Construction work cost and duration analysis with the use of agent-based modelling and simulation

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Construction work cost and duration analysis with the use of agent-based modelling and simulation
Open Engineering 2021; 11: 830–844

Regular Article

Grzegorz Śladowski* and Bartłomiej Sroka

Construction work cost and duration analysis
with the use of agent-based modelling and
simulation
https://doi.org/10.1515/eng-2021-0081
received October 31, 2020; accepted May 19, 2021
                                                                             1 Introduction
Abstract: Assuming a systemic approach, a construction                       Construction projects are complex processes performed
project can be treated as a complex system composed of                       within dynamic environments. Recording and analysing
many different interlinked elements such as construction                      this complexity require system-based thinking wherein
works, human agents, equipment, materials and the                            construction projects are conceptualised as a set of ele-
knowledge needed to perform the said work. The sys-                          ments (construction works, persons, equipment, materials
tem’s structure can be divided into many mutually con-                       and knowledge) that remain in specific relationships. In
nected precision levels. This multilevel decomposition of                    a system-based approach, the complexity of a construc-
the system facilitates a bottom-up approach in assessing                     tion project is first described as its detail complexity,
the performance of a planned project, while starting the                     which is time-independent and arises from the system’s
analysis at its lowest aggregation levels. The basic level                   structure (the type and number of its elements and the
distinguishes three typical units and their attributes: per-                 amount of connections between them). Apart from detail
sons, knowledge and construction resources. Unit attri-                      complexity, a project is also characterised by dynamic
butes and their dynamic interactions under changing                          complexity, which evolves over time and is the effect
environmental conditions affect the properties and per-                       of the system’s operational behaviours, whose cause-
formance of a given construction work and, as a conse-                       and-effect character can be non-linear or even unpredict-
quence, the properties and performance of the project.
                                                                             able [1,2]. One specific property of complex systems (and
The objective of this article is to analyse the attributes
                                                                             construction projects as well) is the fact that changes in
and micro-behaviours of units through bottom-up project
                                                                             some elements can cause unforeseen changes in others,
assessment, allowing the estimation of its parameters
                                                                             while feedback between these elements contributes to
such as completion time and cost. We utilised multiagent
                                                                             the system’s evolution over time [3]. The system’s beha-
modelling that allows for performing micro-simulations
                                                                             viour and its interaction with the environment lead to
in complex systems with adaptive components. The ana-
                                                                             emergent properties, such as susceptibility to threats, its
lysis was backed by a case study of road renovation work
                                                                             adaptive capacity to changing conditions and, as a con-
performed under specific conditions on the grounds of a
                                                                             sequence, the system’s resilience [4]. We can find many
listed heritage site.
                                                                             system performance assessment tools in the literature
Keywords: system of systems, meta-network, multiagent                        that are used on projects similar to construction projects
system, planning a construction project                                      (expressed via, for instance, their completion time and
                                                                             cost), but most of them are based on a top-down
                                                                             approach [5]. This approach does not allow us to detect
                                                                             autonomous micro-behaviours of elements within the

* Corresponding author: Grzegorz Śladowski, Cracow University of             system – their interdependent, non-linear and dynamic
Technology, Faculty of Civil Engineering, Department of                      relationships that change over time – and, as a result,
Management in Civil Engineering, 24 Warszawska Street,                       the project’s performance [3,6]. Recently, a concept of
31-155 Cracow, Poland, e-mail: grzegorz.sladowski@pk.edu.pl
                                                                             an integrated approach to bottom-up construction pro-
Bartłomiej Sroka: Cracow University of Technology, Faculty of Civil
Engineering, Department of Management in Civil Engineering,
                                                                             ject performance assessment has appeared – based on
24 Warszawska Street, 31-155 Cracow, Poland,                                 systems of systems (SoS) [7]. The system’s abstraction at
e-mail: bartlomiej.sroka@pk.edu.pl                                           the basic level and its multilevel aggregation form the

  Open Access. © 2021 Grzegorz Śladowski and Bartłomiej Sroka, published by De Gruyter.         This work is licensed under the Creative Commons
Attribution 4.0 International License.
Construction work cost and duration analysis with the use of agent-based modelling and simulation
Construction work cost and duration analysis with the use of ABMS        831

framework for the effective assessment of construction          impact on its evolution [10]. This top-down approach does
project performance assessment. One of the tools used          not allow us to explore the dynamic micro-behaviours of the
to study the micro-behaviours of a system’s elements           system’s various elements (e.g. people and other resources)
and their dynamic interactions, which lead to assessing        at lower abstraction levels (e.g. at the level of a single con-
its performance, is agent-based modelling and simula-          struction work) – behaviours that directly affect the project’s
tion (ABMS). During the construction of a multiagent           outcome [11]. In recent years, we have been able to observe
model, one identifies active heterogeneous agents with          the development of a new concept of project management
preset attributes. Afterwards, they are placed in a specific    named PM 2.0, whose objective is to provide new tools and
environment, defining mutual relations and the rules of         methods for effectively assessing the performance of com-
their behaviour. Via simulation, dynamic, repeating and        plex projects. As a part of this concept, Zhu and Mostafavi
often competitive agent interactions and their individual      (2014) [7] noted the fact that construction projects demon-
behaviours and adaptation to changing environmental            strate the properties of SoS and should be conceptualised
conditions define the behaviour and evolution of the            and analysed as such. The dynamic of these complex sys-
entire system [8,9]. We can find few examples of ABM            tems and the interdependence between them lead to a situa-
used to simulate user micro-behaviours during construc-        tion in which changes in one subsystem result in unexpected
tion work in the literature. We reviewed these concepts        changes in the remaining subsystems and the feedback
and isolated their key limitations. First, we found that       between them causes these projects to evolve over time.
these agent micro-behaviour analyses were confined only         We can also find several characteristics of SoS in the litera-
to a single type of construction work. Second, the number      ture. Scholars like Maier (1998) [12] or Lewis et al. (2008) [13]
of agents who cooperated and made decisions during this        stressed the operational independence of each subsystem,
work was very limited. Third, these analyses did not           their decision-making autonomy, spatial distribution, dyna-
account for the effects of agents learning and forgetting       mism and their evolutionary character. Pryke et al. [14] also
information, nor did they account for impacts caused by        noted the fact that, apart from technical, co-dependent rela-
adverse events (atmospheric conditions, equipment fail-        tions within construction projects, social relationships were
ures, archaeological discoveries, etc.) which can also affect   likewise significant. These relationships arise from interper-
project efficiency. The objective of our article is to enhance   sonal interactions, including the exchange of information,
ABM usage potential via the elimination of these limita-       which considerably highlight the dynamic of complex sys-
tions, which can allow for more precise modelling and          tems. Emergent properties (e.g. susceptibility to threats, the
                                                               capacity to adapt to changing conditions and resilience) are
bottom-up analysis of construction projects as systems,
                                                               an important characteristic of SoS. These properties were
which they undoubtedly are.
                                                               defined by Johanson (2006) [15] and are the result of the
     The first part of the article will describe the approach
                                                               dynamic behaviours of subsystems and their mutual inter-
of the SoS and provide an overview of the general assump-
                                                               dependence, constituting a trait of the entire system.
tions of ABM micro-simulation. The argument will be
                                                                    Figure 1 presents the conceptual structure of the SoS
backed by an example of assessing the performance of
                                                               concept, which can be used to develop tools and techni-
construction work carried out during the renovation of
                                                               ques of assessment of complex construction projects.
the structural layers of road surfaces present on the
                                                                    The structure of relationships between elements (orga-
grounds of a listed heritage site.
                                                               nisations, tasks and resources) of the sample SoS that can be
                                                               used to describe a construction project requires selecting
                                                               proper analysis methods. This selection depends on the
2 SoS                                                          chosen system aggregation level. To analyse an SoS
                                                               at the project level, we can use the so-called system
In the traditional approach to assessing construction pro-     dynamics method. At the process level, discrete event
jects, their performance analysis is typically reactive and    simulation was found to be effective. One of the tools
disintegrated. The top-down character of this analysis         used to perform bottom-up assessments of complex con-
ends at the level of relations between construction pro-       struction projects is the ABMS approach. ABMS allows
jects at most [5]. In this approach to planning construc-      us to analyse micro-behaviours and micro-interactions
tion projects, there is a general belief that a centrally      between system elements (e.g. people, information and
controlled performance of the project should be con-           other resources) allowing us to understand their dynamic
cordant with its plan and the interactions of entities         and, via multilevel aggregation, impacting the properties
and construction resources will not have any significant        and performance of the entire project.
Construction work cost and duration analysis with the use of agent-based modelling and simulation
832          Grzegorz Śladowski and Bartłomiej Sroka

Figure 1: Conceptual representation of an SoS used for analysing construction project efficiency. Source: original work based on refs [16,17].

    For the purposes of an effective bottom-up perfor-                  environment that enables their interaction. The primary
mance assessment within an SoS, we must consider two                   objective of ABMS is to track the interactions of hetero-
types of abstraction of the construction project under                 geneous agents in their artificial environment and under-
analysis [16,18]:                                                      stand the processes that display global patterns [21]. In
• Basic-level abstraction is associated with perceiving                the literature, we can find many definitions of agents and
  construction projects through the prism of separate                  their environment, e.g.:
  elements like people, information and resources, whose                    Macal and North (2009) [20] defined the agent as
  attributes and interactions with the external and internal           an active component capable of independent decisions.
  environment affect the dynamic properties and ultimately              Epstein and Axtell (1996) [21] defined agents as people
  the performance of these projects.                                   within agent-based modules, who possess their own
• Multi-level aggregation determines effectiveness at higher            traits and behaviour rules. Meanwhile, Nwana (1996)
  levels on performance at lower levels.                               [22] defined agents within three basic behavioural attri-
                                                                       bute categories, with each agent possessing at least two
    In light of the above, the assessment of the perfor-               (Figure 2).
mance of construction projects conceptualised as SoS                        Autonomy means that the heterogeneous agents pos-
requires the adoption of a bottom-up approach for their                sess individual internal states and goals and strive to
analysis.                                                              achieve them. Cooperation with other agents towards
                                                                       achieving specific goals is critical. For agents to be able
                                                                       to cooperate, they must possess the social capacity for
                                                                       interaction. Learning is a key trait of every intelligent
3 Theoretical basis for ABMS                                           being and is based on gaining empirical knowledge and
                                                                       using it to modify one’s behaviour to better adapt to the
The concept of ABMS is a relatively new approach to                    environment.
assessing the behaviour of complex systems [19]. In ref.                    The second critical element of ABMS is the environ-
[20], the authors defined ABMS as a set of agents and an                ment. Weyns et al. (2007) [23] defined the environment as
Construction work cost and duration analysis with the use of agent-based modelling and simulation
Construction work cost and duration analysis with the use of ABMS       833

                                                                     in solving problems affecting the achievement of the
                                                                     intended goal [26].
                                                                          In the construction sector, multiagent models have
                                                                     thus far been used in: managing delivery chains [27,28],
                                                                     analysing procurement procedure strategies [29], analys-
                                                                     ing construction personnel behaviours [30,31], assessing
                                                                     construction site safety [32–34] and analysing mechan-
                                                                     ised excavation work [35,36].
                                                                          The latest application of a multiagent approach con-
                                                                     cerned an SoS-based bottom-up analysis used to assess
                                                                     the performance (duration and cost) of a project which
                                                                     was applied to a case study of tunnelling utilising the
                                                                     New Austrian Tunnelling Method [16]. The article explored
                                                                     the attributes of agents and other system elements, analysed
                                                                     various project variant and assessed their performance. The
                                                                     objective of this article is to further develop this multiagent
                                                                     approach following the SoS concept via introducing a greater
                                                                     project complexity in terms of analysed construction work,
                                                                     introducing a greater number of agents that act while coop-
Figure 2: Three fundamental behavioural attribute categories. Each
                                                                     erating and accounting for the effects of construction-task-
agent must possess at least two. Source: original work based on
ref. [22].                                                           performing agents learning and forgetting, in addition to
                                                                     including the impact of risk factors (weather conditions,
                                                                     equipment failures, archaeological studies, etc.) on the
                                                                     project.
the conditions that surround agents and allow them to
function, providing them with the ability to interact and
use available resources. Bandini et al. (2009) [24] define
the fundamental aspects of the model that are defined by              4 Agent-based approach to analyse
the environment:
• comprehensive modelling of the physical and social pla-              the performance of a sample
  cement of the system;                                                project
• enabling agents to gather information about their environ-
  ment and performing actions based on this information;
• creating conditions for agents to interact with non-               4.1 Agent-based model assumptions and
  agent system elements;                                                 structure
• Defining and modelling dynamic changes that occur in
  non-agent system elements;                                         The example of road surface renovation work under ana-
• Enforcing adherence to the rules defined in the system.             lysis is based on an analogy to the project of the restora-
                                                                     tion of the outer courtyard and its access roads located at
     Every heterogeneous agent individually assesses their           the Royal Castle on Wawel Hill in Krakow, Poland, which
situation and makes autonomous decisions based on a                  was carried out in 2012. The renovation work is associated
specific set of rules [25]. However, the capacity of an               with replacing the surface of the existing square located
individual agent to act is limited by their knowledge,               in an area that is a listed heritage site. The assumed
the availability of resources, computation capacity and              square surface is 10,000 m2. The specificity and character
the perspective of the objective. If the analysed system is          of the renovation work is as follows: the work begins on
particularly complex in terms of structure and dynamics,             the first work plot, with a given surface, where workers,
which is distinct for construction projects, one proven              applying appropriate equipment, dismantle the existing
way to address this is to create conditions for the coop-            surface via stripping the existing wearing course with the
eration of specific and modular components (agents) that              intent to maximise the recovery of stone tiles, followed by
specialise in a given field. The synergetic effect obtained            the dismantlement of the base (Figure 3a), the profiling
this way will allow the system to behave effectively                  and strengthening/stabilisation of the subbase (Figure 3b)
834           Grzegorz Śladowski and Bartłomiej Sroka

Figure 3: Renovation of the surface of the outer courtyard of Wawel Castle: (a) dismantling of existing surface, (b) soil strengthening and
profiling, (c) soil strength verification, (d) application of various variants of soil strengthening, (e) laying the base course and (f) laying the
stone surface layer. Source: photo Grzegorz Śladowski.

Table 1: Probability of soil strengthening variant’s effectiveness depending on soil type (empirical data – an analogy to the project of the
restoration of the outer courtyard and its access routes at the Royal Castle at Wawel Hill)

Soil type                  Variant 1                        Variant 2                                     Variant 3

                           Improved subbase from            Reinforcement with geogrid with a             Cellular geogrid with a height of
                           mechanically stabilised          tensile strength of 150 kN/m +                2 m × 0.2 m filled with
                           crushed aggregate 0/31.5         mechanically stabilised crushed               mechanically stabilised crushed
                                                            aggregate 0/31.5 in two 0.2 m layers          aggregate 0/31.5

Good (secondary            0.5                              1                                             1
modulus above 70 MPa)
Average (secondary         0.25                             0.75                                          1
modulus above 35 MPa
but below 70 MPa)
Poor (secondary            0                                0.25                                          1
modulus up to 35 MPa)

*Post-stabilisation soil strength requirements (secondary modulus = 120 MPa) for KR3 per PN-S-02205:1998.

and an assessment of the soil strength (Figure 3c). Initial               workers on the first plot apply the selected soil strengthen-
studies performed during the design phase reported that                   ing method and verify it. When the desired soil strength
the probability of encountering good soil strength was 0.1,               parameters are not detected, the site manager makes the
average strength had a probability rate of 0.3 and poor                   decision to perform repairs. If the repairs do not produce
strength had a probability rate of 0.6, as the area largely               expected results, the site manager informs the designer
features soil of anthropogenic origin. Based on the soil                  of the need to change the soil strengthening method to a
strength studies, the designer selects the strengthening                  better alternative, which is associated with the additional
method (which varies in terms of cost and performance                     costs of replacing the previous soil strengthening solutions.
time) (Figure 3d) based on empirical data (Table 1) and a                 The site manager (depending on how the situation develops
specific approach to risk (Table 2) [16]. Afterwards, the                  and on their degree of risk aversion), upon finishing the
Construction work cost and duration analysis with the use of ABMS                 835

Table 2: Three approaches towards risk were analysed for the                The model also accounts for the ability of the workers
designer who performs the selection of the soil strengthening          who perform the tasks on successive work plots to learn
variant based on the empirical data depending on soil strength         and forget skills. Learning and forgetting is the object of
analysis, original work based on ref. [16]
                                                                       many types of work in construction. The learning and
                                                                       forgetting mechanism was applied in the study of the
Soil type                        Designer choice
                                                                       construction of underwater caissons [39], applying roof
                Risk approach (conservative/normal/risk-taker)         insulation [40] or finishing work on a multistorey resi-
            Variant 1         Variant 2            Variant 3           dential building [41].
                                                                            The proposed approach utilised the learning and for-
Poor        0/0/0.1           0/0/0.3              1/1/0.6
Average     0/0/0.4           0.6/1/0.6            0.4/0/0
                                                                       getting mechanism introduced by Nembhard and Uzumeri
Good        0.6/1/1           0.3/0/0              0.1/0/0             (2000) [42], which can be used to determine worker
                                                                       effectiveness.
                                                                            In order to do so, one needs to employ the following
proper soil strengthening task, makes the decision con-                formulas:
cerning the area size of the next plot (Table 3). After com-
                                                                                                          xR α + p ⎞
pleting soil strengthening tasks for the entire square,                                       yx = k ⎛⎜ α x         ⎟,

the workers begin to construct the base course from lean                                              ⎝ xRx + p + r ⎠
concrete (Figure 3e) and then proceed to lay the wear-                                                 ∑ix= 1(ti − t0)
ing course from previously recovered stone materials                                            Rx =                     ,
                                                                                                        x (tx − t0)
(Figure 3f). The information about the workload and the
cost of performing each task, including those associated               where k is the asymptotic value limit of y, x is the amount
with technological variants of soil strengthening, were esti-          of accumulated work done, p is the previous experience
mated as average values that occur under normal construc-              in the same unit as x , r is the amount of work required to
tion conditions.                                                       achieve a performance value of k , α is the forgetting coef-
                                                                                                                 2
     We used the UML standard to describe agent inter-                 ficient and Rx is the relation of time that has passed since
relationships and actions. The specificity of construction              the first unit t0 to the time that has passed since the last
projects assumes a discrete time (date) when an agent                  unit produced x .
makes a decision or takes an action. This decision/action                     The parameters were set so that worker performance
is based on a ruleset that depends on experience col-                  could vary between 70 and 130%: k = 260, r = 225 and
lected during previous projects, risk approach and the                 α = 0.3. The value of parameter p depends on the worker
current situation at the construction site. In addition,               experience based on which the following was assumed:
agents do not have their own goals and are not equipped                p = 260 (70% performance), averagely qualified workers
with the function of assessing their own actions. Despite              p = 780 (100% performance) and highly qualified workers
agents being autonomous, they are heavily restricted                   p = 26,000 (130% performance).
by the specificity of construction. Therefore, we found                        A performance of 130% meant that the average cost
presenting the model in a UML standard justified (as                    and duration of a task was lowered by 30%. Thereby,
                                                                                        yx
opposed to using an agent-based standard).                              yx _ laf = 2 − 200 , klaf = yx _ laf ⋅ k and tlaf = yx _ laf ⋅ t , where
     Figures 4 and 5 present two types of diagrams: a class            klaf and tlaf denote the time and duration of a task after
diagram and a sequence diagram of the agent-based                      accounting for the curve of learning and forgetting, while
model as per the OMG UML standard [37,38].                             yx _ laf denotes the performance coefficient. Workers learn

Table 3: Three types of risk approach displayed by the site manager depending on the successful strengthening of the soil; the site
manager’s decision can result in: increasing, decreasing or maintaining the previous area of the subsequent work plot

Risk approach                                Successfully reaching the required soil strength after stabilisation

                 The first time    The second time (after          The stabilisation had to be dismantled and a more effective variant had
                                  repairs)                        to be used

Conservative     Increase         Increase                        Decrease
Normal           Increase         Maintain                        Decrease
Risk-taker       Increase         Increase                        Decrease
836         Grzegorz Śladowski and Bartłomiej Sroka

Figure 4: Class diagram of the agent-based model in question.

and forget every task performed according to a given tech-      validation, extreme condition testing and the tracking
nology independently.                                           technique, which confirmed its validity [16].
     It should also be noted that the project is exposed to
various random adverse effects that can negatively affect
its performance. Based on the specificity of the project,        4.2 Agent-based model analysis
we limited ourselves to accounting for four typical risk
factors in the model. Based on an analogy to the pre-           A block diagram of the simulation algorithm featured in our
viously mentioned project at Wawel Castle, we assumed           method has been presented in Figure 6. For the method to
that these factors materialised with an estimated prob-         function correctly, the following starting data must be available:
ability of 0.5 in the case of archaeological discoveries,       • the various risk approaches displayed by the designer
0.3 in the case of the occurrence of adverse atmospheric          (expressed in percentages of reinforcement choices
conditions, 0.05 in the case of construction equipment            depending on base type),
failure and 0.1 in the case of construction material            • the various risk approaches displayed by the site man-
delivery delays. It was also assumed that the materialisa-        ager (expressed in the manner of site size choice by the
tion of any of these risk factors under specific project           site manager, depending on success or failure in applying
conditions will result in extending its duration by 1             reinforcement at the previous site),
working day each time. In the case of archaeological dis-       • various types of crew experience (expressed via learning
coveries, this assumption can be justified if it occurs in         curve parameters – described in detail further in the
the form of an intervention (under mandatory conserva-            article),
tion guidelines, taking the form of securing any relics         • soil reinforcement methods and their parameters, expressed
without further study).                                           as a method effectiveness percentage depending on soil
     The presented model was implemented in the Python            category.
programming language using the Mesa library, which is
used to model agent-based systems. We can share the                The user should also determine n, the number of
program if needed. The model was subjected to internal          simulations. For each parameter set (for the designer,
Construction work cost and duration analysis with the use of ABMS      837

Figure 5: Sequence diagram of the agent-based model in question.

site manager and workers), n simulations shall be per-             amounted to a total of 8,100 simulations. Tables 4–7 pre-
formed. Every simulation follows the sequence diagram              sent the results that were obtained. Each table shows the
presented in Figure 5. Simulation time and cost shall be           result divided by designer and site manager risk aversions
aggregated for the given agent parameters. The output              and worker experience (divided by semicolons). Table 4
shall be the mean construction time and cost for each              presents the average cost of completing the project (in thou-
agent parameter set.                                               sands of euros). Table 5 presents the standard deviation of
                                                                   cost (in thousands of euros). Table 6 presents the average
                                                                   project completion time and Table 7 presents the standard
4.3 Results                                                        deviation for project completion time.
                                                                       Figures 7 and 8 present selected probability distribu-
Three hundred simulations for each of the 27 different              tions and the distribution function for project completion
parameter sets (three types of designer risk aversion,             cost and duration assuming the following agent attributes:
three types of site manager risk aversion and three types          designer with normal risk aversion, site manager with
of worker experience) were performed for the project, which        normal risk aversion and averagely qualified workers.
838         Grzegorz Śladowski and Bartłomiej Sroka

Figure 6: Block diagram of the simulation algorithm used to analyse the model.

    Figure 9 presents a selected distribution of the                with a normal risk approach, divided by the various worker
relationship between the project’s completion time                  experience ratings.
and cost, assuming the following agent attributes: a                    The results concerning the learning and forgetting
designer with a normal risk approach, a site manager                of skills by workers who perform tasks on subsequent
Construction work cost and duration analysis with the use of ABMS              839

Table 4: Average project completion cost (in thousands of euros) for various worker experience ratings (little; average; high)

                                                                                 Site manager risk approach

                                                    Conservative            Normal                Risk-taker              All

Designer risk                  Conservative         (792;691;588)           (793;694;587)         (789;694;587)           (690;691;690)
approach                       Normal               (768;674;572)           (770;673;572)         (770;676;571)           (671;672;672)
                               Risk-taker           (700;613;527)           (697;616;526)         (700;616;527)           (613;613;614)
                               All                  (753;660;562)           (753;661;561)         (753;662;562)           (658;659;659)

Table 5: Average standard deviation of project completion costs (in thousands of euros) for various worker experience ratings (little;
average; high)

                                                                                     Site manager risk approach

                                                         Conservative            Normal                Risk-taker               All

Designer risk                    Conservative            (22;20;16)              (21;19;17)            (23;22;16)               (85;86;85)
approach                         Normal                  (27;23;16)              (25;24;15)            (26;22;17)               (83;84;84)
                                 Risk-taker              (28;22;17)              (28;25;16)            (27;21;15)               (74;74;73)
                                 All                     (47;40;30)              (48;40;30)            (46;39;30)               (87;88;87)

Table 6: Average project completion time (days) for various worker experience ratings (little; average; high)

                                                                                 Site manager risk approach

                                                    Conservative            Normal                Risk-taker              All

Designer risk                  Conservative         (364;313;252)           (364;312;252)         (362;312;252)           (310;309;309)
approach                       Normal               (356;306;247)           (355;305;246)         (355;306;247)           (303;302;303)
                               Risk-taker           (329;281;229)           (326;281;226)         (327;280;227)           (280;278;278)
                               All                  (350;300;243)           (349;299;241)         (348;299;242)           (297;297;297)

work plots are presented in Figure 10, which also                            Table 8 presents the percentage share of the average
shows a sample performance coefficient yx _ laf depen-                    cost of each work within the overall cost of the entire
dency over project time in reference to soil strength-                  project, while Table 9 presents an analogous share in
ening as per variant 3 by workers with little experience.               respect to project completion time.
The lower the value of yx _ laf , the lower the cost and                     Table 10 presents the average frequency of selecting
completion time of the task. When the value of yx _ laf                 a given soil strengthening variant by the designer in
decreases, this means that worker performance increases                 respect to their risk approach, and Table 11 presents the
when they perform the soil strengthening task as per                    average frequency of selecting plot size depending on the
variant 3.                                                              site manager’s risk approach.

Table 7: Average standard deviation for project completion time (days) for various worker experience ratings (little; average; high)

                                                                                     Site manager risk approach

                                                          Conservative            Normal                Risk-taker              All

Designer risk                    Conservative             (11;10;9)               (11;11;10)            (11;11;9)               (46;47;46)
approach                         Normal                   (13;12;9)               (13;12;9)             (12;11;11)              (45;46;46)
                                 Risk-taker               (12;10;9)               (13;12;9)             (12;11;10)              (42;42;42)
                                 All                      (19;17;13)              (20;18;14)            (19;17;14)              (46;47;46)
840          Grzegorz Śladowski and Bartłomiej Sroka

                                              16%                                                                  100%

                                                                                                                   90%
                                              14%
                                                                                                                   80%
                                              12%
              Probability distribuon
                                                                                                                   70%
                                              10%
                                                                                                                   60%

                                              8%                                                                   50%

                                                                                                                   40%
                                              6%
                                                                                                                   30%
                                              4%
                                                                                                                   20%
                                              2%
                                                                                                                   10%

                                              0%                                                                   0%

                                                            Compleon me in days

Figure 7: Probability distribution and distribution function for project completion time.

5 Discussion                                                            addition, focusing on a greater number of construction
                                                                        work types included in a given sequence allows for effec-
Enhancing construction project modelling and analysis                   tive integration and a transition from multiagent simula-
relative to refs [16,17], as performed through a bottom-                tion to a discrete event simulation, which is often used in
up assessment of their effectiveness by accounting for a                 project analysis at the process level.
greater number of decision-making agents, the effects of                      The graph (Figure 9) demonstrates that under these
learning and forgetting, as well as the impact of risk fac-             assumptions, the project would be completed quickly
tors, allows for a better assessment of a given situation. In           and cheaply by experienced workers, analogously, using

                                              16%                                                             100%

                                                                                                              90%
                                              14%
                                                                                                              80%
                                              12%
                    Probability distribuon

                                                                                                                     Distribuon funcon

                                                                                                              70%
                                              10%
                                                                                                              60%

                                               8%                                                             50%

                                                                                                              40%
                                               6%
                                                                                                              30%
                                               4%
                                                                                                              20%
                                               2%
                                                                                                              10%

                                               0%                                                             0%

                                                    Compleon costs in thousands of euros

Figure 8: Probability distribution and distribution function for project completion cost.
Construction work cost and duration analysis with the use of ABMS      841

                                                               lile experience           average experience            high experience
              Project cost in thousands of euros   850

                                                   800

                                                   750

                                                   700

                                                   650

                                                   600

                                                   550

                                                   500
                                                         200   220     240        260        280       300      320      340      360       380      400
                                                                                          Project compleon me

Figure 9: Cost–time dependency for a designer with a normal risk approach and a site manager with a normal risk approach, divided by
worker experience rating.

workers with little experience would result in the project                                            in respect to soil strengthening variant 3 began after
having the longest completion time and the highest cost.                                              104 days after the project started, as it was the first
In cases where the soil strengthening variant is changed                                              time when the designer decided to apply this solution
(by the designer’s decision) or there is a pause in the                                               (Figure 10). Based on Tables 8 and 9, it can be observed
work (as the result of adverse risk factors), workers’ effec-                                          that work associated with soil strengthening forms the
tiveness and skills associated with variant 3 deteriorate –                                           greatest share of both project cost and time, which con-
 which is the result of the forgetting mechanism. Succes-                                             firms that the detailed analysis of this type of work is
sive project days have been marked on the horizontal                                                  critical in assessing project performance. In one case
axis. The effect of learning and forgetting on workers                                                 (assuming high worker experience), the percentage share

Figure 10: Performance coefficient value yx _ laf for workers with little experience in respect to soil strengthening variant 3.
842           Grzegorz Śladowski and Bartłomiej Sroka

Table 8: Percentage share of the average cost of each stage relative to the average overall project cost for various worker experience ratings
(little; average; high)

Worker                                                    Types of work performed during the project
experience
                   Wearing course        Existing subbase              Soil                     Base course               Laying a new
                   removal (%)           dismantlement (%)             strengthening (%)        construction (%)          stone surface (%)

Little             7.13                  2.92                          37.23                    20.11                     32.60
Average            7.76                  3.13                          35.55                    19.27                     34.29
High               8.50                  3.40                          33.51                    17.93                     36.66
All                7.73                  3.13                          35.61                    19.21                     34.32

Table 9: Percentage share of the average completion time of each stage relative to the average overall project cost for various worker
experience ratings (little; average; high)

Worker                                                    Types of work performed during the project
experience
                   Wearing course        Existing subbase              Soil                     Base course               Laying a new
                   removal (%)           dismantlement (%)             strengthening (%)        construction (%)          stone surface (%)

Little             8.96                  20.61                         34.52                    8.61                      27.30
Average            9.36                  21.36                         33.39                    8.85                      27.04
High               9.73                  22.22                         32.40                    9.39                      26.25
All                9.30                  21.30                         33.56                    8.90                      26.93

in terms of both time and cost was higher and pertained                 rules of the site manager’s behaviour when selecting plot
to laying the wearing course. Based on Table 10, it can be              size, so that the impact of their decision on project cost
observed that a conservative designer is highly inclined                and completion time would be greater.
to choose the third soil strengthening variant, which                        It should be noted that the presented model has its
is the most expensive and the most time-consuming. A                    limitations. First, the project completion time listed in the
risk-taking designer is more prone to select the first var-              model takes on an absolute form (denoted as a working
iant, which is the cheapest, but its performance is not                 form) and does not account for pauses arising from the
high. However, when analysing the results of average                    work schedule. The introduction of the schedule into the
project completion time and costs, the risk taken by the                model, while accounting for the effect of the learning and
designer paid off in this case. The site manager behaved                 forgetting mechanism, could significantly magnify the
as expected, i.e. the greater his risk aversion, the more               latter, which will be explored in further research. The
often they chose a small-sized plot (Table 11). As risk                 second limitation is the small number of risk factors
aversion lowered, they were observed to choose larger                   that we accounted for in the analysis. In future studies,
plots more often. The difference in the frequency of                     the collection of these factors will be expanded based on
selecting each plot size was not substantial. In the future,            project specificity. As we presented a calculation experi-
the authors should investigate possible revisions to the                ment based on a hypothetical case of a renovation of a

Table 10: Average frequency of selecting each soil strengthening
                                                                        Table 11: Average frequency of selecting each working plot size over
variant over the course of the project by designer risk approach
                                                                        the course of the project by designer risk aversion

Designer risk approach              Soil strengthening variants
                                                                        Site manager risk         200 m2         400 m2           600 m2 plot
                             Variant 1      Variant 2     Variant 3     approach                  plot           plot

Conservative                 0.96           3.38          11.57         Conservative              1.26           2.20             10.66
Normal                       1.53           4.52           9.15         Normal                    0.31           0.79             11.93
Risk-taker                   3.33           4.33           4.29         Risk-taker                0.28           0.48             12.14
All                          1.94           4.08           8.33         All                       0.62           1.16             11.58
Construction work cost and duration analysis with the use of ABMS              843

historical road surface, similar studies on actual con-       which would allow for more reliable modelling, under-
struction project cases should be performed in the future,    standing and optimisation of agent micro-behaviours
as it could allow for an effective verification of our          (smart agents) for the purposes of maximising project
findings.                                                      performance.

                                                              Conflict of interest: Authors state no conflict of interest.

6 Conclusion
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