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Dynamic Modeling of Multifactor Construction Productivity for Equipment-Intensive Activities

September 2018
Journal of Construction Engineering and Management 144(9)

September 2018
144(9)

DOI:10.1061/(ASCE)CO.1943-7862.0001549

Authors:

Northumbria University

Construction productivity is a major research interest within the construction domain. Because construction is a labor-intensive industry, previous research has often focused on construction labor productivity (CLP). However, equipment is the main driver of productivity for some construction activities, so-called equipment-intensive activities. Existing models of activity-level productivity often predict a single-factor productivity measure - namely CLP - yet determining multifactor productivity, including labor, material, and equipment, provides more comprehensive predictions of productivity. Construction productivity models are often static in nature, or incapable of capturing the subjective uncertainty of some factors influencing productivity. Fuzzy system dynamics is an appropriate technique for modeling construction productivity because it captures the dynamism of construction projects and addresses the subjective and probabilistic uncertainty of factors influencing productivity. The contributions of this paper are threefold: identifying the key factors influencing the productivity of equipment-intensive activities, developing a predictive model of multifactor productivity for equipment-intensive activities using fuzzy system dynamics technique, and developing an approach to reduce uncertainty overestimation in the simulation results of fuzzy system dynamics models.

Methodology for construction productivity modeling by FSD technique.

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Stock and flow diagram of qualitative FSD model of construction productivity.

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Fuzzy membership functions for representing crew motivation.

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Simulation results for MFP in comparison to actual field data.

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Example of interview survey question

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Figures - uploaded by Nima Gerami Seresht

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Content uploaded by Nima Gerami Seresht

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Dynamic Modeling of Multifactor Construction

Productivity for Equipment-Intensive Activities

Nima Gerami Seresht, Ph.D., A.M.ASCE1; and Aminah Robinson Fayek, Ph.D., P.Eng., M.ASCE2

Abstract: Construction productivity is a major research interest within the construction domain. Because construction is a labor-intensive

industry, previous research has often focused on construction labor productivity (CLP). However, equipment is the main driver of productivity

for some construction activities, so-called equipment-intensive activities. Existing models of activity-level productivity often predict a single-

factor productivity measure—namely CLP—yet determining multifactor productivity, including labor, material, and equipment, provides

more comprehensive predictions of productivity. Construction productivity models are often static in nature, or incapable of capturing

the subjective uncertainty of some factors influencing productivity. Fuzzy system dynamics is an appropriate technique for modeling con-

struction productivity because it captures the dynamism of construction projects and addresses the subjective and probabilistic uncertainty of

factors influencing productivity. The contributions of this paper are threefold: identifying the key factors influencing the productivity of

equipment-intensive activities, developing a predictive model of multifactor productivity for equipment-intensive activities using fuzzy sys-

tem dynamics technique, and developing an approach to reduce uncertainty overestimation in the simulation results of fuzzy system dynamics

Author keywords: Construction productivity; System dynamics; Fuzzy logic; Construction equipment.

Introduction

Construction productivity has been a major research interest within

the construction management domain for some time. Previous re-

search on construction productivity has either focused on identi-

fication of the factors influencing construction productivity or

on the development of predictive models for construction produc-

tivity. Due to the fact that construction is a labor-intensive industry

(Jarkas 2010), previous studies on the activity-level productivity

have primarily focused on construction labor productivity (CLP)

(Tsehayae and Fayek 2014;Naoum 2016;Tsehayae and Fayek

2016a;Mirahadi and Zayed 2016). However, construction equip-

ment is now an important resource in construction projects, and it

is the drivers of productivity for some activities. Goodrum and Haas

(2004) observed substantial long-term improvement in the produc-

tivity of the activities executed using equipment with significant

technological advancements. Goodrum et al. (2010) developed a

predictive model to measure the effect of equipment on construction

productivity; this research confirms that technological advance-

ments in construction equipment affect construction productivity.

Ok and Sinha (2006) argued that accurate prediction of the construc-

tion productivity for some activities (e.g., earthmoving operations)

depends on the accurate prediction of the equipment production

rate. These construction activities are identified as equipment-

intensive activities, in which equipment, rather than labor, is the

driver of productivity. Accordingly, the factors influencing the pro-

ductivity of equipment-intensive activities are different from the

factors influencing the productivity of labor-intensive activities.

Therefore, in order to model the productivity of equipment-intensive

activities, the factors influencing the productivity of these activities

must be identified.

Existing predictive models for construction productivity mostly

focus on predicting CLP, which determines productivity of con-

struction systems (i.e., construction projects or construction activ-

ities) using only one resource input (e.g., labor). Previous studies

confirm that, for determining productivity of construction systems,

using the other resource inputs (i.e., equipment and material) in

addition to labor results in more comprehensive measures of pro-

ductivity compared to CLP (Loosemore 2014). However, Carson

and Abbott (2012) concluded that the construction industry suffers

from a lack of predictive models that determine productivity of

construction systems using such comprehensive productivity

measures.

Existing predictive models of construction productivity were

mostly developed using static techniques (e.g., the artificial neural

network (ANN) model by Heravi and Eslamdoost (2015) and the

fuzzy rule-based system model by Tsehayae and Fayek (2016a),

which means that they predict a single productivity value at a given

point in time. However, due to the dynamic nature of construction

projects, modeling techniques that are able to track project changes

over time are more suitable for modeling construction productivity.

Moreover, the factors influencing construction productivity are

rarely independent from each other, and changes in certain factors

can impact other factors (Mawdesley and Al-Jibouri 2009). There-

fore, the cause and effect relationships between the factors influ-

encing construction productivity need to be captured, along with

their individual impacts on productivity. The fuzzy system dynam-

ics (FSD) technique, which integrates system dynamics (SD) with

fuzzy logic, is an appropriate technique for modeling construction

1Postdoctoral Fellow, Dept. of Civil and Environmental Engineering,

7-203 Donadeo Innovation Centre for Engineering, Univ. of Alberta,

9211 116 St. NW, Edmonton, AB, Canada T6G 1H9.

2Tier 1 Canada Research Chair in Fuzzy Hybrid Decision Support

Systems for Construction, NSERC Industrial Research Chair in Strategic

Construction Modeling and Delivery, Ledcor Professor in Construction

Engineering, Professor, Dept. of Civil and Environmental Engineering,

7-287 Donadeo Innovation Centre for Engineering, Univ. of Alberta, 9211

116 St. NW, Edmonton, AB, Canada T6G 1H9 (corresponding author).

Email: aminah.robinson@ualberta.ca

Note. This manuscript was submitted on November 9, 2017; approved

on April 13, 2018; published online on July 12, 2018. Discussion period

open until December 12, 2018; separate discussions must be submitted

for individual papers. This paper is part of the Journal of Construction

Engineering and Management, © ASCE, ISSN 0733-9364.

J. Constr. Eng. Manage., 2018, 144(9): 04018091

productivity. The SD component of the FSD technique captures

the dynamism of construction projects and the relationships be-

tween the factors influencing construction productivity, whereas

the fuzzy logic component addresses the subjective uncertainty of

these factors.

This paper presents an FSD model of activity-level construction

productivity that measures the productivity of equipment-intensive

activities using the three resource inputs of construction activities

(i.e., labor, equipment, and material). For this purpose, the factors

influencing the productivity of equipment-intensive activities were

first identified. Second, in order to increase the accuracy of the pre-

dictive model, the number of factors influencing construction pro-

ductivity was reduced by feature selection. Third and fourth, the

qualitative and quantitative FSD models of multifactor productivity

(MFP) were developed. Finally, the FSD model was validated using

a case study of earthmoving operations on an actual construction

project. This paper advances the state of the art in construction

productivity modeling by identifying the key factors influencing

the productivity of equipment-intensive activities, and by develop-

ing the FSD model of MFP for equipment-intensive activities. This

FSD model simultaneously captures the dynamism of construction

productivity (i.e., changes in productivity over time) and the cause

and effect relationships between the factors influencing productiv-

ity, as well as the probabilistic and subjective uncertainties of the

factors influencing construction productivity.

Literature Review

Construction Productivity

In general, the productivity of a construction system (e.g., con-

struction activity, construction project) can be calculated as the ra-

tio of the inputs of the system (e.g., labor cost or person-hours) to

its output (e.g., cubic meters of concrete placed). Talhouni (1990)

introduces three different measures for construction productivity:

(1) single factor productivity (SFP), which measures the produc-

tivity of construction systems using only one resource input

(i.e., labor); (2) multifactor productivity (MFP), which measures

the productivity of construction systems using any combination

of three resource inputs (i.e., labor, materials, and equipment);

and (3) total factor productivity (TFP), which measures the pro-

ductivity of construction systems using five resource inputs

(i.e., labor, materials, equipment, energy, and capital). From the

construction management perspective, construction productivity

is often defined at the project level or the activity level using two

measures: construction labor productivity (CLP), which is an

SFP measure that uses labor as the only input of productivity

(Tsehayae and Fayek 2016a), or MFP, which uses any combination

of the three inputs of productivity (i.e., labor, equipment, and

material) (Eastman and Sacks 2008). Measuring the TFP at the

project or activity levels can be inaccurate, due to the difficulties

encountered in predicting the energy and capital inputs at the

project or activity levels (Thomas et al. 1990;Loosemore 2014).

Thus, MFP represents the most comprehensive measure of con-

struction productivity at the project and activity levels. However,

unlike other industries for which MFP measures of productivity

are available, the construction industry suffers from a lack of pre-

dictive models for determining the MFP of construction systems

(Carson and Abbott 2012).

Depending on which resource is the main driver of the produc-

tivity, construction activities can be grouped into two categories:

labor-intensive activities, in which labor is the main driver of pro-

ductivity (e.g., electrical and mechanical activities) (Jarkas 2010),

and equipment-intensive activities, in which equipment is the main

driver of productivity (e.g., earthmoving activities) (Ok and Sinha

2006). Whereas the productivity of labor-intensive activities is

mainly affected by CLP, the productivity of equipment-intensive

activities is mainly affected by the production rate of the equipment

used for the execution of the activity. There are numerous

equipment-intensive activities in different types of construction

projects, including earthmoving (Ok and Sinha 2006;Jabri and

Zayed 2017), pavement construction (Choi and Ryu 2015), pile

construction (Zayed and Halpin 2005), and tunneling (Shaheen

et al. 2009). Because the resource that drives the productivity of

labor-intensive and equipment-intensive activities is different, the

factors that influence the productivity of these two types of activ-

ities are also different. However, previous research on construction

productivity has failed to identify a comprehensive list of factors

influencing the productivity of equipment-intensive activities.

Moreover, traditionally the production rate of the equipment used

for the execution of a given equipment-intensive activity is mea-

sured as the efficiency measure of the activity (Zayed and Halpin

2005;Shaheen et al. 2009;Jabri and Zayed 2017). Zayed and

Halpin (2005) identified 12 factors that influence the production

rate of a piling activity; they developed a statistical model using

the linear regression method to predict the production rate of a pil-

ing activity in terms of number piles drilled per day. Shaheen et al.

(2009) identified 11 factors that influence the production rate of a

tunneling activity using a tunnel boring machine (TBM); they used

an expert-driven fuzzy rule-based system (FRBS) to predict the

production rate of the activity based on these 11 factors. Moreover,

Shaheen et al. (2009) developed a discrete event simulation model

to predict the total duration of the activity based on the production

rate determined by the FRBS. Finally, Jabri and Zayed (2017)

developed a predictive model for the production rate of an earth-

moving operation using the agent-based modeling technique. The

model developed by Jabri and Zayed (2017) predicts the production

rate and total duration of an earthmoving operation based on the

equipment and labor properties and environmental factors that

affect the activity. The production rate is commonly calculated

as the output per unit time. Although the prediction of production

rate in the aforementioned studies facilitates the evaluation of the

duration of equipment-intensive activities, the production rate does

not provide comprehensive information regarding the resource in-

puts (i.e., labor, equipment, and material) and consequently the cost

efficiency of these activities. Moreover, there are also a few predic-

tive models developed for equipment-intensive activities that mea-

sure the CLP of these activities (Choi and Ryu 2015). Choi and Ryu

(2015) identified nine factors that influence the productivity of

highway pavement activities and developed a predictive model

to measure the CLP of such activities using statistical methods.

However, CLP is not an appropriate measure of productivity for

equipment-intensive activities because it does not provide any

information regarding the resource input (equipment) that is the

main driver of productivity for these activities. Therefore, there is

a need to develop a predictive model for determining the MFP of

equipment-intensive activities.

Finally, the existing predictive models of construction produc-

tivity are commonly developed using static modeling techniques,

such as the ANN model developed by Heravi and Eslamdoost

(2015). However, dynamic modeling techniques such as SD and

FSD are more appropriate for modeling construction productivity

because construction systems are dynamic (i.e., changing over

time) and their components interact with each other (Mawdesley

and Al-Jibouri 2009;Alzraiee et al. 2015). Moreover, SD models

of construction productivity (Mawdesley and Al-Jibouri 2009;

Nasirzadeh and Nojedehi 2013) cannot capture the subjective

J. Constr. Eng. Manage., 2018, 144(9): 04018091

uncertainty of the factors influencing productivity. Accordingly,

Nojedehi and Nasirzadeh (2017) suggested that FSD is an appro-

priate technique for modeling construction productivity because

this technique captures the dynamism of construction systems and

the interactions between the factors influencing productivity while

simultaneously representing the probabilistic and subjective uncer-

tainty of these factors. Nojedehi and Nasirzadeh (2017) developed a

predictive model of CLP using the FSD technique. Because their

predictive model is developed for labor-intensive activities and pre-

dicts CLP, it is not an appropriate model for predicting the produc-

tivity of equipment-intensive activities. Accordingly, there is a need

within the existing body of construction research to develop a pre-

dictive model of the MFP for equipment-intensive activities using

FSD technique, which is addressed in this paper.

Fuzzy System Dynamics

SD is a simulation methodology developed by Forrester (1961) for

analyzing complex industrial systems. This modeling technique is

able to model a dynamic system, in which the state of the system

(e.g., construction productivity) changes over time and under the

effect of different factors. Although SD models are able to capture

the probabilistic uncertainties of real-world systems using the

Monte Carlo simulation technique (Sterman 2000), these models

cannot capture the nonprobabilistic uncertainties (i.e., subjective,

imprecise, or linguistically expressed information) of real-world

systems. To address this limitation, Levary (1990) integrated SD

with fuzzy logic and developed the fuzzy system dynamics (FSD)

technique, which is capable of capturing deterministic values, as

well as probabilistic and nonprobabilistic uncertainties. Moreover,

the fuzzy logic component of the FSD technique allows practi-

tioners to evaluate subjective variables using linguistic terms, rather

than precise numerical values.

FSD simulation models are developed through qualitative and

quantitative modeling steps. First, the qualitative FSD model is de-

veloped by identifying and modeling the factors influencing the

system, which are called system variables. Next, the quantitative

FSD model is developed by developing fuzzy membership func-

tions to represent the subjective system variables and defining the

relationships between the system variables quantitatively. The

fuzzy membership functions representing subjective system varia-

bles can be developed by one of the several approaches proposed

in the literature, either by using data (e.g., fuzzy c-means (FCM)

clustering approach) or by using expert knowledge (e.g., Saaty’s

priority approach). The relationships between system variables

are defined by mathematical equations or by fuzzy rule-based sys-

tems (Khanzadi et al. 2012;Nasirzadeh et al. 2013). There are two

types of relationships between system variables: hard relationships,

in which the mathematical form of the relationship is known, and

soft relationships, in which the mathematical form of the relation-

ship is unknown (Coyle 2000). The hard relationships of FSD mod-

els are defined by mathematical equations, and fuzzy arithmetic

operations are used in the mathematical equations that include sub-

jective variables. The soft relationships of FSD models are defined

either by mathematical equations developed statistically, if data are

available to do so, or by FRBS developed by expert knowledge if

data are not available (Khanzadi et al. 2012).

By implementing fuzzy arithmetic in the mathematical equa-

tions of the FSD models, the supports of the membership functions,

which represent the simulation results, grow rapidly, producing a

large amount of uncertainty (Tessem and Davidsen 1994). This

phenomenon is called the overestimation of uncertainty, which

reduces the ability of users to accurately predict the actual system

output (e.g., actual productivity) based on the simulation results

(Lin et al. 2011). The overestimation of uncertainty in the FSD

models may be affected by various factors such as the number

of parameters in the mathematical equations, the number of time

steps, the membership functions of the inputs, and the method

of the fuzzy arithmetic implementation. Fuzzy arithmetic opera-

tions can be implemented using one of the two following methods:

the α-cut method, and the extension principle method, which uses

different t-norms (Pedrycz and Gomide 2007). Implementing fuzzy

arithmetic by the extension principle method using drastic product

t-norm reduces the uncertainty overestimation in comparison to the

α-cut method (Chang et al. 2006;Lin et al. 2011). However, in

previous applications of FSD models in different construction areas

such as risk analysis (Nasirzadeh et al. 2014), project contract

administration (Khanzadi et al. 2012), and construction productiv-

ity (Nojedehi and Nasirzadeh 2017), fuzzy arithmetic is imple-

mented only by the α-cut method due to its simplicity. As an

example, in the results of the FSD model developed by Nojedehi

and Nasirzadeh (2017), the α-cut method causes overestimation

of uncertainty in the fuzzy number that represents the labor produc-

tivity of a concrete pouring activity, ½4.08;29.37ðm3=monthÞ,

where the upper bound of the support is 620% larger than its lower

bound. The large amount of uncertainty in the simulation results

reduces the ability of users (e.g., construction practitioners) to ac-

curately predict the actual productivity, project cost, and project

duration based on the simulation results. In this paper, this limita-

tion is addressed by implementing fuzzy arithmetic operations us-

ing the extension principle method with the min, algebraic product,

Lukasiewicz, and drastic product t-norms, and selecting the most

appropriate method to increase the accuracy of the simulation

results, while simultaneously reducing the amount of uncertainty.

Construction Productivity Modeling Methodology

This section of the paper outlines the development of the FSD

model of activity-level productivity for equipment-intensive activ-

ities; this process was accomplished in the following five steps:

(1) identification of the factors influencing construction productiv-

ity, (2) reduction of the dimensionality of the factors by feature

selection, (3) development of the qualitative FSD model, (4) devel-

opment of the quantitative FSD model, and (5) validation of the

full FSD model. These five steps are presented in Fig. 1.

In the first step, the factors influencing productivity of

equipment-intensive activities were identified through a literature

review. There are numerous studies available in the literature

that identify the factors influencing construction productivity at dif-

ferent levels of analysis (e.g., activity-level or project-level). In

addition to micro-level factors (i.e., crew-level, activity-level,

and project-level), macro-level factors (i.e., organizational-level,

provincial-level, national-level, and global-level) may directly or

indirectly influence construction productivity (Tsehayae and Fayek

2014). However, since the project-level and macro-level factors are

static (i.e., constant) at the activity level, these factors are excluded

from the FSD model presented in this paper. Thus, in this paper, the

crew-level and the activity-level factors that influence the produc-

tivity of equipment-intensive activities were identified through

literature review. Next, the identified factors were verified by expert

knowledge using interview surveys, which were administered to

managerial personnel (i.e., general management, project manage-

ment, project controls, and field engineers), and field personnel

(i.e., laborers/equipment operators and foremen) within a Canadian

company active in the industrial construction sector. Fifteen project

management surveys and 20 tradespeople surveys were collected

and analyzed to verify the factors influencing construction

J. Constr. Eng. Manage., 2018, 144(9): 04018091

productivity identified from the literature review. The respondents

of the managerial personnel survey had an average of six years of

experience in the construction industry and were involved in an

average of six industrial pipeline projects. The respondents of

the field personnel survey were most frequently union members

(i.e., 95% of the respondents), who were involved in numerous

projects with an average of 10 years of experience in industrial

pipeline projects. The interview surveys assessed the impact of

each factor on construction productivity using a seven-point Likert

scale, as suggested by Tsehayae and Fayek (2014) and Dai (2006).

The scale used in the interview surveys had three levels of negative

impact determined by negative impacts scores (i.e., strongly neg-

ative [−3], negative [−2], and slightly negative [−1]), one neutral

point determined by zero (i.e., no impact [0]), and three levels of

positive impact determined by positive impact scores (i.e., slightly

positive [þ1], positive [þ2], and strongly positive [þ3]). Table 1

presents an example of survey questions measuring the impact of

the factors that affect construction productivity.

Consequently, 72 crew-level and activity-level factors were

identified through the literature review and were verified by

expert knowledge to have either a negative or positive impact

on construction productivity; these factors were grouped into

seven categories based on their source (e.g., foreman-related fac-

tors, location-related factors, etc.). These factors were identified

through the following previous studies: Zakeri et al. (1996),

Goodrum and Haas (2004), Zayed and Halpin (2005), Ok and

Sinha (2006), Mortaheb et al. (2007), Goodrum et al. (2010),

Kannan (2011), Choi and Ryu (2015), and Sadeghpour and

Andayesh (2015). Table 2presents the 72 identified factors, their

categories, and their average impact score on construction produc-

tivity; these factors are referred to as the system variables in the

following steps.

Table 1. Example of interview survey question

Factors

Impact

Strongly negative Negative Slightly negative No impact Slightly positive Positive Strongly positive

The crew size is adequate

for the task at hand

−3−2−10123

Fig. 1. Methodology for construction productivity modeling by FSD technique.

J. Constr. Eng. Manage., 2018, 144(9): 04018091

Next, the number of system variables was reduced by feature se-

lection to increase the accuracy of the predictive model for construc-

tion productivity (Ahmad and Pedrycz 2011). There are various

methods for feature selection, out of which correlation-based feature

selection (CFS) is the most common approach, due to its simplicity

(Hall 1998). CFS reduces the dimensionality of the data set by

selecting the subset of the factors that have the highest Pearson

correlation coefficient with the system output (e.g., productivity)

and that have the lowest Pearson correlation coefficient with the

other factors of the subset. For developing FRBS, Ahmad and

Pedrycz (2011) proposed the use of wrapper methods for feature

selection. Wrapper methods are based on evolutionary search meth-

ods [e.g., genetic algorithms (GAs)], which search for the subset of

data in which the FRBS has the highest accuracy (e.g., the lowest

root mean square error). Feature selection was implemented using

the following two approaches: CFS was applied to soft relationships

that are defined by statistically developed mathematical equations,

and the wrapper method using GAwas applied to soft relationships

that are defined by data-driven FRBS.

In the third step, the qualitative FSD model was developed by

identifying two types of relationships between the system variables:

soft relationships and hard relationships. Soft relationships were

identified based on existing knowledge about real-world systems,

which was acquired through a literature review and expert judgment,

as suggested by Sterman (2000). The list of the factors that influence

the productivity of equipment-intensive activities (refer to Table 2)

was developed using literature review, as discussed previously; thus,

the soft relationships between these factors and MFP were con-

firmed by the literature. Moreover, these soft relationships were also

verified by the expert knowledge obtained through the interview

surveys, as discussed earlier. On the other hand, the hard relation-

ships between the system variables were identified using the equa-

tions, which define the relationships. Eq. (1) presents an example of

the hard relationship between crew size, planned crew size, and

absenteeism:

Crew Size ¼Planned Crew Size −Absenteeism ð1Þ

In the fourth step, the quantitative FSD model was developed.

First, the objective and subjective system variables were identified

based on their scales of measure, in which objective variables were

evaluated using crisp numbers (e.g., 10 years of experience) and

subjectivevariables were evaluated using subjective scales (e.g., high

crew motivation) (Tsehayae and Fayek 2016b). Then, objective sys-

tem variables were represented by crisp numbers, and fuzzy mem-

bership functions were developed to represent the subjective system

variables. These fuzzy membership functions can be developed by

one of several approaches proposed in the literature that use either

data or expert knowledge. Fuzzy membership functions were devel-

oped by FCM clustering, which is a machine learning technique that

is commonly used for developing fuzzymembership functions using

data (Pedrycz 2013). FCM clustering was also used to develop the

FRBS for defining the relationships between the system variables by

projecting the clusters into the input space (e.g., the values of the

factors influencing productivity) and the output space (e.g., the value

of productivity) (Pedrycz 2013).

Next, the soft relationships of the system were defined quanti-

tatively. The soft relationships were defined either by data-driven

FRBS developed using FCM clustering (Gerami Seresht and Fayek

2015) or by mathematical equations developed using linear regres-

sion (Nasirzadeh et al. 2014). The performance of the two methods

in defining the soft relationships of the system was evaluated using

the root mean square error (RMSE); then, the method with the

lowest RMSE was chosen for defining each relationship. FCM

clustering and linear regression methods were implemented using

90% cross validation, which uses 90% of the data for training and

10% of the data for validation (i.e., measuring RMSE). Since the

mathematical form of hard relationships was known, unlike soft

relationships, these relationships were defined using mathematical

equations. Fuzzy arithmetic was then used to solve both the soft

relationships defined using mathematical equations as well as all

the hard relationships, since they both contain subjective system

Table 2. Crew- and activity-level factors influencing productivity of equipment-intensive activities

Category Factors (average impact score)

Crew-level factors

Labor and crew Crew size (þ1.94), crew composition (þ1.47), crew experience (þ2.26), adequacy of crew (þ1.94), crew makeup changes

(−0.97), crew turnover rate (−1.66), number of languages spoken in the crew (−2.11), crew motivation (þ2.37), level of

interruptions and disruptions (−1.39), number of consecutive working days (−1.53), total daily overtime work (−1.47), crew

skill level (þ2.26), unscheduled breaks (−1.41), late arrival/early quit (−2.03), level of absenteeism (−1.82)

Material and consumables Material availability (þ2.03), waiting time for material (−1.77), material quality (−1.63), material storage practice (þ1.86),

preinstallation requirements (−1.06)

Equipment and tools Number of equipment (þ1.74), equipment breakdown frequency (−1.51), equipment breakdown downtime (−1.51),

equipment maintenance frequency (−1.43), equipment maintenance downtime (−1.43), work equipment availability

(þ1.74), equipment delivery to working area (−1.80), appropriateness of equipment (þ1.97), equipment ownership (þ1.43),

equipment production capacity (þ1.97), equipment age (−1.29), equipment operator experience (þ2.29), equipment

operator education and trainings (þ2.14), equipment operator skill level (þ2.29), amplification of human energy (þ1.97),

level of control (þ1.88), functional range (þ1.71), equipment ergonomic design (þ1.62), information feedback provision

(þ1.44), moving technology (þ1.88), equipment warranty (þ0.67), equipment specification (þ1.97)

Foreman Foreman experience (þ2.11), change of foreman (−1.74), work planning skills (þ2.14), leadership and supervisory skills

(þ2.14), coordination between labor and equipment operators (þ2.15)

Activity-level

Task characteristics Task complexity (−1.15), total volume of work (þ1.76), task repetitiveness (þ1.38), out-of-sequence work (−1.24),

problems with predecessors (−1.32), construction method (þ1.93), task waste disposal (−0.79), rework frequency

(contractor initiated) (−1.71), rework cost (contractor initiated) (−1.71), balance between labor and equipment (þ1.91)

Location properties Spaciousness of working area (þ1.57), site restrictions (−1.13), soil type (−1.61), soil moisture (−1.61), groundwater level

(−1.24), underground facilities (−1.24), hauling/delivery distance (−0.94)

Engineering/instructions Availability of drawings (þ1.59), quality of drawings (þ1.62), number of revisions on drawings (−1.24), design changes

(−1.24), quality of specifications (þ1.64), time to respond to RFIs (þ1.41), time to do inspections (þ1.35), rework

frequency (design initiated) (−1.71), rework cost (design initiated) (−1.71)

Note: RFI = request for information.

J. Constr. Eng. Manage., 2018, 144(9): 04018091

variables. Fuzzy arithmetic operations were implemented by the

α-cut method and the extension principle method using four

common t-norms (min, algebraic product, Lukasiewicz, and drastic

product).

Finally, in the fifth step, the FSD model of construction pro-

ductivity was validated using a case study of earthmoving oper-

ations. Since the common validation tests such as statistical

hypothesis test are not appropriate for the validation of SD

(and FSD) models (Forrester and Senge 1980), Barlas (1996)

introduced two approaches for validation of the SD (and FSD)

models: structure validity and behavior validity. The structural

validation of the FSD model presented in this paper was deter-

mined using the dimensional consistency test and the structure

verification test (Barlas 1996;Qudrat-Ullah and Seong 2010).

The dimensional consistency test is a simple dimensional analysis

of the mathematical equations of the FSD models that is appro-

priate for validation of hard relationships (Forrester and Senge

1980;Qudrat-Ullah and Seong 2010). On the other hand, soft re-

lationships of FSD models can be validated by the structure veri-

fication test (Forrester and Senge 1980;Qudrat-Ullah and Seong

2010), which compares the structure of the model with the real-

world system empirically using expert knowledge or theoretically

using relevant literature. The behavioral validity of the FSD

model was evaluated using the pattern verification test, as sug-

gested by Barlas (1996). The pattern verification test compares

the pattern of system results (e.g., number of peaks of the simu-

lation results or frequency) to field data.

Fuzzy System Dynamics Model of Multifactor

Productivity for Equipment-Intensive Activities

Seventy-two activity-level factors influencing the productivity of

equipment-intensive activities, hereafter referred to as system

variables, were identified through the literature review and were

verified by expert knowledge. In order to increase the accuracy of

the FSD model of construction productivity, the number of system

variables was reduced by feature selection, as discussed in the

“Methodology”section. Twenty-five system variables, divided into

six categories (e.g., crew-related factors), were selected for the

development of the FSD model, which are presented in Table 3.

Once the system variables were selected, the qualitative FSD

model of construction productivity was developed by identifying

the relationships between the variables. As discussed in the meth-

odology section, at the qualitative FSD modeling stage, the

existence of these relationships is identified only. The soft relation-

ships between the system variables and productivity were verified

by the literature and expert knowledge. Moreover, the soft relation-

ships between the system variables were identified by the research-

ers based on their knowledge about the real-world system (e.g.,

crew motivation and absenteeism). According to previous research,

the soft relationships between system variables need to be identified

by the modelers based on their knowledge about the real-world sys-

tem; once the SD or FSD models are validated, the soft relation-

ships between the system variables will be verified (Nojedehi and

Nasirzadeh 2017;Ding et al. 2018). For presentation clarity, the

qualitative FSD model of construction productivity presented in

this paper is broken into two components: a stock and flow dia-

gram, and a cause and effect diagram. Fig. 2presents the stock

and flow diagram that measures the MFP of the system using

its three inputs (i.e., labor direct cost, equipment direct cost, and

material direct cost), and it measures the total cost rate and the total

activity direct cost using the MFP and the production rate of the

activity.

There are four stock variables (i.e., representing accumulation in

FSD models) in Fig. 2, which represent the cumulative costs of the

three input resources: total equipment cost, total labor cost, and

total material cost, and the total direct cost of the activity, total ac-

tivity direct cost. There are four flow variables (i.e., representing

the rate of increase/decrease in the stock variables of FSD models)

in Fig. 2, which represent the daily cost of the three input resources

(i.e., equipment cost rate, labor cost rate, and material cost rate) and

the total daily direct cost of the activity (i.e., total cost rate). The

MFP, the three inputs of MFP (i.e., labor direct cost, equipment

direct cost, and material direct cost), and the production rate of

the activity are presented as dynamic variables, and their values

are determined by the cause and effect diagram presented in Fig. 3.

In FSD models, the dynamic variables represent the variables that

change in value due to their relationships with other variables. All

relationships between the variables of the stock and flow diagram

(represented by arrows in Fig. 2) are hard relationships. Fig. 3

presents the cause and effect diagram that measures the three inputs

of MFP, and the production rate of the activity (inputs of the stock

and flow diagram) using the system variables (refer to Table 3).

The system variables that are selected for predicting the produc-

tivity of equipment-intensive activities (refer to Table 3) are pre-

sented in Fig. 3as dynamic variables. These variables are used in

the cause and effect diagram to predict the value of the three inputs

of MFP (i.e., labor direct cost, equipment direct cost, and material

direct cost), as well as the production rate of the activity. There are

also two types of relationships that exist between the system var-

iables in the cause and effect diagram: soft relationships, such as the

relationship between crew motivation and equipment direct cost,

and hard relationships, such as the relationships among crew size

and planned crew size and absenteeism.

Next, in order to develop the quantitative FSD model of con-

struction productivity, the objective and subjective system variables

were identified. Referring to Table 3, there are 20 objective system

variables and 5 subjective system variables. The subjective varia-

bles of the system include site restrictions, soil moisture, crew mo-

tivation, material quality, and material preinstallation requirements.

Soil moisture can also be an objective system variable if it is

measured numerically using soil tests; however, this factor is con-

sidered as a subjective system variable because it may also be mea-

sured by subjective expert judgment if the test results are not

available. Once the objective and subjective system variables were

identified, the subjective system variables were represented by

fuzzy membership functions. Each subjective variable was repre-

sented by five—as suggested by Pedrycz (2013)—triangular fuzzy

Table 3. System variables for FSD model of activity-level construction

productivity

Category Factors

Equipment-related factors Number of equipment, equipment capacity,

equipment ownership, equipment functional

range, operator experience, labor and

equipment balance

Location-related factors Distance, site restrictions, underground

facilities, groundwater level, soil type, soil

moisture

Weather-related factors Gust speed, temperature, total precipitation

Task-related factors Daily overtime work, total work volume

Crew-related factors Crew experience, crew composition, crew

size, crew motivation, absenteeism, foreman

experience

Material-related factors Material preinstallation requirements,

material quality

J. Constr. Eng. Manage., 2018, 144(9): 04018091

membership functions, which are commonly used in engineering

applications. As discussed in the methodology section, these fuzzy

membership functions were developed using the FCM clustering

technique, which is a data-driven technique for developing fuzzy

membership functions. Fig. 4shows the fuzzy membership func-

tions developed for the representation of crew motivation, as an

example.

Next, the soft relationships between the system variables were

defined quantitatively, either by data-driven FRBS—developed

by the FCM clustering technique—or mathematical equations—

developed by statistical techniques—as discussed in the method-

ology section. Table 4shows these soft relationships and the

approach by which each soft relationship was defined.

As presented in Table 4, 11 soft relationships in the FSD model

were defined by FRBS, and four of those relationships were defined

by statistically developed mathematical equations. Accordingly, in

some cases, defining the soft relationships of FSD models using

data-driven FRBS developed by FCM clustering can increase the

accuracy of FSD models compared to using statistically developed

mathematical equations. However, neither of the two methods is

universally the best approach for defining the soft relationships

of the system. In order to simulate the FSD model and predict

the productivity of any given equipment-intensive activity, the soft

relationships of the system (presented in Table 4) were evaluated at

each time step (i.e., daily). Once the soft relationships were defined,

the hard relationships were defined quantitatively using mathemati-

cal equations, as discussed in the methodology section. There are

nine hard relationships in the FSD model, which were defined

by the mathematical equations presented in Table 5.

In order to simulate the FSD model and predict the productivity

of any given equipment-intensive activity, the mathematical equa-

tions presented in Table 5were solved at each time step (i.e., daily).

Model Validation and Construction Application

The FSD model of construction productivity was developed by in-

tegrating AnyLogic (version 17 ), Matlab software (version 2017b),

and a Fuzzy Calculator class, which was developed in the Python

programming language. AnyLogic was used to develop the SD com-

ponent of the model; Matlab and the Fuzzy Calculator class were

used to develop the fuzzy components of the model. AnyLogic cal-

culates the results of the mathematical equations, in which all system

variables are objective. The Fuzzy Calculator class calculates the re-

sults of the mathematical equations that include subjective system

variables, and Matlab calculates the results of the FRBS. The Fuzzy

Calculator class was developed by the authors for implementing

fuzzy arithmetic on triangular fuzzy numbers using the α-cut method

and the extension principle method, the latter of which uses min,

algebraic product, Lukasiewicz, and drastic product t-norms.

The FSD model was evaluated through structural and behavioral

validation tests, as discussed in the methodology section. The struc-

tural validity of the FSD model was evaluated using the dimensional

consistency test and the structure verification test. The dimensional

consistency test is implemented by dimensional analysis of the

Fig. 2. Stock and flow diagram of qualitative FSD model of construction productivity.

J. Constr. Eng. Manage., 2018, 144(9): 04018091

Fig. 3. Cause and effect diagram of qualitative FSD model of construction productivity.

J. Constr. Eng. Manage., 2018, 144(9): 04018091

mathematical equations, which defines the hard relationships of the

system. Referring to Table 5, the dimensional consistency test de-

termines if the units of measure on both sides of each equation are

consistent or not. For example, in Eq. (2), the unit of measure for the

left side of the equation is ð$=dayÞ, and the unit of measure for the

right side of the equation is ð$=unitsÞ×ðunits=dayÞ¼ð$=dayÞ,

which shows that Eq. (2) has dimensional consistency

Labor cost rate $

day¼Labor direct cost $

units

×Production rate units

day ð2Þ

The structure verification test was implemented by verifying the

list of the system variables (i.e., factors influencing construction

productivity) and the soft relationships of the system through expert

knowledge, which was acquired by the interview surveys, as dis-

cussed in the methodology section. In order to evaluate the behav-

ior validity of the FSD model, the model was implemented on a

case study of earthmoving operations on a pipeline maintenance

project in Alberta, Canada. This project included 79 work packages

(i.e., digs), each of which includes the following activities: exca-

vation, sandblasting, welding, coating, and backfilling. The case

study presented in this paper is focused on the earthmoving activ-

ities (i.e., excavation and backfilling), which were executed by

eight earthmoving crews. Field data were collected for these two

equipment-intensive activities, excavation and backfilling, by doc-

umenting the value of the factors that influence construction pro-

ductivity. Field data were also collected for the actual activity level

MFP of the two activities, measured in $=m3, using the daily costs

of the input resources (i.e., labor, equipment, and material) mea-

sured in dollars and the daily quantity of work completed measured

in cubic meters (i.e., volume of earth excavated or backfilled).

Fig. 4. Fuzzy membership functions for representing crew motivation.

Table 4. Soft relationships of FSD model of activity-level construction productivity

Relationship output Relationship inputs

Numerical

definition approach

Equipment direct cost Distance, number of equipment, site restrictions, underground facilities, operator experience, equipment

ownership, equipment capacity, daily overtime work, total work volume, soil type, soil moisture,

groundwater level, total precipitation, temperature, gust speed, foreman experience, labor and equipment

balance, crew size

Linear regression

Labor direct cost Crew motivation, crew size, crew experience, absenteeism, gust speed, distance, underground facilities,

temperature, daily overtime work, operator experience, equipment capacity, labor and equipment balance

Linear regression

Material direct cost Material quality, material preinstallation requirements, crew experience, crew composition, operator

experience, distance

Linear regression

Production rate Site restrictions, number of equipment, equipment functional range, equipment capacity, soil moisture,

soil type, gust speed

Linear regression

Number of equipment Equipment ownership, equipment capacity, total volume of work FCM clustering

Equipment capacity Total volume of work FCM clustering

Equipment ownership Number of equipment, total volume of work FCM clustering

Groundwater level Total precipitation FCM clustering

Soil moisture Total precipitation, soil type, groundwater level FCM clustering

Daily overtime work Total volume of work FCM clustering

Total work volume Soil moisture, soil type FCM clustering

Crew experience Crew size, crew composition, operator experience FCM clustering

Crew composition Crew size FCM clustering

Absenteeism Crew motivation FCM clustering

Material quality Material preinstallation requirements FCM clustering

J. Constr. Eng. Manage., 2018, 144(9): 04018091

Various sources were used for field data collection, including con-

tract documents, project scorecards, project timesheets, and onsite

observations by the researchers. Due to confidentiality constraints,

all field data were normalized into the range of ½0;1using Eq. (3)

Vi;normalized ¼Vi−minðViÞ

maxðViÞ−minðViÞð3Þ

where Vi;normalized stands for the normalized value of any system

variable; and Virepresents the original value of the system variable.

In order to run the simulation model, the initial values of the system

variables are entered, where the values of the objective system var-

iables are entered as crisp numbers (e.g., four people for crew size),

and the values of the subjective system variables are entered as

linguistic terms, which are represented by fuzzy membership func-

tions (e.g., high crew motivation). Table 6presents the results of

simulation for the MFP for earthmoving operations in a 30-day

period and compares the results to the actual field data; Fig. 5

presents these results graphically.

The y-axis in Fig. 5shows the normalized value of the MFP of

the earthmoving operations, and the x-axis shows the duration of

earthmoving operations measured in days. The simulation results

can be presented as fuzzy numbers or defuzzified values. Defuzzi-

fication is the process of converting a fuzzy number to a crisp num-

ber. In order to present the simulation results as fuzzy numbers, the

results need to be presented at each time step. Representing the

simulation results as fuzzy numbers is not appropriate for the pat-

tern verification test, since this test compares changes in the results

over the simulation time to the actual field data. The simulation

results presented in Fig. 5are the defuzzified values of MFP for

the earthmoving operations, which are defuzzified using the using

center of area (COA) method. Referring to Fig. 5, behavioral val-

idity of the FSD model may be evaluated by the pattern verification

test, which shows the following: the trends in the actual MFP values

(i.e., an increase or decrease of productivity between any two con-

secutive points) are predicted correctly by the simulation results in

70% of cases (refer to Table 6); and the turning points in the actual

MFP values (i.e., the points in which the trend of productivity

changes) are predicted correctly by the simulation results in 70%

of cases (refer to Table 6). Finally, the RMSE of the simulation

results is 0.11, which is calculated using Eq. (4)

Table 6. Simulation results and actual field data for MFP

Simulation

time (day)

Simulation

results

Actual

field data

Error jsimulation result−

actual field dataj

1 0.321 0.365 0.044

2 0.552 0.582 0.03

3 0.858 0.775 0.083

4 0.949 0.978 0.029

5 0.738 0.749 0.011

6 0.911 0.978 0.067

7 0.798 0.775 0.023

8 0.714 0.500 0.214

9 0.692 0.775 0.083

10 0.320 0.206 0.114

11 0.273 0.146 0.127

12 0.824 0.929 0.105

13 0.810 0.765 0.045

14 0.633 0.765 0.132

15 0.933 0.929 0.004

16 0.857 0.765 0.092

17 0.540 0.765 0.225

18 0.000 0.054 0.054

19 0.234 0.039 0.195

20 0.744 0.926 0.182

21 0.873 0.926 0.053

22 0.873 0.912 0.039

23 0.988 0.912 0.076

24 0.942 0.912 0.03

25 0.551 0.504 0.047

26 0.630 0.450 0.18

27 0.823 1.000 0.177

28 0.949 1.000 0.051

29 0.898 1.000 0.102

30 0.903 0.894 0.009

Table 5. Hard relationships of FSD model of activity-level construction productivity

Relationship output Mathematical equation

Labor cost rate Labor cost rate $

day¼Labor direct cost $

units×Production rate units

day 

Equipment cost rate Equipment cost rate $

day¼Equipment direct cost $

units×Production rate units

day 

Material cost rate Material cost rate $

day¼Material direct cost $

units×Production rate units

day 

Total labor costaTotal labor cost ð$Þ¼∫Labor cost rate $

day·dt ðdayÞ

Total equipment costaTotal equipment cost ð$Þ¼∫Equipment cost rate $

day·dt ðdayÞ

Total material costaTotal material cost ð$Þ¼∫Material Cost Rate $

day·dt ðdayÞ

Multi factor productivity Multi factor productivity $

units¼Labor direct cost $

unitsþEquipment direct cost $

unitsþMaterial direct cost $

units

Labor and equipment

balanceb

Labor and equipment balance ¼Crew size ðpersonÞ

Number of equipment ðcountÞ

Crew sizecCrew size ðpersonÞ¼Planned crew size ðpersonÞ−Absenteeism ðpersonÞ

adt stands for the time step’s duration used for simulation of FSD model that is equal to one day in this paper.

bNumber of equipment which are working on the activity.

cPlanned crew size specified for execution of the activity in planning phase and absenteeism represent the number of absent crew members.

J. Constr. Eng. Manage., 2018, 144(9): 04018091

RMSE ¼ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

PðSimulation result −Actual field dataÞ2

rð4Þ

In addition, the normalized root mean square error (NRMSE)

of the simulation results is 15%. The NRMSE compares the

RMSE of the data to the average value of the actual field data using

Eq. (5)

NRMSE ¼RMSE

Mean ðactual field dataÞð5Þ

Kleijnen (1995) introduced regression analysis of SD (or FSD)

models as an appropriate approach for identification of the most

significant factors in SD (or FSD) models. In this approach, the

value of independent system variables (i.e., system variables that

are not affected by any other system variables) are changed be-

tween the minimum and maximum values (i.e., [0,1] in this case

study) and the effect of these factors on the simulation results is

analyzed using regression analysis (Kleijnen 1995;Phan et al.

2018). Next, the significance of the factors’influence on the FSD

model is identified based on the regression coefficient, in which

the system variable with the highest absolute value of regression

coefficient has the most significant effect on the FSD model. The

FSD model presented in this paper has 12 independent system

variables (refer to Figs. 2and 3): gust speed, total precipitation,

temperature, soil type, underground facilities, site restrictions, dis-

tance, equipment operator experience, foreman experience, crew

motivation, equipment functional range, and material preinstalla-

tion requirements. The regression analysis approach was imple-

mented on these independent system variables, and the results of

the analysis show that the most significant variables in the FSD

model are (1) crew motivation, which has a negative correlation

with the simulation results; (2) equipment operator experience,

which has a positive correlation with the simulation results; and

(3) gust speed, which has a positive correlation with the simulation

results.

By implementing fuzzy arithmetic operations on the mathemati-

cal equations of the FSD model, the support of the resulting fuzzy

numbers grows rapidly, which is interpreted as an overestimation of

uncertainty. In general, an increase in the length of the support of a

fuzzy number shows an increase in the amount of uncertainty

represented by that fuzzy number. The overestimation of uncer-

tainty in FSD models is affected by the chosen fuzzy arithmetic

implementation method, which is used to solve the mathematical

equations of the FSD model. Accordingly, the effects offuzzy arith-

metic implementation methods on the simulation results were

evaluated to determine the most appropriate method. The results

of the simulation for the total cost rate of the activity were calcu-

lated using the α-cut method and using the extension principle

method with the min, algebraic product, Lukasiewicz, and drastic

product t-norms, as presented in Table 7.

The simulation results presented in Table 7show the following:

the implementation of fuzzy arithmetic operations using the α-cut

method and using the extension principle method with the min

t-norm always returning the same results (Elbarkouky et al. 2016);

using the α-cut method and the extension principle method with the

min t-norm returns the largest defuzzified values of the simulation

results, followed by the extension principle method with the alge-

braic product t-norm, Lukasiewicz t-norm, and drastic product

t-norm, respectively; and finally, using the extension principle

method with the drastic product t-norm has the lowest RMSE, fol-

lowed by the extension principle method with the Lukasiewicz

t-norm, algebraic product t-norm, and min t-norm (and the α-cut

method), respectively. In order to compare the uncertainty overesti-

mation caused by the fuzzy arithmetic implementation methods, the

length of the support of the fuzzy number for total cost rate is pre-

sented in Table 7, and it is shown graphically in Fig. 6. The length

of the support of the fuzzy number for total cost rate represents the

level of uncertainty overestimation.

Referring to Table 7and Fig. 6, a comparison of the length of the

support of the fuzzy number for total cost rate shows the following:

the length of the support of the fuzzy number is always equal when

using the α-cut method and when using the extension principle

method with the min and algebraic product t-norms; and using

the extension principle method with the drastic product t-norm re-

turns a fuzzy number with the smallest length of the support, fol-

lowed by the extension principle with the Lukasiewicz t-norm; and

the other methods (i.e., using the α-cut method, using the extension

principle method with the min and algebraic product t-norms) re-

turn a fuzzy number with the largest support length. Based on the

fact that the extension principle method using the drastic product

Fig. 5. Simulation results for MFP in comparison to actual field data.

J. Constr. Eng. Manage., 2018, 144(9): 04018091

Fig. 6. Length of support of fuzzy numbers for total cost rate.

Table 7. Simulation results and actual field data representing fuzzy number for total cost rate

Simulation

time

Min t-norm

Algebraic product

t-norm Lukasiewicz t-norm Drastic product t-norm

Actual field

data

Simulation

results

Support

length

Simulation

results

Support

length

Simulation

results

Support

length

Simulation

results

Support

length

1 0.069 0.154 0.064 0.154 0.062 0.125 0.062 0.125 0.049

2 0.254 0.295 0.249 0.295 0.247 0.232 0.247 0.231 0.261

3 0.075 0.181 0.070 0.181 0.070 0.159 0.069 0.159 0.027

4 0.069 0.154 0.064 0.154 0.062 0.125 0.062 0.125 0.029

5 0.089 0.207 0.084 0.207 0.083 0.184 0.083 0.184 0.027

6 0.382 0.321 0.379 0.321 0.375 0.217 0.375 0.217 0.417

7 0.023 0.070 0.019 0.070 0.018 0.055 0.018 0.055 0.050

8 0.043 0.130 0.039 0.130 0.038 0.115 0.038 0.115 0.054

9 0.165 0.207 0.162 0.207 0.158 0.139 0.158 0.138 0.074

10 0.184 0.222 0.180 0.222 0.177 0.153 0.177 0.152 0.089

11 0.333 0.307 0.329 0.307 0.326 0.217 0.326 0.217 0.424

12 0.154 0.234 0.149 0.234 0.146 0.186 0.146 0.186 0.127

13 0.147 0.216 0.142 0.216 0.139 0.165 0.139 0.165 0.120

14 0.165 0.249 0.160 0.249 0.158 0.202 0.158 0.202 0.134

15 0.177 0.242 0.173 0.242 0.170 0.187 0.170 0.187 0.140

16 0.203 0.249 0.198 0.249 0.195 0.187 0.195 0.187 0.155

17 0.203 0.249 0.198 0.249 0.195 0.187 0.195 0.187 0.155

18 0.206 0.250 0.201 0.250 0.198 0.186 0.198 0.186 0.149

19 0.208 0.254 0.204 0.254 0.201 0.192 0.201 0.191 0.144

20 0.222 0.245 0.218 0.245 0.215 0.169 0.215 0.169 0.156

21 0.205 0.218 0.202 0.218 0.199 0.113 0.198 0.110 0.138

22 0.203 0.249 0.198 0.249 0.195 0.187 0.195 0.187 0.120

23 0.629 0.393 0.626 0.393 0.622 0.235 0.621 0.233 0.544

24 0.259 0.277 0.255 0.277 0.252 0.201 0.252 0.202 0.174

25 0.280 0.275 0.276 0.275 0.273 0.188 0.273 0.188 0.183

26 0.238 0.261 0.234 0.261 0.231 0.187 0.231 0.186 0.132

27 0.069 0.173 0.064 0.173 0.064 0.153 0.064 0.153 0.381

28 0.294 0.285 0.290 0.285 0.287 0.198 0.286 0.198 0.183

29 0.254 0.295 0.249 0.295 0.247 0.232 0.246 0.231 0.120

30 0.320 0.315 0.316 0.315 0.313 0.236 0.313 0.236 0.173

RMSE 0.0915 0.0898 0.0884 0.0883 —

Note: Simulation results are the defuzzified value of the simulation results using the t-norm that is presented in the first row.

J. Constr. Eng. Manage., 2018, 144(9): 04018091

t-norm has both the lowest RMSE and the smallest uncertainty

overestimation, this method was deemed to be the most appropriate

method for fuzzy arithmetic implementation in the FSD model

presented in this paper.

Discussion

The FSD model of construction productivity presented in this paper

can be used to predict the MFP of equipment-intensive activities for

construction projects. Accordingly, the FSD model can facilitate

the construction planning process by allowing users to predict the

productivity of construction activities for different execution plans

prior to the execution phase. Users can change the system variables

based on their execution plans (e.g., changing the crew size or num-

ber of equipment) and simulate the model to predict the productiv-

ity, and accordingly, they can select the most appropriate execution

plan for the activity. The FSD model of productivity can predict the

daily value of MFP, which provides more information about pro-

ductivity, as compared to existing static productivity models, by

allowing users to track changes in productivity over time. More-

over, this model allows construction planners to analyze the effect

of each system variable (e.g., number of equipment) on construc-

tion productivity in order to optimize these variables. For the pur-

pose of analysis, the system variable that is being analyzed must

first be changed in the desirable range, whereas the other system

variables are kept unchanged; once this is accomplished, the FSD

model can then be simulated. Accordingly, the results of simulation

represent the effect of the system variables that were changed in

Step 1 on construction productivity.

The FSD model of construction productivity presented in this

paper is capable of capturing the probabilistic and nonprobabilistic

uncertainties of the system variables, as well as the deterministic

values for the system variables. In order to capture these probabi-

listic uncertainties, the model allows users to represent variables

with probabilistic distributions, such as the temperature in future

projects. For capturing the nonprobabilistic uncertainties of the sys-

tem variables, the model allows users to determine the values of the

subjective system variables using linguistic terms, which are rep-

resented by fuzzy membership functions, such as high crew moti-

vation (refer to Fig. 4). Due to the fact that the case study presented

in this paper was extracted from a previously executed construction

project, the system variables do not exhibit any probabilistic uncer-

tainty; accordingly, in the case study presented in this paper, the

system variables are represented by either deterministic values

or by fuzzy membership functions.

In comparison to the SD models of productivity developed by

Nasirzadeh and Nojedehi (2013) and Mawdesley and Al-Jibouri

(2009), the FSD model of productivity presented in this paper

can increase the accuracy of productivity predictions by capturing

the effect of subjective variables (e.g., crew motivation) on produc-

tivity, as well as allowing practitioners to evaluate these variables

using linguistic terms rather than precise numerical values. In con-

trast to the FSD model developed by Nojedehi and Nasirzadeh

(2017), which is for labor-intensive activities and predicting CLP,

the predictive model presented in this paper predicts MFP, which is

the appropriate measure of productivity for equipment-intensive ac-

tivities. Moreover, the predictive model presented in this paper pro-

vides construction practitioners with information regarding the cost

of the three input resources of an activity (equipment cost, labor

cost, and material cost), whereas the predictive models of CLP pro-

vide this information for one input resource only (i.e., labor).

Finally, the comparison of the two fuzzy arithmetic implementation

methods (i.e., the α-cut method and the extension principle method)

shows that the implementation of fuzzy arithmetic operations by the

extension principle using drastic product t-norm reduces the over-

estimation of uncertainty in comparison to the α-cut method, while

increasing the accuracy of the simulation results, in contrast to pre-

viously developed FSD models (e.g., Nojedehi and Nasirzadeh

2017;Khanzadi et al. 2012), which only use the α-cut method.

Reducing the uncertainty overestimation of the simulation results

increases the ability of construction practitioners to accurately pre-

dict the actual productivity of an activity based on the simulation

results.

The FSD model presented in this paper has a few limitations that

need to be addressed in future research. First, the computational

approach used for implementing fuzzy arithmetic operations is only

applicable to triangular fuzzy numbers; thus, the FSD model is

limited to the use of triangular fuzzy numbers for representing sub-

jective system variables. Next, for defining the soft relationships

of the FSD model, the accuracy of FCM clustering technique

decreases as the number of input variables increases (i.e., high di-

mensionality of soft relationships). Accordingly, in this paper, for

defining high dimensional soft relationships, statistically developed

mathematical equations outperformed the FRBSs developed by

FCM clustering in terms of accuracy. In the future, the accuracy

of the FCM clustering technique for defining high dimensional soft

relationships can be increased by developing a method to increase

the weights of the output variables in comparison to the input var-

iables. Finally, the FSD model of MFP presented in this paper has

been developed using field data collected for earthmoving activ-

ities. In order to develop a generic model of MFP for different types

of equipment-intensive activities, new field data for other types of

equipment-intensive activities need to be collected, and the FSD

model needs to be updated with the new field data.

Conclusions and Future Research

Construction productivity has long been a major research interest

within the construction engineering domain. Due to the fact that

construction is a labor-intensive industry, the majority of previous

studies have been focused on construction labor productivity

(CLP). However, with recent advancement in technology, construc-

tion equipment is now the main driver of productivity for some

construction activities, which are identified as equipment-intensive

activities. Since the main drivers of productivity for equipment-

intensive and labor-intensive activities are different, the factors

influencing the productivity of these two activities are also differ-

ent. Accordingly, the predictive models that have been developed

for labor-intensive activities cannot predict the productivity of

equipment-intensive activities accurately. This paper presents the

list of 72 factors that influence the productivity of equipment-

intensive activities identified through a literature review and veri-

fied by expert knowledge collected through interview surveys. It

presents a predictive model of productivity for equipment-intensive

activities using the FSD modeling technique. The FSD model

presented in this paper predicts the MFP of equipment-intensive

activities considering three input resources of these activities

(i.e., labor, equipment, and material).

In this model, the subjective factors influencing construction

productivity (e.g., crew motivation) are represented by fuzzy mem-

bership functions. Representation of subjective factors by fuzzy

membership functions enhances the applicability of the predictive

model by allowing practitioners to evaluate the value of subjective

variables using linguistic terms (e.g., high crew motivation), rather

than numerical values. Moreover, in this paper, the accuracy of

FCM clustering and linear regression methods was compared for

defining the soft relationships of the FSD model. Although the

J. Constr. Eng. Manage., 2018, 144(9): 04018091

FCM clustering method has not been used for defining soft rela-

tionships in previous research, the results of comparison show that,

in some cases, the use of the FCM clustering method can increase

the accuracy of FSD models as compared to the use of the linear

regression method. However, neither of the two methods is univer-

sally the best method for defining the soft relationships of the sys-

tem. Previous applications of the FSD modeling technique in

construction show that the use of fuzzy arithmetic operations for

solving the mathematical equations of the FSD model can cause

overestimation of uncertainty in the fuzzy numbers representing

the simulation results. In this paper, the two methods of fuzzy arith-

metic implementation (i.e., the α-cut method and the extension

principle method using min, algebraic product, Lukasiewicz, and

drastic product t-norms) were evaluated in order to reduce the over-

estimation of uncertainty and increase the accuracy of the FSD

model. Accordingly, the extension principle method using the dras-

tic product t-norm was found to be the most appropriate method for

implementing fuzzy arithmetic in the FSD model because it has the

highest accuracy in calculating the simulation results and the lowest

level of uncertainty overestimation.

This paper contributes to construction productivity research

by identifying the key factors that influence the productivity of

equipment-intensive activities and developing a predictive model

of MFP for equipment-intensive activities using FSD technique.

The MFP model presented in this paper provides practitioners with

information regarding the cost of the three input resources of an

activity, in contrast to existing models that predict CLP, which

provide information for only one input resource. This paper also

contributes to the application of FSD technique in construction

research by developing an approach to reduce the uncertainty over-

estimation in the simulation results of FSD models. Reducing the

uncertainty overestimation in the simulation results increases the

ability of practitioners to accurately evaluate the actual system

output (e.g., actual productivity) based on the simulation results.

In the future, this study will be extended by developing an FSD

model for the activity-level MFP of labor-intensive activities.

Moreover, the FSD model of project-level MFP will be developed

as an integration of the two activity-level FSD models of MFP,

equipment-intensive and labor-intensive, as well as by including

the factors influencing construction productivity at the project

level. The soft relationships of the FSD model were defined either

by mathematical equations developed using linear regression or by

FRBS developed using FCM clustering, the latter of which is a

machine learning technique. In order to increase the accuracy

of the FSD models in future studies, other machine learning tech-

niques, such neuro-fuzzy systems and ANNs, will be evaluated for

the purpose of defining the soft relationships between the system

variables.

Data Availability Statement

All data generated or analyzed during the study are included in the

published paper. Information about the Journal’s data sharing policy

can be found here: http://ascelibrary.org/doi/10.1061/%28ASCE

%29CO.1943-7862.0001263.

Acknowledgments

This research is funded by the Natural Sciences and Engineering

Research Council of Canada Industrial Research Chair in Strategic

Construction Modeling and Delivery (NSERC IRCPJ 428226–15),

which is held by Dr. A. Robinson Fayek. The authors gratefully

acknowledge the support and data provided by the industry part-

ners, construction companies, and all personnel who participated

in this study. The authors also thank Mr. Ming kit Yau, who

diligently helped in the data entry process.

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Apr 2016

Witold Pedrycz

Information granules, as encountered in natural language, are implicit in nature. To make them fully operational so they can be effectively used to analyze and design intelligent systems, information granules need to be made explicit. An emerging discipline, granular computing focuses on formalizing information granules and unifying them to create a coherent methodological and developmental environment for intelligent system design and analysis. Granular Computing: Analysis and Design of Intelligent Systems presents the unified principles of granular computing along with its comprehensive algorithmic framework and design practices. Introduces the concepts of information granules, information granularity, and granular computing Presents the key formalisms of information granules Builds on the concepts of information granules with discussion of higher-order and higher-type information granules Discusses the operational concept of information granulation and degranulation by highlighting the essence of this tandem and its quantification in terms of the associated reconstruction error Examines the principle of justifiable granularity Stresses the need to look at information granularity as an important design asset that helps construct more realistic models of real-world systems or facilitate collaborative pursuits of system modeling Highlights the concepts, architectures, and design algorithms of granular models Explores application domains where granular computing and granular models play a visible role, including pattern recognition, time series, and decision making Written by an internationally renowned authority in the field, this innovative book introduces readers to granular computing as a new paradigm for the analysis and synthesis of intelligent systems. It is a valuable resource for those engaged in research and practical developments in computer, electrical, industrial, manufacturing, and biomedical engineering. Building from fundamentals, the book is also suitable for readers from nontechnical disciplines where information granules assume a visible position.

Assessment of the vulnerability of a coastal freshwater system to climatic and non-climatic changes: A system dynamics approach

Article

May 2018
J CLEAN PROD

Water resources management faces many challenges in coastal areas of developing countries, where climate change coupled with high rates of population growth and urbanization have the potential to cause severe water scarcity. Of particular concern, are sea level rise and altered precipitation regimes that will influence spatial and temporal patterns of river discharge, water levels and saltwater penetration in estuaries. A sound understanding of factors affecting the vulnerability of coastal freshwater systems is therefore needed to mitigate the potential impacts of climatic and non-climatic changes. In this study, a system dynamics modeling approach was employed to explore the vulnerability of the coastal freshwater system in Da Do Basin, Vietnam to projected sea level rise, upstream flow decline and socio-economic development. This system includes the Da Do River and irrigation channels that receive freshwater through sluice gates from the Van Uc and Lach Tray rivers. The model was developed as a learning tool for decision-makers to improve their understanding of the spatial and temporal dynamic behaviors of the system and to inform adaptation decision-making by allowing exploration of plausible future scenarios. The model was developed, calibrated and validated using both historical data and expert knowledge elucidated via stakeholder consultation. Model results indicate that under current conditions, freshwater availability is sufficient to meet existing domestic, industrial and agricultural demands. However, the coastal freshwater system changes significantly and collapses under several plausible future scenarios. Future projections suggest that declining upstream flows will be the strongest threat to the system’s vulnerability. System dynamics models enable consideration of the interactive effects of a range of climatic and non-climatic drivers on water resources availability thereby facilitating improved planning for collective and proactive adaptation actions to efficiently secure freshwater resources to support socio-economic development of coastal basins in the face of climate change.

A system dynamics-based environmental benefit assessment model of construction waste reduction management at the design and construction stages

Article

Mar 2018
J CLEAN PROD

Construction waste generation and its environmental impact reduction have become an urgent issue to be solved with the acceleration of urbanization process in China. However, limited research has been conducted to cover both the design stage and the construction stage such that the overall construction waste reduction outcome could be comprehensively assessed. Based on interview data and literature review, Vensim software was used to build a two-stage environmental benefit assessment system dynamics (SD) model which covered construction waste reduction management subsystem, waste generation and disposal subsystem, and environmental benefit assessment subsystem. Simulation results highlight that the reduction management can reduce 40.63% of waste generation. In the meantime, the reduction management achieves good environmental benefits including the reduction of greenhouse-gas emissions of 12,623.30 kg, saving waste landfill of 3901.05 m³ and reducing the use of public vacant site for the illegal dumping of 688.42 m³. The simulation results demonstrate that the dynamic model could assess the environmental benefits of construction waste reduction effectively at the design and the construction stage. This research can provide insight to the design and construction professionals for waste reduction measures such as prefabricated components application, reduced design modification at the design stage, on-site sorting and material reuse at the construction stage, and to provide references for governments in assessing the reduction management outcomes of construction projects and the environmental benefits.

Agent-based modeling and simulation of earthmoving operations

Article

Jun 2017
AUTOMAT CONSTR

Discrete-Event Simulation (DES) models are constructed from sequential duration-based activities. DES is used in modeling several construction operations including earthmoving. Current earthmoving models cannot accommodate equipment units with different specifications performing the same task. In addition, activity durations are calculated based on primitive methods such as interpolating existing durations of similar activities in previous projects. Finally, model elements behave in a predetermined manner, ignoring special operational real-life scenarios that occur due to resource constraints. These limitations often lead to inaccuracies in calculating productivity and equipment utilization. This paper applies Agent-Based Modeling and Simulation (ABMS) as an effective bottom-up tool to modeling earthmoving operations. An Agent-Based (AB) earthmoving model consisting of smart, adaptive agents is developed. Each agent is assigned a state chart and a set of static and dynamic properties (attributes and variables) to direct its interactions with the environment and with other agents. This framework proves how modeling earthmoving from the agent's prospective and basing agents' interactions on their properties allow for modeling equipment units with different specifications performing the same task (e.g. trucks of different capacities), as well as for an accurate representation of activity durations, resource handling and resource constraint scenarios. A Java-based application named Agent-Based Simulator for Earthmoving Operations (ABSEMO) is developed as an implementation of the proposed model. ABSEMO will be helpful to contractors in planning earthmoving operations according to the AB approach. A real-life case study of a riverbed excavation in a dam construction project is simulated using ABSEMO, and the results are compared with those obtained from existing simulation models to verify ABSEMO's logic. A percentage difference of 0.42% from the existing results is obtained, indicating that the model's flow of resources is indeed accurate.

A hybrid simulation approach to model and improve construction labor productivity

Article

Oct 2016

This research presents an integrated fuzzy System Dynamics (SD) approach for modeling and improving of labor productivity. The complex inter-related structure of different factors affecting labor productivity is modeled using SD approach. Owing to the imprecise and uncertain nature of many factors affecting the labor productivity, fuzzy logic is integrated into system dynamics to account for the existing uncertainties. The values of different uncertain factors affecting the labor productivity are determined by fuzzy numbers based on the opinions of different experts involved in the project. Using the proposed fuzzy-SD approach, the value of labor productivity is determined as a fuzzy number considering the effects of all the influencing factors. Different alternative solutions are then defined to improve the labor productivity. The impact of the alternative solutions on project performance is simulated using the proposed fuzzy-SD model prior to their actual implementation. Using the proposed integrated fuzzy-SD approach, the project manager may decide on the most appropriate alternative solution to improve the labor productivity.

Fuzzy Arithmetic Risk Analysis Approach to Determine Construction Project Contingency

Article

Jun 2016

The use of proper risk analysis techniques and contingency determination procedures in construction projects improves project efficiency and effectiveness. However, the uncertainty inherent in risk and the lack of sufficient related historical data on risks make it difficult to precisely assess a project’s degree of risk exposure using classical deterministic or probabilistic risk analysis techniques. This paper provides an alternative to these techniques that uses fuzzy logic and expert judgment. It proposes a fuzzy contingency determination model (FCDM) that utilizes a novel and transparent fuzzy arithmetic procedure to determine construction project contingency using the α-cut method and the extension principle, based on t-norms. Linguistic scales, represented by fuzzy numbers, enable experts to use natural language to assess the probability and impact of risk and opportunity events instead of depending on historical data. The model expresses contingency either as confidence intervals at different levels of confidence, or as a single crisp value resulting from defuzzification. A software tool, the Fuzzy Contingency Determinator (FCD), has been developed to implement the FCDM’s fuzzy arithmetic procedure. The model is validated by comparing its results—work package and project contingencies—to those of a Monte Carlo simulation model, using actual project data. The main contributions of this paper are (1) providing a systematic, transparent, and flexible methodology to identify and assess risk and opportunity events and determine construction project contingency, using a novel and highly flexible fuzzy arithmetic procedure based on the α-cut method and the extension principle, the latter of which uses different t-norms—an approach that has not been previously applied in the construction domain to determine project contingency; (2) offering an alternative to traditional deterministic and probabilistic risk analysis approaches by using expert judgment, linguistic scales, and fuzzy numbers to overcome their limitations; (3) incorporating opportunity in its assessment procedure, which has been rarely applied in other risk assessment models; and (4) implementing the fuzzy arithmetic procedure of the FCDM using a simple, flexible, and user-friendly software tool: FCD. The ability to explore the effect of different fuzzy arithmetic procedures on contingency determination provides a generalizable approach that can be applied to different cases of risk analysis.

System model for analysing construction labour productivity

Article

Apr 2016
Construct Innovat

Purpose Despite long-term, sustained research and industry practice, predicting construction labour productivity (CLP) using existing factor and activity modelling approaches remains a challenge. The purpose of this paper is to first demonstrate the limited usefulness of activity models and then to propose a system model approach that integrates factor and activity models for better prediction of CLP. Design/methodology/approach The system model parameters – comprising factors and practices – and work sampling proportions (WSPs) were identified from literature. Field data were collected from 11 projects over a span of 29 months. Activity models based on the relationship between CLP and WSPs were created, and their validity was tested using regression analysis for eight activities in the concreting, electrical and shutdown categories. The proposed system model was developed for concreting activity using the key influencing parameters in conjunction with WSPs. Findings The results of the regression analysis indicate that WSPs, like direct work, are not significantly correlated to CLP and fail to explain its variance. Evaluation of the system model approach for the concreting activity showed improved CLP prediction as compared to existing approaches. Research limitations/implications The system model was tested for concreting activity using data collected from six projects; however, further investigation into the model’s accuracy and efficacy using data collected from other labour-intensive activities is suggested. Originality/value This research establishes the role of WSPs in CLP modelling, and develops a system modelling approach to assist researchers and practitioners in the analysis of productivity-influencing parameters together with WSPs.

Factors influencing labor productivity on construction sites

Article

Mar 2016
Int J Prod Perform Manag

Shamil george Naoum

Purpose – Productivity is a worldwide problem and efforts have been made over the last three decades or so to explore ways to increase the rate of productivity on construction sites. The purpose of this paper is to investigate the state of the art in productivity research and to present the findings of a survey into the factors that can impair productivity on site. Design/methodology/approach – A literature review is structured under five general headings: pre-construction activities; activities during construction; managerial and leadership issues; motivational factors; and organizational factors. In total, 46 determinants were extracted from the above headings and were assessed by 36 main contractors. Findings – The literature review revealed that while there has been an advancement in developing techniques and tools to improving productivity on site, more need to be done to invest in technology and innovation. The interview survey indicated that factors associated with pre-construction activities, namely, the “experience of the selected site and project managers,” “design errors,” “buildability of the design,” “project planning,” “communication,” “ leadership style” and “procurement method” as the most critical factors influencing site productivity. Other highly ranked factors are “mismanagement of material” and “the work environment.” Research limitations/implications – The survey is based on main contractors and thus not generalized to cover other sectors of the building team such as designers and engineers. Practical implications – Outcome of this research can be used to provide professionals and contractors guidance for focussing, acting upon and controlling the most significant factors perceived to influence the construction labor productivity (CLP) on site. Originality/value – First, reviewed the state of the art and trends in construction productivity research. Second, primary survey with industry experts to rank the relative importance of factors that can influence CLP on site.

Developing and Optimizing Context-Specific Fuzzy Inference System-Based Construction Labor Productivity Models

Article

Feb 2016

Construction labor productivity (CLP) is affected by numerous context-sensitive influencing variables made up of subjective and objective factors, practices, and work sampling proportions (WSPs), which cause complex variability. Modeling CLP is challenging because for any given context, the complex impacts of multiple variables have to be considered simultaneously, without sacrificing accuracy or interpretability. Such challenges are addressed in this paper through the development of a methodology that explicitly represents context in CLP modeling and optimizes context-specific CLP models in order to improve accuracy. In addition, interpretable, fuzzy inference system (FIS)-based, and context-specific CLP models have been developed for the purpose of modeling concrete pouring activity. The performance of the context-specific CLP models is then compared with a generic CLP model, which is developed by combining the context-specific data sets. The results of the investigation showed that the key variables vary between the studied contexts and that the respective context-specific models have better prediction accuracy than the generic one. This study contributes to the body of knowledge in construction project management by demonstrating the essential role of context in the CLP model development process using context attributes, which provide a useful approach for characterizing existing CLP models and facilitate the use and adaptation of existing CLP models in new project contexts. In addition, this study presents a series of highly interpretable, context-specific CLP models to predict labor productivity in various building project contexts.

Dynamic Modeling of Multifactor Construction Productivity for Equipment-Intensive Activities

Abstract and Figures

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