures arethe most adequate for developing TCR models. The implicationsrelated to the selection of the quantitative and qualitative variablesto include in the TCRmodels was discussed earlier. In this regard, itshould be noted that implications related to the selection of bothtypes of variables are cumulative. To illustrate the practical conse-quences of the combined effect, consider a TCR model with adummy variable used to estimate the time of a project of a nondo-minant class with values of the quantitative predictors significantlydifferent from the range of values of the projects of the correspond-ing class in the data set (but within the overall range of values of theentire data set). In this situation, the bias in the prediction wouldresult from (1) the assumption that the TCR model representsequally the time of all the project classes defined by the dummyvariable, and (2) the extrapolation of the quantitative variable be-yond the range of values of that particular project class within thedata set. Furthermore, if the assumption of equal slope of the quan-titative predictor for each class of projects defined by the dummyvariable is incorrect, the estimated bias that may exist because ofthe extrapolation will be augmented.

These examples further demonstrate the importance of the roleof engineering judgment in developing, testing, and validatingstatistically sound TCR models. TCR models are an extremesimplification of the construction stage of a construction project;therefore, a solid statistical base (e.g., Hammad et al. 2010) anda correct engineering judgment are needed in their developmentand use to balance the practical aspects regarding the complexityof the time performance of construction projects.

Concluding Remarks

Dating back to 1969, the original TCR model (BTC), and also thesimilar TCR models that have been proposed by various authorssince then, continue to be a topic of interest for the constructionindustry. This is because the more sophisticated alternative ap-proaches for estimating total project time do not provide the samelevel of simplicity of use. However, there is a need to ensure therobustness and reliability of TCR models by balancing the statis-tical and practical dimensions of the problem using engineeringjudgment. This will provide additional accuracy and confidenceon the time estimates.

TCR models are but approximations deriving from informationgathered from a limited sample of previous projects. This papershows a survey of proposed TCR models and provides a criticalanalysis of the different approaches and assumptions leading totheir development. It also identifies some of the most importantstatistical and practical issues to be taken into consideration whendeveloping TCR models. Engineering judgment is proposed asthe necessary tool to balance the use of sound statistics withpractical aspects, namely regarding the process of selecting thequantitative and qualitative variables to use in a TCR model witha power law mathematical structure. The analysis undertakensuggests that the inclusion of an interaction term in TCR modelsincluding qualitative variables improves the robustness of themodel because it makes it possible to account for different slopesof the quantitative variable for each class of projects defined by thequalitative variable.

TCR models only provide a partial prediction of the time per-formance of a construction project. There are several other factorsinfluencing the time performance of construction projects that arenot accounted for by the TCR models (e.g., Odeh and Battaineh2002; Sambasivan and Soon 2007; Sweis et al. 2008). Future work

will evaluate the possibility of using the confidence intervals of theTCR models and engineering judgment to account for those factorsin estimating the duration of each specific construction project.

Acknowledgments

The authors acknowledge ICIST-IST Research Institute, in particu-lar for supporting research at Florida International University, theCalouste Gulbenkian Foundation grant supporting research atRyerson University, the Fulbright grant supporting research atUCDavis and the Portuguese National Science Foundation forthe grants SFRH/BD/35925/2007 and SFRH/BD/39923/2007.

References

Aibinu, A. A., and Jagboro, G. O. (2002). “The effects of construction de-lays on project delivery in Nigerian construction industry.” Int. J. Proj.Manage., 20(8), 593–599.

Aibinu, A. A., and Odeyinka, H. A. (2006). “Construction delays and theircausative factors in Nigeria.” J. Constr. Eng. Manage., 10.1061/(ASCE)0733-9364(2006)132:7(667), 667–677.

Alfred, L. E. (1988). Construction productivity–On site measurement andmanagement, McGraw-Hill, Sydney, Australia.

Al-Momani, A. H. (2000). “Construction delay: A quantitative analysis.”Int. J. Proj. Manage., 18(1), 51–59.

Blyth, S. M. (1995). “An investigation into the development of a bench-mark for UK construction time performance.” M.Sc. thesis, Univ. ofGlamorgan, Pontypridd, U.K.

Bromilow, F. J. (1969). “Contract time performance—Expectation and thereality.” Build. Forum, 1(3), 70–80.

Bromilow, F. J., Hinds, M. F., and Moody, N. F. (1988). “The time and costperformance of building contracts 1976–1986.” The Australian Instituteof Quantity Surveyors, Sydney, Australia.

Building Cost Information Service (BCIS). (2004). Guide to buildingconstruction duration, London.

Building Cost Information Service (BCIS). (2005). Time and cost predict-ability of construction projects: Analysis of UK performance. London.

Chan, A. P. C., and Chan, D. W. M. (2004). “Developing a benchmarkmodel for project construction time performance in Hong Kong.” Build.Environ., 39(3), 339–349.

Chan, D. W. M., and Kumaraswamy, M. M. (1995). “A study of the factorsaffecting construction durations in Hong Kong.” Constr. Manage. Econ,13(4), 319–333.

Chan, D. W. M., and Kumaraswamy, M. M. (1999a). “Forecasting con-struction durations for public housing projects: A Hong Kong perspec-tive.” Build. Environ., 34(5), 633–646.

Chan, D. W. M., and Kumaraswamy, M. M. (1999b). “Modelling and pre-dicting construction durations in Hong Kong public housing.” Constr.Manage. Econ., 17(3), 351–362.

Chan, W. M. (1998). “Modelling construction durations for public housingprojects in Hong Kong.” Ph.D. thesis, Univ. of Hong Kong, Hong Kong.

Chen, W. T., and Huang, Y.-H. (2006). “Approximately predicting the costand duration of school reconstruction projects in Taiwan.” Constr. Man-age. Econ., 24(12), 1231–1239.

Chou, J.-S. (2009). “Generalized linear model-based expert system for es-timating the cost of transportation projects.” Expert Syst. Appl., 36(3),4253–4267.

Gunduz, M., Ugur, L. O., and Ozturk, E. (2011). “Parametric cost estima-tion system for light rail transit and metro trackworks.” Expert Syst.Appl., 38(3), 2873–2877.

Hammad, A. A. A., Ali, S. M. A., Sweis, G. J., Sweis, R. J., and Shboul, A.(2010). “Statistical analysis on the cost and duration of public buildingprojects.” J. Manage. Eng., 10.1061/(ASCE)0742-597X(2010)26:2(105), 105–112.

Hegab, M. Y., and Smith, G. R. (2007). “Delay time analysis in microtun-neling projects.” J. Constr. Eng. Manage., 10.1061/(ASCE)0733-9364(2007)133:2(191), 191–195.

© ASCE 04014034-9 J. Constr. Eng. Manage.

J. Constr. Eng. Manage.

Dow

nloa

ded

from

asc

elib

rary

.org

by

Suny

At B

uffa

lo o

n 05

/30/

14. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.

Hegazy, T., and Ayed, A. (1998). “Neural network model for parametriccost estimation of highway projects.” J. Constr. Eng. Manage.,10.1061/(ASCE)0733-9364(1998)124:3(210), 210–218.

Hoffman, G. J. (2005). Estimating performance time for air force militaryconstruction projects.” M.Sc. thesis, Dept. of the Air Force, Air ForceInstitute of Technology, Wright-Patterson Air Force Base, OH.

Hoffman, G. J., Thal, A. E., Jr., Webb, T. S., and Weir, J. D. (2007).“Estimating performance time for construction projects.” J. Manage.Eng., 10.1061/(ASCE)0742-597X(2007)23:4(193), 193–199.

Hola, B., and Schabowicz, K. (2010). “Estimation of earthworks executiontime cost by means of artificial neural networks.” Autom. Constr., 19(5),570–579.

International Organization for Standardization (ISO). (2012). “Guidance onproject management.” ISO 21500, Geneva.

Irfan, M., Khurshid, M. B., Anastasopoulos, P., Labi, S., and Moavenzadeh,F. (2011). “Planning-stage estimation of highway project duration onthe basis of anticipated project cost, project type, and contract type.”Int. J. Proj. Manage., 29(1), 78–92.

Kaka, A., and Price, A. D. F. (1991). “Relationship between value and du-ration of construction projects.” Constr. Manage. Econ., 9(4), 383–400.

Karshenas, S. (1984). “Predesign cost estimating method for multistorybuildings.” J. Constr. Eng. Manage., 10.1061/(ASCE)0733-9364(1984)110:1(79), 79–86.

Khosrowshahi, F., and Kaka, A. P. (1996). “Estimation of project total costand duration for housing projects in the U.K.” Build. Environ., 31(4),373–383.

Kim, G.-H., An, S.-H., and Kang, K.-I. (2004). “Comparison of construc-tion cost estimating models based on regression analysis, neural net-works, and case-based reasoning.” Build. Environ., 39(10), 1235–1242.

Kumaraswamy, M. M., and Chan, D. W. M. (1995). “Determinants of con-struction duration.” Constr. Manage. Econ., 13(3), 209–217.

Le-Hoai, L., Lee, Y. D., and Nguyen, A. T. (2013). “Estimating timeperformance for building construction projects in Vietnam.” KSCE J.Civ. Eng., 17(1), 1–8.

Love, P. E. D., Tse, R. Y. C., and Edwards, D. J. (2005). “Time-cost rela-tionships in Australian building construction projects.” J. Constr. Eng.Manage., 10.1061/(ASCE)0733-9364(2005)131:2(187), 187–194.

Lowe, D. J., Emsley, M. W., and Harding, A. (2006). “Predicting construc-tion cost using multiple regression techniques.” J. Constr. Eng. Man-age., 10.1061/(ASCE)0733-9364(2006)132:7(750), 750–758.

MacKenzie, J. (1996). “The influence of a benchmarking system for con-struction time performance of contracts in SouthWales.” M.Sc. thesis,Univ. of Glamorgan, Pontypridd, U.K.

Martin, J., Burrows, T., and Pegg, I. (2006). “Predicting constructionduration of building projects.” Shaping the Change, XXIII FIGCongress, Munich, Germany.

Meng, X. (2012). “The effect of relationship management on projectperformance in construction.” Int. J. Proj. Manage., 30(2), 188–198.

Ming, C. W. (1998). “Modelling construction durations for public housingprojects in Hong Kong.” Ph.D. thesis, Univ. of Hong Kong, Hong Kong.

Nguyen, L. D., Kneppers, J., de Soto, B. G., and Ibbs, W. (2010). “Analysisof adverse weather for excusable delays.” J. Constr. Eng. Manage.,10.1061/(ASCE)CO.1943-7862.0000242, 1258–1267.

Nkado, R. N. (1992). “Construction time information system for the build-ing industry.” Constr. Manage. Econ., 10(6), 489–509.

Odabaşi, E. (2009). “Models for estimating construction duration: An ap-plication for selected buildings on the Metu campus.” M.Sc. disserta-tion, Dept. of Architecture, Middle East Technical Univ., Ankara,Turkey.

Odeh, A. M., and Battaineh, H. T. (2002). “Causes of construction delay:Traditional contracts.” Int. J. Proj. Manage., 20(1), 63–73.

Sambasivan, M., and Soon, Y. W. (2007). “Causes and effects of delaysin Malaysian construction industry.” Int. J. Proj. Manage., 25(5),517–526.

Shehab, T., and Farooq, M. (2013). “Neural network cost estimating modelfor utility rehabilitation projects.” Eng. Constr. Architect. Manage.,20(2), 118–126.

Skitmore, R. M., and Ng, S. T. (2003). “Forecast models for actual con-struction time and cost.” Build. Environ., 38(8), 1075–1083.

Song, L., Mohamed, Y., and Abou Rizk, S. M. (2009). “Early contractorinvolvement in design and its impact on construction schedule perfor-mance.” J. Manage. Eng., 10.1061/(ASCE)0742-597X(2009)25:1(12),12–20.

Sonmez, R. (2004). “Conceptual cost estimation of building projectswith regression analysis and neural networks.” Can. J. Civ. Eng., 31(4),677–683.

Sonmez, R. (2008). “Parametric range estimating of building costs usingregression models and bootstrap.” J. Constr. Eng. Manage., 10.1061/(ASCE)0733-9364(2008)134:12(1011), 1011–1016.

Sousa, V., Almeida, N. M., Dias, L. A., and Branco, F. A. (2014). “Risk-informed time-cost relationship models for sanitation projects.”J. Constr. Eng. Manage., 10.1061/(ASCE)CO.1943-7862.0000848,06014002.

Sweis, G., Sweis, R., Hammad, A. A., and Shboul, A. (2008). “Delays inconstruction projects: The case of Jordan.” Int. J. Proj. Manage., 26(6),665–674.

Thal, A. E., Jr., Cook, J. J., and White, E. D., III (2010). “Estimationof cost contingency for air force construction projects.” J.Constr. Eng. Manage., 10.1061/(ASCE)CO.1943-7862.0000227,1181–1188.

Toor, S.-U.-R., and Ogunlana, S. O. (2008). “Problems causing delaysin major construction projects in Thailand.” Constr. Manage. Econ.,26(4), 395–408.

Walker, D. H. T. (1994). “An investigation into factors that determine build-ing construction time performance.” Ph.D. thesis, Royal Melbourne In-stitute of Technology, Melbourne, Australia.

Yeh, S. F., Lin, M. D., and Tsai, K. T. (2008). “Development of costfunctions for open-cut and jacking methods for sanitary sewersystem construction in central Taiwan.” Pract. Period. Hazard. ToxicRadioact. Waste Manage., 10.1061/(ASCE)1090-025X(2008)12:4(282), 282–289.

Yousef, G., and Baccarini, D. (2001). “Developing a cost–time model forestimating construction durations of sewerage projects in Perth, WesternAustralia.” J. Constr. Res., 2(2), 213–220.

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