Designing and building a complex of single-family houses, with a holistic focus on sustainable development, and construction and occupancy costs, is a problem that is very difficult to solve. It is a multi-aspect problem, in which decision variables include, among others: selecting construction materials, building services, the parameters of the shape of the buildings, their placement on the site, the sequence in which individual buildings are to be constructed and the completion deadlines for individual tasks. During the occupancy stage, one should add an analysis of the impact of the change in energy costs. When considering the entire life-cycle of the buildings, renovation and repair costs should also be included, in addition to any remodelling and demolition expenses. In recent years, the focus on the energy efficiency and pollution emission of buildings has grown exponentially and has had an immense impact on the real estate market and property values. The paper [1
] presents an analysis of the profitability of investing in a selection of three systems based on renewable energy sources, using a semi-detached house as an example.
One of the components of designing a complex of single-family houses is establishing its urban layout. Multi-criteria methods are proposed by scholars who specialise in the optimisation of spatial planning, urban and architectural design, as well as construction project organisation and management increasingly often. In practice, general urban layout planning decisions are typically made as a result of many different approaches and factors, as well as under the influence of numerous stakeholders who may have different goals and hierarchies of values. Decision-making at this level should be supported by decision-making support methods during various stages and at different scales of design and planning. This should particularly apply to land use management and planning, which has been widely discussed in [2
]. The authors of [3
] have discussed the problem of uncertainty mapping using Monte Carlo analysis plugged into the Analytic Hierarchy Process (AHP) method, using the case of Howth, Dublin, in this context. However, this approach primarily focused on allowing decision-makers to gain insight into how much expert opinions can be trusted, specifically focusing on the AHP method, which can be considered a limitation.
The use of multi-criteria decision-making methods to support the planning of complexes of buildings of various sizes—ranging from entire districts to smaller compounds—is a field that can be considered to be fragmented in terms of research focus. However, such methods have been used to analyse various aspects of designing building complexes, ranging from those of placement within the wider urban fabric, the layout of buildings within complexes themselves, construction costs, the sequence of constructing individual buildings, as well as matters related to sustainability. Therefore, the authors are of the opinion that a broad characterisation of this use is justified. In the field of spatial planning, numerous authors have discussed the use of geographic information system (GIS) tools in combination with multi-criteria analysis methods. The authors of [4
] analysed the problem of the optimal placement of housing estates within the structure of the city. In [5
], a fuzzy version of the Decision Making Trial and Evaluation Laboratory (DEMATEL) method, coupled with Covariance Matrix Adaptation Evolutionary Strategy (CMA-ES) and Weighted Linear Combination (WLC) was used to model the suitability of sites for specific forms of use. The authors of [6
], in turn, performed a comprehensive and cross-sectional review of the use of multi-criteria analysis methods in the field in question. In [7
], the Ordered Weighted Averaging method (OWA) was used in conjunction with GIS tools to analyse the suitability of the territory of the Shavur Plain in Iran for various forms of use. It can therefore be concluded that GIS tools offer considerable potential for application in conjunction with multi-criteria analysis methods and that this field merits further study, particularly in light of the constant development of said tools. However, the utility of GIS tools appears to largely be confined to their role as information repositories and many of the proposals remain vague on whether or not they intend to automate data collection from these systems in any way. Multi-criteria methods have also been used to determine and investigate various indicators associated with sustainability and resilience.
The authors of [8
] investigated potential use of multi-criteria methods in assessing sustainability, noting that new alternatives constantly become available, which can make method choice and weight setting difficult. In [9
], the authors proposed a process of selecting multi-criteria analysis methods for renewable energy projects, thereby highlighting the immense variety and complexity of decision problems in the field and that there is no single best method that can be applied to them all. The authors of [10
] used an expert system based on multi-criteria decision-making support to assess the impact of climate change, proposing a new method called MCDM-based expert system for adaptation analysis under changing climate, abbreviated as MAEAC. The authors applied it to a large territory and primarily focused on policy analysis and its impact on climate change. A model of selecting a method of assessing sustainable urban revitalisation strategies was proposed in [11
], while the authors of [12
] discussed the use of multi-criteria methods in environmental planning and management, similarly as in [13
], where the objective was to arrive at a decision-making process associated with a sustainable approach to energy. The authors of [14
] used the Discrete Linear Programming method (DLP) to analyse development projects associated with urban revitalisation. A comprehensive overview of the suitability of the use of multi-criteria methods to assess building-integrated green technologies, ultimately using the AHP method, was featured in [15
]. The same method was also used by the authors of [16
] to investigate construction project management in which sustainability was deemed a key factor.
Multi-criteria methods have also found use in studies of urban and architectural design. In [17
], the AHP method was used to organise an architectural competition held in Italy. The authors of [18
] used the Evaluation Based on Distance from Average Solution (EDAS) and Step-wise Weight Assessment Ratio Analysis (SWARA) methods to assess the shape of the floor plan of a newly-designed building, while in [19
] a hybrid model was proposed—based on game theory, the AHP method, the Simple Additive Weighting method (SAW), Multiplicative Exponential Weighting, the Technique for Order of Preference by Similarity to Ideal Solution method (TOPSIS), EDAS, New Additive Ratio Assessment (ARAS), Full Multiplicative Form, as well as the rules of Laplace and Bayes. This approach is particularly noteworthy as it explores the simultaneous use of numerous (six) multi-criteria analysis methods in a single problem, thereby highlighting the importance of experts’ opinions. The author of [20
] studied the suitability of land for infill development using multi-criteria methods supported by GIS tools. In [21
], the authors holistically investigated the problem of decision-making during the pre-design stage of an architectural design project. The impact of the shape of the building on its energy efficiency and the costs of its construction was analysed in [22
], while [23
] found use in architectural and urban design. The authors of [24
] used the TODIM method (a Portuguese acronym for Interactive Multi-criteria Decision Making) to conduct a multi-criteria analysis of housing properties.
In summary, it can be stated that very few approaches that enhanced existing methods that had specifically been used to address problems in the field of spatial planning, urban and architectural design can be found, particularly as the range of problems said methods are applied to varies greatly between each case.
The works of Tawfik et al. [25
], as well as Koenig etal. [26
] merit particular attention, as they directly explore the problem of the multi-criteria selection of an urban layout or its determination. The proposals by Koenig et al. concerning the automated generation of pre-defined urban layouts for various plots currently occupied by informal settlements is also highly interesting [27
1.1. The Scale of the Problem
According to the Eurostat Agency [30
], in 2017, as much as 33.6% of the population of the European Union resided in detached single-family houses, while 24.0% of the population lived in semi-detached single-family houses. According to data provided by the Polish General Construction Inspector’s Office [31
], in 2018, a total of 98,915 building permit applications were filed for residential buildings, out of which 93,714 building permits were issued for single-family houses (almost 94.8%), which constituted a 3% increase from the previous year [31
]. The results of statistical studies presented by BPD Europe BV [32
] indicate that 12% of respondents from The Netherlands, 16% of respondents from France and 17% of respondents from Germany who had been searching for a new place of residence pointed to a single-family house as a preferred option in a situation in which they would have to move to a different dwelling. This proves that single-family buildings remain popular in many developed countries, while in countries such as Poland they continue to enjoy very high popularity. The design of single-family building complexes can therefore be considered an important field, both to planners who design urban layouts for individual projects, as well as designers who work on projects composed of many such buildings.
The necessity of considering parameters associated with energy efficiency is dictated by, among other things, the current energy policy vector of the European Union, expressed by such documents as Directive 2010/31/EU on the energy performance of buildings [33
]. This EU document introduced the following definition of nearly-zero energy buildings (NZEB): nearly zero-energy building’ means a building that has a very high energy performance, as determined in accordance with Annex I. The nearly zero or very low amount of energy required should be covered to a very significant extent by energy from renewable sources, including energy from renewable sources produced on-site or nearby”. However, every European Union Member State has adopted its own NZEB parameters, which are adapted to local conditions.
The implementation of the Directive into Polish state law has introduced a new standard of near zero-energy buildings (NZEBs). The document that has been amended to include the standard, as stipulated in the Directive, is the Ordinance on the Technical Conditions that Must be Met by Buildings and their Placement [34
]. In the Polish definition of NZEBs there are two criteria. The first criterion is ensuring proper building envelope thermal insulation. The second criterion for NZEB buildings in Poland applies to Primary Energy (PE), which cannot exceed a set value for different types of buildings. For single-family residential buildings without cooling installations, the maximum PE value is 70 kWh/(m2
/annum). The buildings analysed in the article meet both criteria, thus being compliant with NZEB standards as stipulated in Polish regulations.
Selecting the appropriate orientation of buildings, their shape, construction materials, building services and shading system solutions leads to lower energy demand and costs and affects the comfort of use of the buildings themselves, reducing overheating. This subject has been discussed in, among others, [35
]. It can therefore be argued that the application of research findings in the field of energy efficiency and thermal comfort optimisation in the design of buildings and complexes that enjoy significant popularity on the real estate market should be incorporated into current design methodology. It can also be argued that by increasing the energy efficiency of buildings forming market-preferred layouts one can contribute to increasing the popularity of such solutions in areas where detached or semi-detached houses are the most popular.
1.2. Cost Estimation Methods
Calculating the overall costs of construction is a difficult task. Typically, the overall costs of construction are divided into indirect and direct costs. However, this is a major oversimplification. Situations that can significantly affect the expenditures of the contractor can take place over the course of working on a construction project. Some of these are difficult to predict (e.g., natural disasters, economic and social changes), while others can be prepared for during a project’s planning stage. The predicted additional costs can include penalties for failing to meet planned deadlines or penalties for failing to maintain the continuity of construction crew operation.
Furthermore, every project is subjected to certain technological and organisational constraints, such as the time during which construction crews or buildings are available, or technological and organisational requirements concerning ongoing work performed by a given crew on a specific building. Numerous cost estimation or total construction project cost optimisation methods have been developed. They usually utilise metaheuristic methods, such as simulated annealing, hybrid algorithms [43
] and genetic algorithms [44
]. Mathematical programming methods are also used, such as the Decision model for planning material supply channels in construction [45
]. In [46
], an innovative approach was proposed, in the form of a stochastic decision network. It enables the integration of random and decision-based aspects of planned projects. This approach allows the decision-maker to obtain a solution that is optimal in terms of the expected time and cost. They can do so by defining their preferences as to the results of the planned project and setting their risk aversion accordingly. In the case of multi-criteria analysis of time and cost, the decision-maker can also define weight values for the expected project time and cost. The methods listed above do not incorporate all of the essential costs of carrying out construction projects, such as direct costs, indirect costs, penalties for failing to meet contractual deadlines, as well as the costs of discontinuities in the work of construction crews. They also do not take into account technological and organisational constraints. Furthermore, metaheuristic methods involve lengthy calculations when compared to linear programming.
1.3. Previously Used Methods
Multi-criteria decision-making analysis methods that have been applied in urban design and spatial planning have been predominantly focused on large-scale planning. As Afshari and Vatanparast [6
] have indicated, such proposals utilised the Preference Ranking Organisational method for Enrichment Evaluation (PROMETHEE and PROMETHEE-2) methods in combination with Hasse Diagram Technique (HDT), the AHP method, Fuzzy AHP, Weighted Linear Combination (WLC), a combination of the AHP and TOPSIS methods, the ELECTRE-2 method (ELimination Et Choix Traduisant la REalité), the EXPROM-2 method (an extended version of the PROMETHEE method), as well as evolutionary algorithms. Guarini, Battisti and Chiovitti [23
] also pointed to the possible use of Multi-attribute Utility Theory (MAUT) and Measuring Attractiveness by a Categorical Based Evaluation methods (MACBETH).
The selection of the multi-criteria analysis method depends on the specificity of the decision problem at hand. For instance, in [47
] the author referred to studies in which they used the ELECTRE III and AHP methods to analyse the possibility of using an alternative version of the BIPOLAR method to solve the problem of selecting a construction company for partnering cooperation during a construction project. The study included a calculation example and verified the results of previous studies by applying an alternative BIPOLAR method version. Ultimately, its use produced the same end result as when using two other methods.
Multi-criteria methods that incorporate co-dependencies between decision-making criteria and alternatives have seen considerable development in recent years. In [48
] the authors analysed a multi-criteria problem of selecting a new function for historical buildings in light of the proposed selection criteria. Apart from the economic aspect and cultural heritage, these criteria also included sustainability. The Weighted Influence Non-linear Gauge System method (WINGS), which was extended to incorporate the uncertainty of expert opinions and their aggregation, was applied to model the structure of the problem and analyse the dependencies between alternatives and criteria. The method had to be extended because of the specificity of the problem discussed in the paper. The majority of previously used methods did not analyse interdependencies between decision-making criteria despite such interdependencies actually existing, as proven by the authors. Similarly, the authors of [49
] proposed a multi-criteria hybrid model, using the Decision Making Trial and Evaluation Laboratory method (DEMATEL) and the Analytic Network Process (ANP) to select a utility function for the purpose of adapting the building of ‘Stara Polana’, located in Zakopane. Both in this publication and in [50
], a group of experts and specialists used a questionnaire to assess dependencies between factors that affect the criterion of societal benefits and the benefits associated with preserving cultural heritage. These were some of the parameters selected for analysis and rating in association with the investigated alternative forms of adaptive reuse of the Stara Polana heritage site in Zakopane. The remaining parameters, associated with, among others, acoustics, vibrations or thermal comfort, were studied using specialist technical instruments. These interdisciplinary studies became a basis for a multi-criteria analysis performed using a proposed hybrid model of selecting a form of use for a heritage site adaptation project.
1.4. The Significance of the Method Proposed in the Article
The innovative method proposed in this paper is an important contribution to the professional toolkit of designers and can significantly aid real estate developers in tailoring their offering. The method presented by the authors includes elements and criteria that are important during many stages of the design process: the conceptual urban design and site plan stage, the conceptual and technical architectural stage, as well as the structural system design and building services design stages. It also pertains to project cost assessment in the context of building single-family residential NZEBs, which are an important part of the housing sector. This approach can be considered a holistic perspective of the design task and the project as a whole, which is both necessary and desirable from the point of view of sustainable design. The necessity of this approach has been confirmed by, among others, Garau and Pavan [51
] in a broader context.
The method developed by authors assumes a multi-criteria analysis that includes aspects of sustainability, as well as the costs of the construction and occupancy of a complex of single-family houses. Sustainability parameters, such as the energy demand of the buildings and greenhouse gas emissions (depending on the given building variants and their siting) have been determined through analyses using the EnergyPlus tool [52
]. The energy analysis took the life-cycle stages of the buildings into consideration. The cost parameter was determined by including direct and indirect costs, the costs of construction (taking technological and organisational constraints into consideration), as well as the costs of building occupancy—the authors performed calculations for different building types and urban layout alternatives. Indirect and direct costs, as well as construction costs, were determined using a specifically-tailored optimisation model and the concept of priority scheduling. Occupancy costs were calculated using energy demand and the discount rate. Using previously selected parameters as a basis, the authors carried out a multi-criteria analysis using the Weighted Aggregated Sum Product Assessment method (WASPAS). This made it possible to determine the optimal solution for the problem in question.
3. Case Study—Housing Complex in Mogilany near Krakow, Poland
The planned housing complex which is the subject of the case study in this article is planned to be built on a 3-hectare plot in Libertów, in the municipality of Mogilany near Krakow, in the Lesser Poland Voivodship (Poland). The site is adjacent to an expressway which leads in the direction of Zakopane, a popular tourist destination located in the mountains. There is a lot of traffic along this road, particularly during weekends and holidays. The location of the experimental housing complex has been shown in Figure 3
The site plan for the plot (MU1) has been shown in Figure 3
b. Figure 3
c shows an aerial view of the plot. The housing complex was assumed to be composed of 40 single-family residential buildings, with various building layouts (detached and/or semi-detached buildings).
Three proposals of the urban layout of the complex’s buildings were analysed (Layout A, B and C). They will be presented in Figure 4
. The expressway runs near the plot, to its south-east (SE). To the north of the plot is the direction towards Krakow, while from the south, to the holiday resort—Zakopane. The urban layouts that were analysed are a reflection of the preferences of persons who buy single-family houses in Poland in terms of their view of property desirability. Their selection is the result of the actual housing market situation in Poland. The proposed urban layouts are options that the developer offers for sale to their clients on the open market. The authors are aware of the precepts of sustainable design concerning the planning of small-scale urban complexes, but in this case the intent is to provide an iteration of the method for a more market-oriented approach. The authors do not rule out preparing a modification of the method that would feature other sustainability metrics in the future.
features a listing of the number of detached and semi-detached buildings for each layout alternative.
The housing complex will be composed of buildings with different floor areas and layouts. The types of individual buildings will be presented in Figure 5
The buildings under analysis were assumed to be built using timber framing technology with thermal insulation composed of wood wool. The ground floor plan, assumed to have a usable floor area of 110 m2
, in a detached building, is to be presented in Figure 5
a, and in a semi-detached building—in Figure 5
b. The geometric models of the buildings subjected to the analysis have been presented in Table 3
. B1 type buildings are linked with a common wall that separates the bathrooms of both buildings.
The cost of individual buildings was calculated based on “Biuletyn cen obiektów budowlanych (BCO) część I a—obiekty kubaturowe” (in English: Construction price bulletin, Part Ia—buildings) [71
]. It is a cost bulletin that lists the mean prices of buildings in Poland. The BCO can be used to estimate the cost of constructing buildings or their fragments for the purposes of cost assessment or preparing financial schedules for construction projects. Direct cost was assessed using the construction price bulletin and includes labour, construction materials and machinery. The completion time for individual works was estimated on the basis of available material costs catalogues. The values for completion times and costs were assessed for both types of buildings featured in the case under analysis. Table 4
includes the values for a detached building with a usable floor area of 110 m2
In order to determine the overall construction costs, the following parameter values were assumed:
indirect construction costs, estimated at 400 €/day; Indirect costs include the general costs of construction (wages for the site director, works managers, construction site infrastructure costs), as well as management costs (the cost of maintaining the project, company offices, costs of office work, etc.). Indirect costs were assessed as per the construction price bulletin. The bulletin lists the value of indirect costs at a level of ca. 15% of the total cost. The cost per day was calculated using an estimate of the project’s duration.
costs of failing to meet planned deadlines, estimated at 150 €/per day of delay; Penalties for failing to meet planned deadlines are defined in contracts between the developer and the buyer of the building. There is no official data on this subject and in the experience of the authors such penalties in Poland can range from 0.05% to even 1% of a contract’s value per day of delay. It should be noted that penalties amounting to 0.5% of a contract’s value per day are not considered unjustified by Polish courts of law. Furthermore, it should be noted that the penalty is not applied when the developer cannot be held responsible for the cause of the delay. It is impossible to factor in unforeseen events that can cause delays and for which the developer is not responsible during the construction planning stage, which is why this aspect was ignored in the paper. A penalty value of 0.2% per day per individual building was assumed in the paper.
it was assumed that agreements with some contractors specified penalties for failing to ensure the continuity of crew operation. For the third crew, a 150 € penalty for each day of pause in the work was assumed, with 200 € per day assumed for the fourth crew. The penalty value for failing to ensure crew work continuity is a direct result of contracts with specific contractors. If a contractor performs a highly specialised section of the work, these penalties will be higher. This is why the third crew, which was assumed to assemble the innovative roof structure, and the fourth crew, which was assumed to handle building services installation, were assigned such high penalties for work discontinuity.
it was determined that the first building is to be completed within 90 days. Every subsequent building was to be completed 14 days after the completion of the previous one. Planned deadlines are a direct consequence of contracts or agreements between potential buyers and the developer.
In addition, it was assumed that technological continuity was to be maintained between footing, foundation wall construction and insulation application, as well as the construction of load-bearing walls, decks, roof structure and roofing.
includes the standard and limit costs of construction work, as well as the standard and limit completion times for individual works.
The optimisation process produced schedules for each of the analysed layouts that were optimal in terms of cost. For layout A, an overall cost of 3034 thousand euro was obtained, along with an overall completion time of 629 days. For layout B, the costs amounted to 2928 thousand euro, while the overall completion time was 629 days. For layout C, the costs amounted to 3233 thousand euro and the overall completion time was 680 days. The completion time was taken into consideration when calculating the costs of failing to meet planned deadlines for each building.
The buildings under analysis were designed to have a timber frame structure. The external partitions of the analysed buildings were assumed to be built using timber framing technology. The technology selection was primarily dictated by the developer’s guidelines, who had the technical infrastructure enabling them to manufacture prefabricated timber elements. Figure 6
is to show a cross-section of the external wall.
U heat transfer coefficients [W/(m2
K)] for elements of the buildings’ envelope were calculated in accordance with the methodology outlined in [72
]. The U heat transfer coefficients have been listed in Table 5
, along with the standard requirements for NZEBs applicable in Poland [34
The windows of the buildings meet Polish requirements for NZEBs. They were partially fitted with external blinds. The geometry of the buildings was also subjected to optimisation. Their massing is simple and thermal bridges were minimised. Their orientation relative to the cardinal directions is determined by local development guidelines. The structure of the buildings, material choices and their mass were determined by the developer. The air-tightness of the external envelope of the buildings was assumed to be n50
= 1.5 [1/h]. In Polish regulations concerning building design [34
] there are two requirements concerning building air-tightness. For buildings with gravitational ventilation it is a value of 3.5 air exchanges per hour [1/h], while for buildings with mechanical ventilation, the number of air exchanges per hour is 1.5 [1/h]. This is why the authors assumed a value of 1.5 [1/h]. The analysis was performed during the buildings’ design stage. At present, the first buildings have already been built. Air-tightness inspections performed on site indicate that the precise construction of the buildings has ensured a much greater air-tightness than initially assumed during the design stage. The air-tightness achieved during construction has a value of n50
= 0.6 [1/h], and is at a level expected of passive buildings [34
]. The internal temperatures were assumed in accordance with the PN-EN 12831 standard [74
Occupancy-related (metabolic) gains were defined in accordance with the ASHRAE 140/BESTEST standard [75
], depending on the form of use of the spaces.
The buildings were assumed to be equipped with mechanical supply and exhaust ventilation with heat recovery. Supply air streams were assumed as in [76
The Central Heating installation was designed in the form of gas-powered heating using a dual purpose gas-powered condensation boiler with a total efficiency rating of 0.95.
The indoor air temperature was assumed per PN-EN 12831:2006. Instalacje ogrzewcze w budynkach—Metoda obliczania projektowego obciążenia cieplnego—a Polish standard for heating installations governing methods of calculating heat loads during the design stage [74
]. Per this standard, spaces for permanent occupancy by persons without outdoor clothing should be designed to have a temperature of +20 °C, while spaces meant for occupancy by persons potentially without clothing (such as bathrooms), should have a temperature of +24 °C. This temperature difference can be obtained by properly setting a building’s thermostats or by using BMS installations. Concerning the schedule, it was assumed that such temperatures should be kept 24 h per day throughout the entire year. In residential buildings with building automatics systems it is much easier to assume periods of lowered temperature (e.g., at night) or when residents leave the building to work. However, most buildings in Poland do not feature elaborate BMS installations. The analyses assumed the buildings to have such systems, which is why no temperature drops were accounted for.
Design Builder Software uses Occupancy model data which defines the number of people in a space and occupancy times according to a set schedule. The Occupancy schedule setting is also used to control internal gains and/or HVAC systems. In DesignBuilder, schedules can be used to define:
For the purpose of the simulation, the authors used a slightly modified Design Builder template with default data for residential buildings occupancy was used, to better reflect Polish living conditions, hours of work etc.
Lighting was designed in compliance with the PN-EN 12464-1:2012 standard [77
]. Lighting was assumed to be energy-efficient, with a value of 3.3 [W/m2
] per 100 [lux]. The lighting intensity level was assumed as in [78
The remaining parameters were assumed in accordance with the principles of construction, technical knowledge and applicable standards.
6. Discussion and Conclusions
The results presented in Table 13
can aid the decision-maker in making decisions in selecting an architectural design alternative. The results were obtained for weights as defined by the developer and formulated to their individual preferences. An initial analysis of standardised values can provide valuable information about each alternative. Alternative B appears to clearly outrank the two other alternatives (highest value in four parameters). It also appears that alternative A is better than alternative C, as it has higher
scores in all parameters except thermal comfort. The WASPAS method confirms this analysis. Alternative B was selected as the best, followed by alternative A, with alternative C ranked the lowest. The differences in
scores were not significant (a difference of 1.5% and 2.8% relative to alternative B, for alternatives A and C, respectively).
An analysis of different weight values on the final results of the overall analysis was also performed (see Table 14
). Generated with a uniform distribution, the weights and values from the Case Study were used to calculate
score values in the WASPAS method. Statistically, alternative B was indicated to be the best (it ranked first in 80% of cases). Of note is that alternative C (ranked first in 20% of cases) was shown to be markedly better than alternative A (no first ranks). Therefore, it can be concluded that alternative A was dominated by alternatives B and C, which indicates that it can be excluded from the decision-making process. Alternative C outranked alternative B when a sufficiently high value (ca. 0.3) was assigned to the weight associated with thermal comfort. It is interesting that alternative B received the lowest rank in 10% of cases. It was even outranked by alternative A when thermal comfort was assigned a weight with an appropriately high value (ca. 0.3) and urban layout assessment was assigned a low value (ca. 0.05). However, alternative C was shown to outrank the remaining alternatives each time when this was the case.
In the presented Case Study, only three alternatives of the design of the housing complex were formulated. The proposed model can be used to support decision-making problems with a greater number of alternatives. The method can also support the decision-maker in rejecting dominated alternatives, reducing the number of analysed alternatives.
It should be noted that analysing such complex cases, which incorporate parameters with different units, value ranges and significance, is impossible without using multi-criteria analysis methods. Despite the significant contribution of these methods to analysis, the decision-maker is irreplaceable. It is up to the individual to quantify their preferences and expectations and it is they who make the final decision. The method presented in the paper can only support them in this.
The work presents pioneering research associated with formulating a method of determining the optimal urban layout of a complex of single-family houses. The study took various cost factors into consideration. The method presented in the article is compliant with the concept of sustainable development. The article does not refer to the results of the work of other scholars as no direct counterparts were found in the literature. The discussion presented in the article covers the results of a multi-criteria assessment meant to aid in the selection of an optimal urban layout of timber single-family houses while taking different types of building layouts into account. The discussion concerning the results of the study took into consideration energy demand, the direct costs of construction and its organisation, occupancy costs, thermal comfort, energy consumption, greenhouse gas emissions and the results of a survey concerning preferences as to the proposed architectural and urban layouts conducted among potential home buyers. The authors assumed a goal function in the form of a sum of all essential costs, which, along with the constraints, is linear. The Simplex method was used to solve the linear model. Sustainability parameters were determined through analyses employing EnergyPlus code. Afterwards, using the procured data, a multi-criteria optimisation was performed, using the WASPAS method. The results of this optimisation made it possible to report a solution that can be considered optimal in light of the adopted assessment criteria.
Future Research Directions
Future analyses should automatically include the possibility of selecting construction materials, the shape of the buildings themselves and their placement. The user would define permissible alternatives and a computer program would, through discrete optimisation, set parameters that could prove useful in multi-criteria optimisation.