A hybrid approach using AHP–TOPSIS–entropy methods for sustainable ranking of structural materials

Abstract

Nowadays, many countries are looking towards sustainability as a goal because our world has limited resources and serious environmental impacts. In the construction industry, the process of sustainable selection of structural material is considered one of the keys to achieve more sustainable construction. In this paper, the theories of decision making are utilised to develop an approach for evaluation and ranking the structural materials over their total life based on sustainability criteria using multi-attribute decision-making methods. One of them is Analytical Hierarchy Process which is utilised to build the problem hierarchical structure and assign weights of the predetermined sustainable factors. The other is Technique for Order Preference by Similarity to the Ideal Solution which is utilised to rank the structural materials within both each material life cycle phase and the complete material life cycle phases. The third is the concept of entropy by Shannon to evaluate the weight factor for each phase of material life cycle. The proposed approach presents an objective, systematic and comprehensive method for the sustainable ranking of materials that links between the structural element design and the sustainable selection of materials.

Keywords:

• multi-attribute decision making
• structural materials
• sustainability

1. Introduction

Due to the increasing interest in sustainable construction, engineers are motivated to select materials that are more sustainable. However, it is not a straightforward due to the multiple and conflicting criteria which increase the complicity of this selection process (Obla 2009). Therefore, engineers need to be assisted by decision analysis methodologies to help them in the decision-making process related to evaluation and selection of the materials. This process can be classified as multi-attribute analysis problems such as different types or real-life problems in management practice. Multiple attribute decision-making (MADM) methodology which is aimed at improving decision quality can play an important role in that decision-making process because it can address the different characteristics of sustainability criteria and aid in evaluating competing alternatives defined by their multiple attributes (Yoon and Hwang 1995, Omann 2004).

Sustainability is concerned by making a balance for the natural resources with the environmental, social and economic requirements of the human society. The Institution of Civil Engineers defined sustainable development as ‘a process that enables all people to realise their potential and improve their quality of life in ways that simultaneously protect and enhance the earth's life support systems’ (ICE 2002). Sustainable development related to the construction industry involves the efficient allocation and use of natural resources, reduction in consumed embodied energy, minimise pollution, reuse and recycling materials, alleviating poverty, creating healthy and safe working environment, facilitating employment creation, developing human resources and uplifting financial benefits (Yang et al. 2005, Ding 2008).

Sustainability is an issue that has a great importance for society and for construction sector because 50% of material resources taken from nature are building related, over 50% of national waste production comes from the building sector and 40% of the energy consumption in Europe is building related (Anink et al. 1996). Making construction activity sustainable is a major challenge due to the limited resources and serious environmental impacts of the world (Rameezdeen and Manewa 2006). Therefore, the department of trade and industry recommended making decisions about construction projects based on sustainable whole life value (DTI 2006).

The structural material is defined as the material, which is used to make those parts of the structure that carry the load and give it strength and stability such as steel, concrete or stone. For instance, in a steel-framed office building, the steel is the structural material (Francis 1989).

Multi-criteria decision making is a well-known branch of decision making that deals with decision problems under the presence of a number of decision criteria. This paper presents an approach using this technique that is based on sustainability criteria to evaluate and rank the structural materials.

2. Problem definition

Engineers have choices of the structural materials they use to design structures. However, recently many structural materials that have long been used in the construction industry are being replaced by newer or improved materials. Therefore, civil engineers are faced with an ever-growing number of choices for use in the construction industry. In addition, the number of possible combinations and configurations of structural materials is too large for engineers to be able to find optimal solutions.

In fact, engineers have turned their attention to developing material selection systems because they know that the correct material selection is an integral part of good design. However, there is a major problem with the quality of the decision-making process regarding the evaluation and selection of the optimum sustainable structural materials due to the following reasons:

•	Most developed strategies for selection of materials are based on the combination of physical and mechanical properties regardless of the sustainability basis.
•	The few methodologies that are concerned with sustainability used only a single dimension, that is the environmental impact. Sometimes, cost factor may be combined.
•	Presenting the sustainability information for each material has a bias due to adopting a specific material to present it as the most sustainable one.
•	The structural design process is not linked by sustainability requirements.

3. Objectives and limitations

The objective of this paper is to utilise the theories of decision making using the multi-criteria decision analysis methods to develop an approach for evaluation and ranking the structural materials on a sustainability basis over their total life. This approach is limited to structural elements and systems of buildings.

4. Methodology

a.

Evaluation criteria: • Defining sustainability as the evaluation criteria by assigning sustainable factors related to the structural materials, phases of material total life and the sustainability measurements. It is based on a literature review related to sustainable construction and materials, sustainability. • Defining life cycle assessment (LCA) method as a tool that can be used to achieve sustainable development. In addition, review the buildings' environmental assessment methods as well as existing LCA tools to present the technique used and their limitations.

b.

Development of the MADM approach: • Review the different types of MADM methods to determine the limitations, application fields, advantages and disadvantages for each method in order to select the appropriate MADM methods for the defined problem including the criterion weights and decision rules. • Build the hierarchical structure of the problem by dividing the problem into small items: relative weights of sustainable factors, relative weights of phases of the material life cycle and the decision rule for ranking of the structural materials. • Prepare the procedure chart of the developed MADM approach to demonstrate its framework and how it works. • Approach testing and verification by applying it on a numeric application.

5. Sustainable construction

Nowadays, sustainable development is a goal for many countries. Sustainable construction is considered as a key concern in order to achieve this goal (Rajagopalan 2007). The key themes that can form a framework for the sustainable construction criteria are as follows: design for change, design for minimum waste, aim for lean construction, minimise energy use, reduce pollution, preserve and enhance biodiversity, conserve water resources, respect people and their local environment (Corus 2006).

The following key areas were stated by the Chartered Institute of Building (CIOB 2003) as well as other studies – such as studies by Harrison (2005) and Ljungberg (2007) – to contribute towards a sustainable future for the construction industry:

•	Energy: reduce energy consumption, use renewable energy and increase energy efficiency.
•	Materials: reduce resource requirements (select recycle and durable materials).
•	Waste: produce less waste, recycle more and
•	Pollution: produce less toxicity, water, noise and reduce emissions.

A series of framework indicators have been established by governments to ensure that construction makes progress in all areas of sustainable development. These indicators cover many issues relating to construction (DTI 2006). A set of standardised key performance indicators (KPIs) were developed by industry and the DTI, with industry performance against the KPIs published annually. The existing industry KPIs are currently being extended in a number of areas (ICE 2002):

•	Environmental performances that cover operational energy, embodied energy, transport energy, water use, waste in the construction process and biodiversity.
•	KPIs for construction consultants that focus on client satisfaction, value for money, profitability, timely delivery, investment in training and health and safety.
•	Construction Products Industry KPIs that focus on customer satisfaction, people, environmental impacts, production and consumption of aggregates.

On the other hand, there are different approaches that have been developed to assist measuring the building sustainability. For example, the methodology developed by Seo et al. (2004) that used a fuzzy-set approach for evaluating sustainability of residential buildings under uncertainty. Another study by Yagi and Halada (2001) discussed the guiding principles for materials development towards a sustainable society from the viewpoint of environment and safety. It is concluded that it is important to define the goal of materials development under the consideration of total life of materials. In addition, it should be looking for the optimum solution to materials development by better selection of technology and systems.

Technology plays a very important role in sustainable development in the construction industry because it is one of the most significant ways in which we interact with our environment (Vanegas et al. 1995). Technology can play its role through one of the following areas: hard technology related to equipment and materials, soft technology such as systems, support decision making, monitoring and evaluation, and knowledge and information such as databases, benchmarks, guidelines, manuals and handbooks (Plessis 2007).

6. Life cycle assessment

6.1 Definition, steps and framework of LCA

An LCA is a methodology that attempts to assess the environmental performance of a product – such as a building – over its total life cycle by considering the flow of raw materials and energy into a system and relating them to the environmental impacts (Curran 2006). ISO 14040 regulation defines life cycle as the ‘consecutive and interrelated stages of a product system, from the acquisition of raw materials or the generation of natural resources until its final elimination’.

The LCA process is a systematic, phased approach according to the following four phases as per ISO Standard 14040 (Nebel 2006, Khasreen et al. 2009):

•	Goal definition and scoping that defines the product and identifies the boundaries.
•	Inventory analysis that identifies and quantifies energy, water and materials usage and environmental releases (e.g. air emissions, solid waste, etc).
•	Impact assessment that assesses the potential human and ecological effects of energy, water and material usage and the environmental releases.
•	Interpretation that evaluates the results of the inventory analysis and impact assessment to select the preferred product.

A life cycle inventory (LCI) is ‘a process of qualifying energy and raw material requirements, atmospheric emissions, waterborne emissions, solid wastes and other releases for the entire life cycle of a material’ (Curran 2006). LCI analysis is concerned with the data collection and calculation procedures. For most available data-sets, they have no transparency and they depend only on local and simple materials. Therefore, international data-sets have to be produced based on the results of accurate local data-sets (Khasreen et al. 2009).

LCA can be used both as a tool for assessments and a concept in evaluations. As a tool, it can study the required raw materials and energy in order to produce products as well as identify the discharges arises to air, water and soil to assess the environmental impact of it. As a concept, LCA can be used as a way of thinking about products from cradle to grave to assign priorities in finding a solution. Sustainability should be integrated in the building project under the consideration of its LCA (Mora 2007).

6.2 Environmental building assessment methods

In 1990, the Building Research Establishment Environmental Assessment Method (BREEAM) was the first such comprehensive assessment method for building performance. BREEAM assesses the performance of buildings in the areas of management, energy use, health and well-being, pollution, transport, land use, ecology materials and water (Corus 2006). After that, many other assessment methods have been developed around the world for environmental building assessment. For example, Building environmental performance assessment criteria (Canada-1993), Leadership in energy and environmental design (LEED) (USA-2000), Comprehensive project evaluation (UK-2001), Comprehensive assessment system for building environmental efficiency (Japan-2004), Eco-Quantum (Netherlands) and others worldwide.

Most of the environmental building assessment tools cover the building level, and are based on some forms of LCA database. Tools are in two categories: the first tool is the assessment tools that provide quantitative performance indicators for design alternatives. The other is rating tools that determine the performance level of a building using a star rating (Ding 2008). LEED is building rating tool in the USA which provides a complete framework for assessing building performance and meeting sustainability goals (Nebel 2006).

Actually, the current methods of environmental building assessment have a significant contribution in achieving the aims of sustainable construction development because the scores obtained for the evaluation indicate the building environmental performance. However, the following items present the weakness of these methods:

•	They only consider the environmental effects in a single tool which is not enough to assist in achieving the overall assessment of sustainable development.
•	Inflexibility, limitation and complexity of these methods.
•	Lack of consideration of a weighting system.
•	There is no clear basis for methods of awarding the maximum number of points to each criterion.

6.3 LCA tools

There are several building decision support tools that are based on the LCA concept around the world, for example, there are Envest in the UK, Eco-Quantum in the Netherlands and ATHENA in North America. Each tool uses a different modelling approach in a specific region. However, all of them consider the whole buildings in their assessment using LCI data to produce indicators of the environmental impacts of design alternatives (Trusty and Horst 2002). The following items present a review of the LCA tools for applications to buildings.

ATHENA is an LCA tool developed by the National Resources Canada for buildings. The model produces a detailed LCI for an entered design using six environmental measures. ATHENA's Environmental Impact Estimator is a whole building life cycle environmental assessment tool that allows the user to compare the relative environmental effects among alternative design solutions at the conceptual stage over the expected life of a building. However, it cannot calculate the operating energy use in a building and does not implement the weighting step in Life Cycle Impact Assessment (LCIA) (EMSD 2006).

Building for Environmental and Economic Sustainability (BEES) software includes environmental and economic performance data. The impact categories that BEES covers include the 12 categories. Users are provided with weighting factors obtained from a Science Advisory Board Study and a Harvard University Study and are also allowed to set their own weights. Furthermore, BEES performs life cycle costing, based on the US prices. However, BEES can only be used to compare the environmental and economic performance among the included building products. Its strengths are it is convenient, easy-to-use tool and allows user to evaluate environmental impacts as well as costs using life cycle perspective. Its weaknesses are that it is limited to North American data and data quality is questionable (Young et al. 2002).

Eco-Quantum is a commercial product developed by the IVAM in the Netherlands. It is a tool for analysing and developing innovative and complex designs for sustainable buildings and offices. It is an LCA-based tool intending to estimate the environmental effects of a building on the basis of energy and material flows. The final output will be given in the form of four environmental indicators (EMSD 2006).

Envest is a web-based program developed by the Building Research Establishment Ltd (BRE). It is a building design LCA tool which intends to help the users to compare the environmental and financial impacts associated with different building materials and building services systems. The final outputs will express 12 environmental impacts. Its strengths are as follows: it is configured for rapid and easy use, the UK data provided is maintained and updated by BRE using its environmental profiles, database collected with the help of both private and public stakeholders. Its weaknesses are the methodological choices for recycling which are already included in the database, thus their influence is not transparent and only contains the UK data (Young et al. 2002).

Building LCA tools can be classified as follows (Haapio and Viitaniemi 2008):

	Level 1: product comparison tools and information sources (e.g. BEES). This tool is used primarily at the procurement stage, may include economic as well as environmental or other data and may have LCA in the background.
	Level 2: whole building decision support tools (e.g. ATHENA, Eco-Quantum and Envest). These tools are typically intended for use by design team members at as early a stage as possible during the design phase.
	Level 3: whole building assessment frameworks or systems (e.g. BREEAM, LEED).

6.4 Assessment of environmental tools

Actually, building environmental assessment tools have been developed for different purposes. Therefore, they vary largely in goals, factors and the weights of these factors. The tools can assess both existing and new building and building products. The tools can assess different types of buildings: residential buildings, office buildings and other types of buildings.

Some of the tools can assess the whole range, whereas some of the tools can only be used for assessing new buildings or office buildings. The tools cover the life cycle of a building based on different guidelines and databases. The tools hand out different labels and certificates. In addition, different cultural factors and various regulations in different countries may complicate the situation. Building environmental assessment tools are not commensurable. The existing building environmental assessment should be transferred into sustainability assessment tools that include economic and social aspects in addition to the environmental aspect.

The comparison of the tools and their results is difficult because the field of building environmental assessment tools is vast. In general, using of these tools is not obvious for the following reasons (Haapio and Viitaniemi 2008):

•	It is difficult to determine where and when they should be used, and who should use them.
•	There is no obvious way to utilise the results from the assessment.
•	The selection of suitable tool for a certain building is not clear, and determining of the tool that can give the best results is unknown.
•	The uncertainties and margin of results' error are not indicated in the tools; therefore, the reliability of the results cannot be estimated.

The development of reliable LCI data requires considerable expert time inputs and expense. LCAs are generally considered to be too expensive and time consuming because of the lack of widely available, critically reviewed, comprehensive LCI databases. Although there are a few LCI databases available in the market, access to the information contained in them is generally restricted or protected by copyright agreements or the data are not verifiable. Public availability of the LCI data would make LCAs easier to carry out. Ultimately, a national database can then be established to serve the needs of the potential data (Çakmakli 2007).

There is a lack of the advancement in LCA for buildings rather than other industries. However, researchers are making an effort to enhance LCA to be used in the design phase as a decision-making support tool. LCA has limitations, however, it can be considered as a powerful tool to evaluate the environmental impacts on buildings. It can make a strong contribution to the sustainability goals (Khasreen et al. 2009).

7. Review for MADM methods

MADM means ‘Making preference decisions (e.g. evaluation, prioritisation and selection) over the available alternatives that are characterised by multiple, usually conflicting, attributes’ (Yoon and Hwang 1995). There are many MADM methods, the most often used are as follows: simple additive weighting (SAW), the value/utility function methods, ordered weighted average, outranking methods, the ideal point methods (Technique for Order Preference by Similarity to the Ideal Solution, TOPSIS) and analytical hierarchy process (AHP). Each method has its own characteristics, advantages and shortcomings. They differ in the complexity of use and the need of introducing additional subjective variables like weights. Mixed methods can be applied to various problems.

The comparative performance of some methods has been investigated in a few studies such as a simulation carried to investigate the performance of different methods: ELECTRE, TOPSIS, SAW and AHP. It is concluded that AHP behaves similarly and closer to SAW than the other methods. ELECTRE is the least similar to SAW. TOPSIS behaves closer to AHP and differently from ELECTRE, except for problems with few criteria (Zanakis et al. 1998).

AHP was developed by Saaty (1980) as a technique to analyse and support decisions in the complex problems related to the alternative's selection from several alternatives. It is based on structuring the problem in a hierarchical form. AHP reduces complex decision by transforming it into a series of simple comparisons and rankings, then synthesising the outcomes and helps the decision maker to obtain the best decision (Mahmoodzadeh et al. 2007). The AHP has widespread use due to its flexibility, ease of use, and it can even be implemented in spreadsheets.

The TOPSIS which was developed by Hwang and Yoon (1981) is one of the most popular ideal point methods. In the ideal point method, the alternatives are ranked according to their separation from an ideal point. It is based on the concept that the chosen alternative should have the shortest distance from the positive ideal solution and the longest distance from the negative ideal solution. TOPSIS is very easy to implement and a spreadsheet for large problems can easily be produced (Brown 2003).

Shannon entropy which also called informational entropy is defined by Shannon (1948). It measures a quantity of uncertainty with a probability distribution in terms of entropy (for the alternatives with respect to the decision metrics) considering all available information. Therefore, entropy can be used as a measure of uncertainty degree represented by the probability distribution and as a measure of the lack of information quantity about a system. In case of the availability of complete information, entropy = 0. Otherwise, it is greater than zero. The entropy theory is versatile, robust and efficient. It permits determination of the least-biased probability distribution of a random variable subjected to the available information (Singh 2000).

TOPSIS and AHP methods have been widely applied in various construction fields separately, combined, or even used under the fuzzy applications. For example, AHP as a decision-making method is used in project management to solve the problem of contractor prequalification and selection of the optimum contractor (Al-Harbi 2001, Moustafa 2001). Similarly, a hierarchical fuzzy TOPSIS method is applied for the evaluation and selection of suppliers in companies (Taghavifard and Mirheydari 2008).

In addition, AHP method is used to derive prioritised scales for the constructability factors and the relative contribution of construction systems in a building superstructure concluding that the precast method is the most constructible construction method due to its better performance, facilitating efficiency and safety (Patrick et al. 2007). Moreover, AHP is applied to identify the relative importance of the different factors that have an impact when deciding the proper project delivery option based on a high degree of technical factors and low construction costs (Mahdi and Alreshaid 2005).

Improved fuzzy AHP is integrated with TOPSIS algorithm to produce an approach to assess alternative projects and support project selection decisions (Mahmoodzadeh et al. 2007). Similarly, a fuzzy AHP is combined with the grey relation model based on the concepts of TOPSIS to determine the weighting of subjective judgements, fuzzy integral to derive the performance values of each host country alternative and select the best alternative (Chen and Tzeng 2004).

Another approach utilised the theories of decision making: one of them is the concept of entropy to evaluate the weight factor for each material property or performance index, and the other is TOPSIS to rank the candidate materials, for which several requirements are considered simultaneously (Jee and Kang 2000).

8. Sustainability criteria in the developed approach

Each problem has multiple attributes that may be referred to as ‘criteria’. The evaluation criterion of this approach is sustainable development that includes environmental, social, economical and technological aspects. The decision problem attributes are designed and presented as 10 sustainable factors related to structural materials based on Bakhoum thesis study (Bakhoum 2011) that developed and presented a flow chart for these factors. In addition, the sustainability of materials is linked with the design of the structural element and defined through the consideration of total life of materials by dividing the life cycle of structural materials into three phases: manufacturing, construction and demolition. Figure 1 presents the hierarchical structure of the problem and the used evaluation criterion.

Figure 1 System hierarchical structure.

Most of decision-making problems for material selection have two dimensions: the evaluation criteria (attributes) and the alternatives (materials) that formulate the matrix. However, the problem of this approach has the following three dimensions as presented in Figure 2:

Figure 2 Dimensions of the sustainable MADM problem.

•	The sustainable factors which represent the problem evaluation criteria.
•	The phases of material life cycle.
•	The structural materials which represent the problem alternatives.

The sustainable factors include climate change, pollution, energy consumption, resources and waste, life cycle cost, recyclability, local economic development, health and safety, human satisfaction and practicability. This list of factors includes two groups. The first group includes five factors related to structural element design and linked to the design phase by depending on the structural element design (weight of the structural element). The second group includes five factors related to general material properties.

Complete life cycle analysis is a key point of materials development. Therefore, it is necessary to understand the material's properties and establish the method of material evaluation under consideration in total life. Therefore, the material life cycle is divided into three phases according to the developed sustainable scoring system developed by Bakhoum and Brown (2012). Manufacturing phase starts from extraction of raw materials and embraces all the processes for producing the structural material and its components. This phase include material extraction, transportation and manufacturing. Construction phase corresponds to the construction of a building including the material transportation to the construction site. Demolition phase starts from the occupation of a building and lasts until the building is demolished. This phase includes material maintenance, repairing and finally demolition. The demolished material may be reused, recycled or land filled. Transportation of demolished material is included in this phase.

The sustainability of materials can be measured using either percentage values or LCI values for the predefined sustainable factors concerning each material. In the case of using LCI values, maximum and minimum LCI values for each sustainable factor should be determined to enable the model to convert these values to percentage values.

9. Criterion weights

9.1 Review for previous weights of LCA tools

Many studies and methods established the weights for the sustainable factors of different impact categories such as USEPA and Harvard studies as well as BEES, Envest and BREEAM methods.

For example, the weight sets derived in an EPA Science Advisory Board study and a Harvard University study in the USA are provided in the BEES manual. Both of them used the AHP as a multi-attribute decision analysis method to establish numerical importance weights. The major differences of these two studies lie on the number of impact categories used and the number of countries from which people are being surveyed (EMSD 2006, Lippiatt 2007).

In addition, the BREEAM standard (BES 5058) produced weights for the major environmental issues that affect buildings throughout their operational life. This standard enables provision of information about the environmental performance of the building, the building operation and the organisational rating (BRE 2011). Moreover, BRE has produced the weighting scheme for Envest II through consultation with a cross section of interested parties. These weighting factors are used to produce a UK Ecopoints score.

Data from these studies/methods were investigated and analysed to determine the pairwise comparison values. These values were expected to be used as an input of the pairwise comparison matrix in the AHP method to calculate the relative weights of sustainable factors. However, from the results of this analysis, it appears that the values cannot be used directly for the following reasons:

•	There is a significant difference between the different methods in determining the relative importance between the factors, i.e. the range between the maximum and minimum values is very wide.
•	There is no consistency ranking between the different factors.
•	The data from these methods do not cover all sustainable factors. Only some environmental factors are covered. For example, cost, practicability and local economic development factors are not considered in any method. In addition, the factors covered may include only one sub-factor. For example, the raw material consumption sub-factor in resource use is not considered in USEPA, Harvard or BEES.
•	The collected data are general and not specified for a specific phase. Therefore, it cannot be divided into the three phases of material life. Moreover, it does not concern the material itself but the building.

Consequently, the data collected from previous studies and methods can only be used as guidance.

9.2 Determined weights for the approach

A weight can be defined as a value assigned to an evaluation criterion that indicates its importance relative to other criteria under consideration (Yoon and Hwang 1995). Many methods can be used to calculate the relative weights. Depending on the nature of the problem, pairwise comparison and entropy are selected in the proposed model to determine weights. Pairwise comparison is used to assign weights to the predetermined sustainable factors related to structural materials. The entropy is used to evaluate the weight factor for each phase of material life cycle.

In the pairwise comparison method, a ratio matrix is created using pairwise comparisons as input and produce relative weights as output. Input data of the ratio matrix are calculated based on the level of importance scale developed by Bakhoum (2011). The advantages of this method are that only two criteria have to be considered at a time and it can be implemented in a spreadsheet environment.

The entropy is applied in this model because the pairwise comparison method could not be applied to the material phases as there is no basis to compare and determine their weights. Therefore, the entropy method is used to calculate the entropy-based weights, which are variables depending on the results of the TOPSIS method for each phase. In entropy-based weights, if all of the alternatives have the same value in one of the decision metrics, its ‘entropy’ is maximised. If a metric is at maximum ‘entropy’, it is of no importance to the decision-maker since each of the alternatives is indifferent. Alternatively, a metric well below its maximum entropy implies that the alternatives are highly differentiated and, therefore, have a higher relative importance weight. It follows that the relative importance weight of a given metric is inversely proportional to its entropy.

10. Decision rules

The overall evaluation of alternatives is provided by integrating the weightings into a suitable decision rule. The decision rule provides an ordering of alternatives based on their performance with respect to the criteria (attributes). Based on the review of different types of decision rules, AHP and TOPSIS are selected to formulate the decision rules of the developed MADM approach.

The TOPSIS method was used to rank the alternatives (structural materials) according to the evaluation criteria. TOPSIS is selected as one of the known classical MADM methods. It provides an attractive mechanism in which it follows automatic machine learning principles, because it can consider a number of attributes in a systematic way without very much subjective human input. Data, whether discrete or continuous, are standardised to a range between 0 and 1. In addition, it provides a complete ranking and information on the relative distance of each alternative to the ideal point showing how much better one alternative is than another.

However, the classical TOPSIS methods cannot support the hierarchy concept. AHP is the only technique that considers hierarchical structure for criteria and sub-criteria. Therefore, the AHP was used to build the problem hierarchical structure and to assign the relative weights of the sustainable factors using the pairwise comparison method. Consequently, a hybrid of AHP, TOPSIS and entropy theory are used to formalise the framework for the approach to achieve its goal for sustainable material selection. In the proposed model, the sustainability of materials is linked with the design of the structural element and defined through the consideration of total life of materials.

11. Model procedure

Figure 3 presents the procedure chart for the developed MADM approach that has the following steps.

Figure 3 Model procedure chart.

11.1 Step 1: building the system hierarchical structure

The AHP method is used to build the problem hierarchical structure that is presented in Figure 1. In this hierarchy, the top level is the main goal of the decision and then it decreases from the general to more specific as follows: the phases of structural material life cycle, the sustainable factors related to the structural materials and the alternatives (structural materials).

11.2 Step 2: relative weights of sustainable factors

In this step, the AHP is applied using the pairwise comparison method. It is applied to determine the relative weights of sustainable factors for each phase of material life cycle. It starts by developing a pairwise comparison matrix for the sustainable factors, then applying the calculation procedure of the method ending by checking the consistency ratio (CR). This step should be repeated for each phase of material life.

11.3 Step 3: measurement of sustainability of materials

In this step, the sustainability of materials is calculated as percentage scores for all sustainable factors to be used in the TOPSIS method in the next step. The model has the ability to consider the sustainable scores of structural material in either of the following two ways: using the percentage values or the actual LCI values of materials. In the second case, the model can compile these values to percentage values using the defined maximum and minimum LCI values for each sustainable factor.

For the first five factors that relate to the design of structural elements, the percentage scores for the designed structural element can be calculated as follows:

•	From structural design process, calculate the dimensions of the designed structural element by each material (alternative) and calculate the structural element weight (w i ). Then, get the maximum value of the structural element weights (w max).
•	In case of w max >1000 kg, the normalised weight ‘W i ’ is calculated as follows: Otherwise, .
•	In the case of using the LCI number (L), the percentage sustainable score regarding the unit of material (P) can be calculated as follows: where M is the maximum LCI value, N the minimum LCI value and T the LCI step value.
•	The LCI number for the designed structural element (L SE) can be calculated as follows:
•	The percentage sustainable score for the designed structural element (P SE) can be calculated as follows: where N is the MSMS minimum value of LCI number.

Finally, this step should be repeated for each phase of material life cycle.

11.4 Step 4: sustainability ranking of materials for each phase

In this step, TOPSIS is applied to determine sustainability ranking of materials by calculating the materials (‘alternatives’) relative closeness to the ideal solution for each phase of material life cycle. It starts by developing a matrix of each structural material with two virtual materials (alternatives) and the sustainable factors (attributes) using the final percentage score of sustainable factors for the alternatives (resulting from Step 3). In addition, it utilises the weights of sustainable factors (resulting from Step 2).

Furthermore, the calculation procedure of the TOPSIS method is applied ending by getting the Rank Preference Order for the alternative according to maximum Relative closeness to the ideal solution (R⁺) for each alternative (material).

Two virtual alternatives are added to the list of alternatives (materials) to fix both positive and negative ideal solutions to their extreme values that are ‘1’ and ‘0’, respectively. One of them presents the best sustainable material that has a score ‘100%’ in all sustainable factors. The other alternative presents the worst sustainable material that has a score ‘0%’ in all sustainable factors. These two alternatives are out of ranking. The main objective of adding these extreme alternatives is to ensure R⁺ (relative closeness to the ideal solution number) for each material is reliable and can indicate the sustainability of material without relation to the other accompanying alternatives. This step should be repeated for each phase of material life cycle.

11.5 Step 5: relative weights of material life cycle phases

In this step, the entropy by Shannon is applied to determine the relative weights of material life cycle phases. It starts by developing a matrix of the alternatives (structural materials) and the phases of material life cycle utilising the relative closeness to the ideal solution that resulted from Step 4. The weight factor to each of material life cycle phase is as follows:

where m is the number of alternatives (structural materials)

where E is the entropy of normalised values

where w is the weight factor of the material life cycle phase.

11.6 Step 6: final sustainability rank of materials

In this step, TOPSIS method is applied to calculate the relative closeness to the ideal solution for each material and determine the final material sustainability rank. It starts by developing a matrix of the structural materials (alternatives) and the phases of material life cycle (attributes). It utilises the weights of phases (resulting from Step 5) and the relative closeness to the ideal solution (resulting from Step 4). Furthermore, the calculation procedure of TOPSIS is applied ending by getting the final Rank Preference Order for the alternative according to maximum Relative closeness to the ideal solution.

12. Numeric application of the proposed approach

The proposed model is applied to three common structural materials (alternatives): reinforced concrete (RC), steel and Glulam timber. The structural element considered is a simple beam which is designed for the three alternatives using the same loading conditions for a span of 6 m. The weights of the beams designed by each material are (W _RC = 1800 kg; W _Steel = 402 kg; W _Glulam = 410 kg).

Table 1 presents the development of the pairwise comparison matrix for the sustainable factors as well as the computation of the sustainable factors weight (for Phase I). Then, lambda (λ), consistency index (CI) and the CR are calculated where λ = 11.17, CI = 0.13 and CR = 0.09.

Table 1 Calculation of sustainable factors weights.

	SF1	SF2	SF3	SF4	SF5	SF6	SF7	SF8	SF9	SF10
Pairwise comparison matrix
SF1	1.000	1.250	0.952	1.300	1.200	1.050	1.450	1.500	1.550	1.350
SF2	0.800	1.000	0.769	1.050	0.952	0.833	1.200	1.250	1.300	1.100
SF3	1.050	1.300	1.000	1.350	1.250	1.100	1.500	1.550	1.600	1.400
SF4	0.769	0.952	0.741	1.000	0.909	0.800	1.150	1.200	1.250	1.050
SF5	0.833	1.050	0.800	1.100	1.000	0.870	1.250	1.300	1.350	1.150
SF6	0.952	1.200	0.909	1.250	1.150	1.000	1.400	1.450	1.500	1.300
SF7	0.690	0.833	0.667	0.870	0.800	0.714	1.000	1.050	1.100	0.909
SF8	0.667	0.800	0.645	0.833	0.769	0.690	0.952	1.000	1.050	0.870
SF9	0.645	0.769	0.625	0.800	0.741	0.667	0.909	0.952	1.000	0.833
SF10	0.741	0.909	0.714	0.952	0.870	0.769	1.100	1.150	1.200	1.000
Sustainable factors weights
Weights (%)	12.27	9.95	12.76	9.53	10.39	11.78	8.39	8.05	7.74	9.13
Note: SF, sustainable factor.

Table 2 presents the alternatives' sustainable percentage scores for each factor per unit of material and their final percentage scores for the designed structural element.

Table 2 Calculation of sustainable scores for TOPSIS matrix.

	SF1	SF2	SF3	SF4	SF5	SF6	SF7	SF8	SF9	SF10
Percentage score of sustainable factors per unit of material
RC	93	91	95	77	97	6	50	88	50	50
Steel	31	36	32	38	61	49	50	88	50	63
Glulam	74	38	59	75	00	00	50	88	50	100
Final percentage score of sustainable factors for the designed structural element
RC	93	91	95	77	97	6	50	88	50	50
Steel	85	86	85	86	91	49	50	88	50	63
Glulam	94	86	91	94	77	0	50	88	50	100

After identifying the positive and negative ideal solutions, the separation measures (S⁺ and S⁻ ), the relative closeness to the ideal solution (R⁺) and the Rank Preference Order should be calculated. All these calculations should be repeated for both phases II and III. Table 3 presents the calculated S⁺, S⁻ , R⁺, phases weights and rank for each phase and overall.

Table 3 Alternatives' rank by TOPSIS.

	S^+	S^−	R^+				Rank
Phase	I		I	II	III	Overall	I	II	III	Overall
RC	0.11626	0.20099	0.54	0.58	0.72	0.54	2	3	3	2
Steel	0.06218	0.18606	0.69	0.65	0.79	0.69	1	1	1	1
Glulam	0.12507	0.20191	0.53	0.62	0.74	0.52	3	2	2	3
Phases weights by entropy
	Phase I		Phase II				Phase III
Weights (%)	81		10				9

That numeric application is presented as an example to demonstrate the model calculations and verify it. It can be seen that RC has better sustainable scores than steel and Glulam as a unit of material. However, functionally steel has better sustainable scores than RC because it has a smaller weight of the designed structural element. Therefore, the steel beam has better sustainable scores than the RC beam that has better sustainable scores than Glulam. It can be noticed that the steel has better sustainable scores than RC and Glulam during the three phases and RC is little better than Glulam in phase I only. In addition, phase I has the highest weight due to the higher difference between alternatives in R⁺ in this phase.

Note: the details of structural design and sources of LCI data for alternatives as well as full system testing and verification including comparing studies are presented in the study thesis by Bakhoum (2011).

13. Conclusion

As the decision analysis is a set of systematic procedures for analysing complex decision problems (Zanakis et al. 1998), the decision problem – in this paper – is divided into smaller more understandable parts, analysing each part and integrating the parts in a logical manner to produce a meaningful solution.

The sustainable criteria are utilised as the attributes in the MADM approach to move towards sustainable construction which is a key part of the global sustainability of society. LCA is a good and useful tool for understanding the impact on the environment; in addition, it is considered as a key tool to the achievement of sustainable development (Ljungberg 2007).

The proposed MADM approach presents an objective, systematic and comprehensive method that utilises the theories of MADM based on the sustainability evaluation criteria for ranking and selection of structural materials during the initial phases of construction projects. The proposed approach links between the structural element design and the sustainable selection of materials.

MADM methodology that provides a useful index from multidimensional data to evaluate competing alternatives is a suitable tool for evaluation and ranking of materials based on multi-criteria of sustainability. A combination between AHP (including pairwise comparison method), TOPSIS and entropy is selected as the most appropriate tool for the proposed model due to limitations in each method separately. Moreover, the advantages of each method have been gained such as the hierarchical map and weights by AHP, the complete ranking and information on the relative distance of each alternative to the ideal point by TOPSIS and the phase weights that based on TOPSIS results from entropy theory.

Additional information

Notes on contributors

David C. Brown

1

Notes

1. [email protected]