The Decision-Making Trial and Evaluation Laboratory Approach to the Assessment and Hierarchy of Factors Shaping the Costs of Facade Systems

Abstract

Cost estimation is the process of creating cost forecasts by quantitative determination and pricing of the necessary resources for a project’s implementation. This process is iterative, where estimates are regularly updated based on the available information. Studying the relationship between the costs of construction projects is crucial for establishing reliable practices of cost estimation and management. Variability in construction costs can significantly impact investors’ or clients’ decisions. Greater coherence and confirmed relationships between construction costs and factors influencing them can assist investors, developers, and contractors in making informed decisions and ensuring effective cost management. Therefore, the aim of this article is to identify the factors shaping the costs of facade systems of public utility buildings and to examine the mutual influences and dependencies that occur between these factors. The factors were selected based on an analysis of project documentation, and then their assessment was made through expert opinions. The DEMATEL method was used to investigate the mutual relationships and dependencies between the factors as one of the tools of multi-criteria analysis. Through the analysis, it can be pointed out that factors such as the height of the building, the type of facade analyzed, and the level of complexity of the facade have the greatest impact on the cost of facade systems. Moreover, the type of facade analyzed and the number of floors are the factors showing the greatest direct influence on the other factors of the cost of facade systems. The identification and prioritization of factors carried out by the authors provide a basis for future research, which are models that support the prediction of the cost of making facade systems.

1. Introduction

The execution of a construction project is a comprehensive process aimed at creating a facility in accordance with the budget, time, and quality requirements established by the investor [1,2,3]. The success of the entire endeavor and the fulfillment of the investment intentions depend on effective planning and organization of construction works, including technology and material analysis, compliance with building regulations, logistics management, and risk assessment [4,5,6,7,8]. All these elements directly impact the project budget. Shortening the execution time and raising quality and aesthetic standards entail increased costs. Therefore, it is essential to accurately estimate the implementation costs according to the project documentation and the client’s expectations [9].

Cost estimation is the process of creating cost forecasts by quantitative determination and pricing of the necessary resources for a project’s implementation. It is an iterative process where estimates are regularly updated based on the available information during the design phase, which is crucial for decision-making [10]. Conducting cost estimates allows for determining the economic feasibility of the entire project.

Studying the relationship between the costs of construction projects is crucial for establishing reliable practices of cost estimation and management [11]. Variability in construction costs can significantly impact investors’ or clients’ decisions [12]. More coherent and confirmed relationships between construction costs and the factors influencing them can support investors, developers, and contractors in making informed decisions and ensuring well-planned cost management [13].

Furthermore, factors influencing the costs of building construction vary depending on different research and literature reviews [14]. Although there are numerous sets of factors influencing building construction costs in the literature, they differ depending on the location, time, and nature of the construction project being carried out [15,16]. Moreover, in practice, many influencing factors do not directly impact construction costs.

The exterior facades of buildings and structures shape the image of any structure, forming the architecture of cities. The dynamic development of technology, artificial intelligence, and the uncovering of new and innovative building materials, as well as the ever-increasing technical, manufacturing, and performance capabilities, have meant that exterior walls can take on complex shapes and forms. The exterior facades of such buildings are no longer just an external enclosure but a combination of many interdisciplinary functions. They combine stability and reliability with aesthetics, utility [17], energy efficiency, and ecology [18]. All these aspects affect the variability of facade costs. For example, the paper [19] presented the costs of facade solutions for office buildings in Estonia, and the paper [20] analyzed the costs and benefits of economic green facades. On the other hand, in paper [21], the authors made an analysis of the cost of a facade depending on the change of its color and the impact of facade color on integration with the environment. Moreover, the authors of the publication focus on optimizing the life cycle cost of exterior facades [22] depending on the material used [23], present prototype tools to estimate the value of facades [24], and also analyze the cost of integrated photovoltaic systems with facades [25,26].

Facade systems in public buildings constitute a significant portion of the construction costs of a given building. Cost calculation for facade systems involves a variety of structural, architectural, systemic, production, and assembly information. In the paper [27], the authors present the material costs of making aluminum–glass facades depending on the system (mullion and transom, structural and semi-structural) and the glass used. Based on their analysis, the authors conclude that the most economically viable system is the mullion and transom system, and the total cost of the exterior facade depends on the package of glass chosen. The authors point out in their study that the total cost of facade systems depends on the body of the building, function, technical parameters of the glass, and other factors. Therefore, an important aspect of estimating costs is to analyze the factors affecting the cost of building construction [28,29].

In this study, the authors focused on identifying factors influencing the costs of facade systems in the form of aluminum–glass facades and ventilated facades, derived from an analysis of project documentation. Factors directly impacting costs were described, relating to the characteristics of a specific project, as well as the materials and systemic solutions employed. The DEMATEL method was utilized to analyze the direct influences and dependencies between the selected factors. The paper [30] made a similar structural analysis of the factors affecting the cost of facade systems. In the study, the authors considered micro and macroeconomic factors and analyzed indirect influences and relationships between factors. In this study, however, the authors focused on factors affecting the cost of facade systems directly related to completed facilities. They did not address the costs and factors affecting them related to the economic situation of the country, the labor market situation, or the quality of the exterior facade construction. The analysis of facade realization cost factors directly related to the object is more universal and can be used in different countries around the world.

2. Materials and Methods

2.1. The DEMATEL Method

The DEMATEL (Decision-Making Trial and Evaluation Laboratory) method enables the identification and analysis of factors as a cause-and-effect chain [31,32,33]. Initially used as a tool to support the resolution of global and local problems in the realms of economic, social, and environmental data, it now finds application in analyzing cause-and-effect problems in various areas of enterprise management, such as human resources, marketing, and production engineering [34].

Interest in the practical application of this technique initially emerged in the early 1980s in the Far East. However, this technique quickly spread and found application in new, diverse areas [35,36]. According to the Scopus database of publications, interest in and utilization of the DEMATEL method in scientific research continues to grow. Over the past 10 years (2013–2023), the number of publications related to the use of the DEMATEL method for multi-criteria analysis in research areas has increased from 98 to 911 (Figure 1).

The flexibility of the DEMATEL method has made it a valued tool for solving various problems across different fields of science [37,38,39]. The highest number of publications were recorded in the Scopus database in the broadly defined field of Engineering (2052 publications) (Figure 2).

The DEMATEL method has been used many times in the construction industry to analyze the causal relationships of the area under study. For example, the authors of the paper [40] conducted an analysis of the hard-to-measure factors of the failure of historic structures. Other studies using the DEMATEL method present an analysis of factors affecting the environmental impact of concrete structures [41], factors related to integrated design [42], and analysis of barriers to the use of green building technologies [43]. In turn, the authors of the paper [44] presented a multi-criteria approach based on DEMATEL to assess the key factors for the success of a construction project; in another paper, the authors analyzed the factors of delay on the project schedule [45,46], and in the paper [47], the causes of construction defects were analyzed. The DEMATEL method was also used to distinguish the attributes of factors affecting the application of BIM in prefabricated buildings [48]. The DEMATEL method has also been used by researchers to analyze the factors affecting the cost of construction projects [49,50] or factors affecting building costs [51,52]. The above are just a few areas of construction where the DEMATEL method has been successfully used to analyze the interactions and relationships between the factors indicated.

The universal nature of the DEMATEL method allows for obtaining information regarding the overall structure and total impact of all considered factors, as well as the direct relationships between them. The concept of impact is adapted to the specific context of the problem, meaning it can involve different types of interactions. To fully utilize the information about direct relationships, the DEMATEL methodology relies on expert opinions that are based on a multi-level scale of assessments of interactions between individual factors [53]. Therefore, pairwise comparison analysis is employed to obtain a comprehensive picture of the direct relationships between the factors under study. Assessments of the mutual influences of individual factors are made using a discrete rating scale from 0 to N [33]:

• 0—describes no influence of the first factor on the second;
• 1—slight influence of one factor on another;
• 2 … N − 1—intermediate levels describing the degree of influence of the first factor on the second;
• N—extremely large influence of the first factor on the second.

Initially, the scale of direct influence contained five levels; currently, due to the diverse research context, any number of scale levels is permissible [54].

The complete set of ratings of direct influences is contained in the direct influence matrix A (1):

$$A=\left(\begin{array}{ccccc}0& x_{12}& x_{13}& \cdots & x_{1n}\\ x_{21}& 0& x_{23}& \cdots & x_{2n}\\ x_{31}& x_{32}& 0& \cdots & x_{3n}\\ ⋮& ⋮& ⋮& \ddots & x_{n-1n}\\ x_{n1}& x_{n2}& x_{n3}& \cdots & 0\end{array}\right)$$

(1)

Each row and column of this matrix corresponds to consecutive factors. The element located in the i-th row and j-th column of the matrix represents the rating of the direct influence of the i-th factor on the j-th factor. According to the DEMATEL methodology, the direct influence of a factor on itself is not assessed.

The next stage of the analysis involves determining the total influence matrix T by utilizing the normalized direct influence matrix that satisfies condition (2) [33]:

$$\underset{k\to \infty }{\lim X^k}=0$$

(2)

To determine the normalized matrix, the maximum row sum of elements of the direct influence matrix is utilized (3):

$$X=\frac{1}{\underset{i=1,2\dots n}{\max }\left\{{\displaystyle \sum _{j=1}^n{x}_{ij}}\right\}}\cdot A$$

(3)

The total influence matrix T then takes the following form (4):

$$T=X+∆X$$

(4)

Information exploration with regard to the total influence leads to obtaining two indicators that enable the classification of factors. The first of these indicators is called exposure (or prominence) and is denoted as S⁺ for the i-th factor. It serves to determine the strength of connections of a given factor with other factors and is calculated by adding the sum of components constituting the i-th row and i-th column of matrix T (5):

$$\underset{i=1,2\dots n}{\forall }\hspace{1em}{s}_i^{+}={\displaystyle \sum _{j=1}^n{t}_{ij}}+{\displaystyle \sum _{j=1}^n{t}_{ji}}$$

(5)

The second indicator, S⁻, is called relation and indicates the actual cause-and-effect role of the i-th factor. It is worth noting that its value can be both positive and negative. A positive value demonstrates the actual causality of the factor, while a negative value expresses its consequential role. The greater the absolute value of this indicator for a given factor, the clearer its cause or effect. The value of this indicator is the difference between the corresponding row and column sums (6):

$$\underset{i=1,2\dots n}{\forall }\hspace{1em}{s}_i^{-}={\displaystyle \sum _{j=1}^n{t}_{ij}}-{\displaystyle \sum _{j=1}^n{t}_{ji}}$$

(6)

2.2. Factors Influencing the Costs of Facade Systems

The identification of factors influencing the costs of facade systems was based on the analysis of contractual documentation for 209 cases of completed public utility buildings from 2018 to 2021. The buildings were constructed in central and southern Poland. Contractual data were obtained from companies specializing in the execution of facade systems. As a result of research on project documentation, 14 factors shaping the costs of facade systems were selected and then assigned to 3 groups directly related to the building’s characteristics and parameters or directly related to the characteristics of the analyzed facade. The research process is illustrated in Figure 3.

Group I—General building characteristics. This section presents the basic characteristics of the analyzed public utility buildings. Within this group, 3 factors influencing the costs of facade systems have been established.

X₁—location—includes information regarding the building’s placement. The identified factor primarily impacts the transportation costs of large-scale components of aluminum–glass facades, such as glass panels, columns, mullions, or pre-assembled structural elements. The proposed division of the factor encompasses 3 categories: downtown, outskirts of the city, and suburban area.

X₂—type of public utility building—analysis of project documentation allows for the classification of 5 categories of public utility buildings: commercial and retail buildings, office and service buildings, residential buildings (hotels), educational and research institutions (universities, schools, research and development centers, libraries), and healthcare buildings (clinics, hospitals).

For X₃—building shape—based on the analysis of project documentation, the factor has been divided into 2 categories: cuboid and other shapes.

Group II—Building size description. This group describes the basic technical parameters of the analyzed public utility buildings. Within this group, 4 factors have been identified:

X₄—building height—the analyzed buildings ranged in height from 3.65 m to 49.12 m.

X₅—building length—the analyzed buildings ranged in length from 18.72 m to 136.00 m.

X₆—building width—the analyzed buildings ranged in width from 8.96 m to 98.00 m.

X₇—number of floors—the analyzed buildings had between 1 and 12 floors.

The above parameters influence the building’s surface area and its shape. Additionally, the building height factor has an additional impact on costs associated with mobilizing equipment necessary for the installation of facade structures or ventilated facades. In the case of tall buildings, it is necessary to consider additional costs related to the use of scaffolding, cranes, hoists, and specialized suction cups for glass panels.

Group III—Facade characteristics. Within this group, 7 factors have been determined, describing the surface area, type of facade, and the materials used.

X₈—surface area of the analyzed facade—the analyzed buildings had a surface area ranging from 355.45 square meters to 9872.99 square meters.

X₉—level of facade complexity—the factor has been divided into 3 categories: low, medium, and high. The low level is characterized by a simple installation method, without the need for additional equipment (such as hoists, scaffolding, etc.), and glass facade panels are standard solutions. The medium level of complexity corresponds to facades with simple structures, using basic equipment and easy access to the building. The high complexity level is designated for sloped or curved facades, often in urban spaces where access to the building is limited, and the installed glass panels exceed standard dimensions and are characterized by significant weight.

X₁₀—type of analyzed facade—this factor has been split into 3 types of facades: vertical facade, curved facade, and sloped facade.

X₁₁—type of aluminum–glass facade—within this factor, 3 types of facades have been described: mullion and transom facade, semi-structural facade, and fire-resistant facade.

X₁₂—type of glass used—this factor has been divided into 3 categories: fire-resistant glass, opaque glass, and transparent laminated glass.

X₁₃—type of cladding for ventilated facade—based on the analysis of project documentation of the analyzed public utility buildings, cladding materials used for ventilated facades were listed such as composite panel, quartz composite, HPL panel, wooden cladding, and fiber-cement panel.

X₁₄—type of fenestration system—in the analyzed public utility buildings, the following types of doors were used: hinged doors, sliding doors, fire-resistant doors, as well as tilt-turn windows and structurally bonded windows.

The identified factors are presented in

Table 1. Factors influencing the costs of facade systems.

Lp.	Factors and Groups of Factors	Symbol
I	General building characteristics	-
I.1	location	X1
I.2	type of public utility building	X2
I.3	building shape	X3
II	Building size description	-
II.1	building height	X4
II.2	building length	X5
II.3	building width	X6
II.4	number of floors	X7
III	Facade Characteristics
III.1	surface area of the analyzed facade	X8
III.2	level of facade complexity	X9
III.3	type of analyzed facade (vertical, curved, sloped)	X10
III.4	type of aluminum–glass facade	X11
III.5	type of glass used	X12
III.6	type of cladding for ventilated facade	X13
III.7	type of fenestration system	X14

:

3. Results

According to the proposed DEMATEL method, the authors initially assembled a group of 15 experts who assessed the influence strength of each listed factor. The experts comprised the target group, possessing over 5 years of professional experience related to facade systems. The target group consisted of employees associated with the design, manufacture, installation, and pricing of facade systems. These included installation managers, building engineers, architects, designers, and cost estimators. To introduce expert ratings into the algorithm, a 4-point discrete rating scale was used, where 0 denotes no influence, 1 denotes the slight influence of the first factor on the second, 2 denotes the moderate influence of the first factor on the second, and 3 denotes the strong influence of the first factor on the second. For example, experts assessed that factor X₁₀, the type of facade analyzed (vertical, arched, sloped), strongly influences factor X₁₁, the type of aluminum–glass facade. This is dictated by the fact that not every type of aluminum–glass facade system (mullion and transom, semi-structural, structural) can be used in arched or sloping elevations. Quite often, these are customized solutions, which are much more expensive than standard facade systems.

The obtained expert opinions constituted components of the matrix of average direct influence A (7):

$$A=\left(\begin{array}{cccccccccccccc}0& 1& 1& 2& 1& 1& 2& 0& 0& 0& 0& 1& 1& 0\\ 0& 0& 0& 0& 0& 0& 1& 0& 0& 0& 0& 1& 1& 0\\ 0& 0& 0& 0& 0& 0& 0& 1& 3& 2& 1& 0& 0& 0\\ 0& 0& 1& 0& 0& 0& 0& 3& 2& 0& 2& 2& 2& 0\\ 0& 0& 1& 0& 0& 0& 0& 3& 1& 0& 0& 0& 0& 0\\ 0& 0& 1& 0& 0& 0& 0& 3& 1& 0& 0& 0& 0& 0\\ 1& 0& 1& 3& 0& 0& 0& 3& 2& 0& 2& 0& 2& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 1& 0& 0& 1& 0& 0\\ 0& 0& 0& 1& 0& 0& 0& 0& 0& 0& 2& 2& 2& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 3& 0& 3& 3& 2& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 2& 0& 1\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 2& 0& 0\end{array}\right)$$

(7)

According to the applied Formula (8), the total matrix T was calculated.

$$T=X{(I-X)}^{-1}$$

(8)

where

• T—total matrix;
• X—normalized form of the direct influence matrix;
• I—identity square matrix.

The matrix T, representing direct and indirect influence, has taken the following form (9):

$$T=\left(\begin{array}{cccccccccccccc}0.000& 0.071& 0.071& 0.143& 0.071& 0.071& 0.143& 0.00& 0.000& 0.000& 0.000& 0.071& 0.071& 0.000\\ 0.000& 0.000& 0.000& 0.000& 0.000& 0.000& 0.071& 0.000& 0.000& 0.000& 0.000& 0.071& 0.071& 0.000\\ 0.000& 0.000& 0.000& 0.000& 0.000& 0.000& 0.000& 0.071& 0.214& 0.143& 0.071& 0.000& 0.000& 0.000\\ 0.000& 0.000& 0.071& 0.000& 0.000& 0.000& 0.000& 0.214& 0.143& 0.000& 0.143& 0.143& 0.143& 0.000\\ 0.000& 0.000& 0.071& 0.000& 0.000& 0.000& 0.000& 0.214& 0.071& 0.000& 0.000& 0.000& 0.000& 0.000\\ 0.000& 0.000& 0.071& 0.000& 0.000& 0.000& 0.000& 0.214& 0.071& 0.000& 0.000& 0.000& 0.000& 0.000\\ 0.071& 0.000& 0.071& 0.214& 0.000& 0.000& 0.000& 0.214& 0.143& 0.000& 0.143& 0.000& 0.143& 0.000\\ 0.000& 0.000& 0.000& 0.000& 0.000& 0.000& 0.000& 0.000& 0.071& 0.000& 0.000& 0.071& 0.000& 0.000\\ 0.000& 0.000& 0.000& 0.071& 0.000& 0.000& 0.000& 0.000& 0.000& 0.000& 0.143& 0.143& 0.143& 0.000\\ 0.000& 0.000& 0.000& 0.000& 0.000& 0.000& 0.000& 0.000& 0.214& 0.000& 0.214& 0.214& 0.143& 0.000\\ 0.000& 0.000& 0.000& 0.000& 0.000& 0.000& 0.000& 0.000& 0.000& 0.000& 0.000& 0.143& 0.000& 0.071\\ 0.000& 0.000& 0.000& 0.000& 0.000& 0.000& 0.000& 0.000& 0.000& 0.000& 0.071& 0.000& 0.000& 0.000\\ 0.000& 0.000& 0.000& 0.000& 0.000& 0.000& 0.000& 0.000& 0.000& 0.000& 0.000& 0.000& 0.000& 0.000\\ 0.000& 0.000& 0.000& 0.000& 0.000& 0.000& 0.000& 0.000& 0.000& 0.000& 0.000& 0.143& 0.000& 0.000\end{array}\right)$$

(9)

The next stage of the analysis of mutual influences of factors is the calculation of the prominence index S⁺ and the relation index S⁻. The results are presented in

Table 2. The values of the S⁻ and S⁺ indices.

Symbol	Factors and Groups of Factors	Prominence S+	Relation S−
X1	location	0.786	0.643
X2	type of public utility building	0.286	0.143
X3	building shape	0.857	0.143
X4	building height	1.286	0.429
X5	building length	0.429	0.286
X6	building width	0.429	0.286
X7	number of floors	1.214	0.786
X8	surface area of the analyzed facade	1.071	−0.786
X9	level of facade complexity	1.429	−0.429
X10	type of analyzed facade (vertical, curved, sloped)	1.714	0.643
X11	type of aluminum–glass facade	1.000	−0.571
X12	type of glass used	1.071	−0.929
X13	type of cladding for ventilated facade	0.714	−0.714
X14	type of fenestration system	0.214	0.071

.

The results have also been presented in Figure 4.

Based on the calculated S^- and S⁺ indices, factors classified as causes are the number of floors (X₇), location (X₁), type of the analyzed facade (X₁₀), building height (X₄), building length (X₅), building width (X₆), building shape (X₃), type of public utility building (X₂), and type of fenestration system (X₁₄).

On the other hand, factors classified into the effects group are the type of glass used (X₁₂), type of cladding for the ventilated facade (X₁₃), type of aluminum–glass facade (X₁₁), surface area of the analyzed facade (X₈), and level of facade complexity (X₉).

The factors that obtained the highest S⁺ prominence indicator values are the type of the analyzed facade (X₁₀), level of facade complexity (X₉), and building height (X₄). Their high values mean the strongest influence on the costs of facade systems. Conversely, the factors with the smallest S⁺ indicator values are the type of fenestration (X₁₄) and the type of public utility building (X₂). These factors demonstrate the least impact on the costs of facade systems.

The final result of the DEMATEL method is a directed graph illustrating the strength of influences and dependencies between individual factors, as shown in Figure 5.

4. Discussion

Survey research carries the risk of obtaining results that may be inconsistent and subjective. To assess the quality of the collected data, the Kendall–Smith concordance coefficient [30] was applied according to Formula (10):

$$W=\frac{12\mathrm{S}}{m^2(n^3-n)}$$

(10)

where

• m—number of experts;
• n—number of variants and number of factors assessed by experts.

The assessment of the proposed factors was made by experts using a 4-point scale. The proposed response options allowed for several identical ratings for individual issues. To accurately calculate the concordance coefficient, it is necessary to determine average ranks by creating a similar series to the strong ordering, where all objects are distinguishable [55]. Introducing average ranks requires correction of the denominator of the concordance coefficient. For series with tied ranks, the value of coefficient W should be calculated according to Formula (11):

$$W=\frac{S}{\frac{1}{12}{m}^2\left(n^3-n\right)-mT}$$

(11)

where

• S—the sum of squares of deviations for individual sums from the arithmetic mean of the sum of ranks for all n objects.

For the received expert opinions, the average coefficient W is 0.744, indicating that the respondents were in agreement in their responses, graded as “plus good” [56].

Table 3. The value of Kendall coefficient (W).

Symbol	Factors and Groups of Factors	Kendall Coefficient	Concordance Assessment
X1	location	0.794	plus good
X2	type of public utility building	0.519	good
X3	building shape	0.985	perfect
X4	building height	0.892	good
X5	building length	0.794	plus good
X6	building width	0.728	plus good
X7	number of floors	0.888	very good
X8	surface area of the analyzed facade	0.672	plus good
X9	level of facade complexity	0.729	plus good
X10	type of analyzed facade (vertical, curved, sloped)	0.829	very good
X11	type of aluminum–glass facade	0.682	plus good
X12	type of glass used	0.497	good
X13	type of cladding for ventilated facade	0.567	good
X14	type of fenestration system	0.839	very good

presents the calculated coefficient of agreement of expert opinions for individual factors.

The experts least agreed when assessing the influence of factor X₂—type of public utility building—on the other factors shaping the costs of facade systems. Conversely, they almost perfectly agreed when assessing the influence of factor X₃—building shape—on the other selected factors.

Based on the conducted DEMATEL analysis, it can be concluded that factors described as causes of facade system costs include the number of floors (X₇), location (X₁), type of analyzed facade (X₁₀), building height (X₄), building length (X₅), building width (X₆), building shape (X₃), and type of public utility building (X₂). On the other hand, factors classified into the end effects group include the type of glass used (X₁₂), type of ventilated facade cladding (X₁₃), type of aluminum–glass facade (X₁₁), area of the analyzed facade (X₈), and level of facade complexity (X₉).

The type of fenestration system factor (X₁₄) does not play a significant role in the costs of facade systems.

Furthermore, the factors that obtained the highest values of the S⁺ prominence indicator exhibit the greatest influence on the costs of facade systems, namely the type of analyzed facade (X₁₀), the level of facade complexity (X₉), and the building height (X₄). Conversely, factors such as the type of fenestration (X₁₄) and the type of public utility building (X₂) demonstrate the least impact on the costs of facade systems.

The DEMATEL method provided results confirming that the greatest influence on the other identified factors was exhibited by the type of analyzed facade factor (X₁₀) and the number of floors factor (X₇). On the other hand, the factors most dependent on other factors influencing the costs of facade systems are the area of the analyzed facade (X₈) and the level of facade complexity (X₉).

5. Conclusions

Cost calculation for implementing facade systems poses a challenge for contractors, both in terms of difficulty and workload. Diverse resources regarding structural, architectural, system, production, and assembly aspects, which the estimation is based on, make it a complex task requiring expertise. Typically, such calculations are conducted in the form of individual assessments, depending on the contractor’s skills and experience. When estimating the costs of facades implementation, we must approach each investment separately, carefully analyzing the project documentation and considering various logistical and organizational aspects. This requires specialized knowledge and experience, which are crucial for the accuracy of the estimation, both in terms of construction costs and expected profit.

Many factors influence the costs of facade systems. The analysis of documentation for public utility buildings performed by the authors allowed them to select factors directly related to the analyzed construction project. These factors pertain to the parameters and characteristics of the specific building as well as the materials used. To assess the quality of the gathered data, the Kendall–Smith concordance coefficient was employed. Its value of 0.744 indicates that the respondents were in agreement with their opinions regarding the factors, graded as “plus good” on average, which can be considered a satisfactory result.

Furthermore, the applied DEMATEL method enabled the examination of the strength of influences and dependencies between the identified factors. Based on this analysis, it can be inferred that factors such as building height, type of analyzed facade, and its level of complexity have the greatest influence on the costs of facade systems. Moreover, this method facilitated the grouping of factors that exhibit the greatest influence on other factors (type of analyzed facade and number of floors) as well as factors that show a high level of dependence on other factors (area of the analyzed facade and level of facade complexity).

The obtained results of the factors analysis using the DEMATEL method indicate, in a practical way, the most important factors affecting the cost of facade systems. For the recipients, this is feedback on which aspects to pay attention to in order not to exceed the cost of the budget. The presented research shows that not only the area of the analyzed facade has an impact on facade costs but also the height of the building. For tall buildings, it is necessary to take into account additional costs such as the cost of scaffolding, the cost of specialized equipment (e.g., high rise, glass suckers), or, in hard-to-reach areas, the cost of mountaineering services for the installation of glass packages. In addition, the analysis of factors carried out by the authors in a practical way also indicates factors with a high impact on the cost of facade systems, which are the factor of the level of complexity of the facade and the factor of the type of facade analyzed. This feedback for designers and architects that facades of complex form, with arched, sloping facades, often require the design of an individual solution is associated with additional, much higher implementation costs than standard system solutions.

The authors’ research in this work focused on the identification and analysis of factors affecting the cost of facade systems for public buildings in the form of aluminum and glass facades along with ventilated facades, and the authors’ identification and prioritization of factors provide a basis for future research, which is models to assist in the prediction of the cost of making facade systems. In the future, the authors also plan to expand this study to include new cases of public buildings with green facades, smart facades, multimedia facades, or hi-tech facades. In addition, this study presents factors extracted from the contractual documentation of completed public utility buildings relating to specific buildings and applied facade system solutions. Micro- and macroeconomic factors that affect construction costs, i.e., inflation, labor market situation, environmental aspect, quality of workmanship, etc., were not included in the analysis. This is also a basis for further research on estimating the implementation costs of facade systems.