Implementing Sustainability Criteria for Selecting a Roof Assembly Typology in Medium Span Buildings

Canto-Perello, Julian; Martinez-Garcia, Maria P.; Curiel-Esparza, Jorge; Martin-Utrillas, Manuel

doi:10.3390/su7066854

Open AccessArticle

Implementing Sustainability Criteria for Selecting a Roof Assembly Typology in Medium Span Buildings

by

Julian Canto-Perello

¹,

Maria P. Martinez-Garcia

²,

Jorge Curiel-Esparza

^3,* and

Manuel Martin-Utrillas

³

¹

Department of Construction Engineering and Civil Engineering Projects, Universitat Politecnica de Valencia, 46022 Valencia, Spain

²

Department of Applied Physics, Universitat Politecnica de Valencia, 46022 Valencia, Spain

³

Physical Technologies Center, Universitat Politecnica de Valencia, 46022 Valencia, Spain

^*

Author to whom correspondence should be addressed.

Sustainability 2015, 7(6), 6854-6871; https://doi.org/10.3390/su7066854

Submission received: 27 March 2015 / Revised: 5 May 2015 / Accepted: 21 May 2015 / Published: 28 May 2015

(This article belongs to the Special Issue Green Building)

Download

Browse Figures

Versions Notes

Abstract

:

Technological advances have allowed the development of new roof assembly typologies with higher efficiency and less waste. However, in the construction sector the focus is generally on reducing cost and not in sustainable development factors. Short-sighted building planning based only on economic criteria should be avoided improving decision support systems. In addition, the selection of an appropriate roof assembly in a building’s design stage is a complex problem due to the existence of different tangible and intangible factors and the multiple alternatives available. The roof typologies under study involve prefabricated concrete, steel and laminated wood structures. This research work applies a multi-criteria hybrid model combining the Analytical Hierarchy Process with the Delphi method and the VIKOR technique for implementing sustainability criteria in the selection of a roof assembly in medium span buildings. The proposed decision support system enables the use of the triple bottom line that considers economic, social and environmental criteria. Under the criteria analyzed, the compromise solution found is the self-supporting curved system.

Keywords:

roof assembly; triple bottom line; multicriteria decision making

Graphical Abstract

1. Introduction

Buildings account for forty percent of total energy consumption in Europe [1]. Therefore, the reduction of energy consumption in the buildings sector constitutes a key measure needed to improve the efficient energy use, greenhouse gas emissions, and will contribute towards fulfillment of the Kyoto Protocol [2]. For this reason, there is an increasing interest in studying sustainability [3,4,5] in the field of building design, mainly in residential and office buildings [6]. In this sector, the facade assembly chosen is the major design factor. However, when the function of the building requires greater spans than the ones used more commonly in this kind of building, the most important decision is the roof, not the facade. The roof typology chosen will determine the rest of the elements of the building: vertical structure, foundation, facades and building systems.

The choice of an assembly is the most important decision with long-term consequences and it must be made in terms of sustainability, not only taking into account the traditional bottom line reference to one metric (financial performance or cost), but also maintaining an interest in the triple bottom line that refers to the consideration of economic, social, and environmental concerns [7,8,9,10]. In addition, progressive industrialization, technological advances and innovation, both in materials and construction techniques, have allowed the development of new solutions to be used in each of the building’s elements. Efforts to achieve sustainability must include innovation to all types of infrastructure [11]. However, construction is a sector that accepts innovations slowly. Therefore, a decision-making model for the assessment of technological solutions will facilitate the design and construction of sustainable buildings.

The selection of the appropriate building assembly is a complex decision-making problem because many alternatives and multiple selection criteria exist. For example, the cost of the materials depends on the energy used for its manufacturing. This energy determines the environmental impact. Thermal insulation influences the operating energy and a better insulation decreases the impact on the environment. This complexity often makes it difficult to decide on which alternative outweighs the others. A multi-criteria model and different techniques provide the means to solve the problem. Collier et al. [12] appointed the use of multi-criteria decision analysis with the triple bottom line for sustainable roofs. The novelty of this research work is the proposed hybrid decision-support system integrating the Analytical Hierarchy Process (AHP) with the Delphi method and the VIKOR technique (see Figure 1). The different criteria considered will be economic, social and environmental. Each of these, with their different weights, will be analyzed in relation to the possible alternatives. Decision support systems have been widely used in analyzing different building and environmental issues. The AHP is a theory of relative measurement on absolute scales, capable of dealing with intangible criteria and based on the paired comparison judgment of experts [13,14,15,16,17]. The Delphi technique is well suited for consensus-building by using a series of questionnaires to collect data from a panel of experts [18,19,20,21]. A systematic expert panel assessment process is carried out using Delphi Method and AHP as shown in Figure 1. Expert panelists were invited to participate according to their knowledge and experience in construction and environmental engineering. The experts are required to be chartered engineers and have applied experience in the building sector. The expert assessment process is supported by three surveys, the first is an open questionnaire while the second and third are based on pairwise comparisons with linguistics terms as illustrated in Table 1 and Table 2. The resulting values from experts’ answers in the form of linguistic terms are shown in Table 3 and Table 7. The aggregation of the judgements made by the individuals is undertaken using the Aggregation of Individual Priorities method (AIP) as illustrated in Table 6. Finally, the VIKOR method finds a compromise solution to decision problems containing conflicting and non-commensurable criteria [22,23,24,25,26,27,28]. The alternatives are evaluated according to the criteria and the achieved compromise solution provides a maximum utility of the majority, and the minimum individual regret. This research work has focused on implementing sustainability criteria in decision making during the project of medium span roofs. This paper presents a decision support system capable of dealing with the triple bottom line that considers economic, social and environmental criteria, instead of the traditional bottom line referring only to economic criteria.

Figure 1. Workflow diagram.

2. Setting Hierarchy Structure in Medium Span Roofs

From an environmental perspective, waste prevention should be the first priority of waste management [29], and prevention must be considered from the design stage. In buildings with medium-sized spans, traditional roofs are commonly used without a detailed study of the different existing solutions with less waste production. In order to find the optimal roof assembly, the problem is structured into a hierarchy of levels including as many relevant details as possible (see Figure 2). The Delphi technique was used to obtain this hierarchical structure. The first phase of the Delphi technique is to develop a set of criteria and alternatives by asking a panel of experts to complete an anonymous questionnaire.

In the proposed hierarchy, the highest level is the overall objective: Implementing sustainability criteria for selecting a roof assembly in medium span roofs. While the lowest level includes the different roof assemblies, which are:

Prefabricated concrete and purlins (PCP). Main structure made of precast prestressed concrete beams, the secondary structure consists of precast concrete purlins roof serving as support for flat steel panels.
Prefabricated concrete and self-supporting curved system (PSS). Main structure made of precast prestressed concrete beams serving as support for curved cold formed steel panels.
Steel lattice and purlins (SLP). Main structure made of steel lattices, the secondary structure consists of steel purlins roof serving as support for flat steel panels.
Self-supporting curved system (SSC). Self-supporting curved panels made out of steel ribs covering the largest span leaning on the facade beams.
Laminated wood and purlins (LWP). Main structure made of wood lattices, the secondary structure consists of wood purlins roof, serving as support for flat steel panels.

In all options the same thermal properties have been considered. Panels are made up of two corrugated ribbed sheets which are separated by an auxiliary profile. An insulating material is placed between them.

The intermediate level of the hierarchy analyzes three criteria for evaluating the roof as shown in Figure 2. The first one is the economic criterion (ECO). This criterion is structured in three subcriteria: manufacturing cost (MFC), transport and assembly cost (TAC) and roof maintenance cost (RMC). A roof’s economic operation should be considered throughout the construction stage and also in terms of its maintenance and conservation throughout its life cycle [30,31]. Manufacturing costs refer to the cost of acquiring raw materials, the manufacturing and material affordability. Transport and assembly costs refer to the cost of the transportation and positioning of the components, execution speed, supply storage and control that are necessary in the construction stage [32]. In roof maintenance costs the durability of the material must be taken into account [33]. This means its capability of maintaining its physical and mechanical properties over its life cycle: reaction with oxidizing agents; resistance in acidic or alkaline environments; and water resistance based on water absorption. It includes also the cost of inspections, necessary means for auscultation of the structure and essential procedures for the maintenance, repairs and reinforcement of both the structural and auxiliary elements [34,35].

The second criterion studied is the social criterion (SOC). The social criterion is arranged in three subcriteria: satisfactory fireproofing (SFP), requirements in materials and resources or use of local materials (ULM) and aesthetic or versatility when choosing the shapes (AST). User satisfaction and safety are key factors in the design stage. Fireproofing is an important quality for a structural material. It reduces the risk of a disaster, and lowers the need for additional protection to comply with the minimum required standards [36]. In addition, materials that are extracted, processed and manufactured regionally are considered preferable materials because they are easily accessible and help to develop regional economies [37]. In addition, last, aesthetic subcriterion assesses the visual quality achieved inside the building and the flexibility of the materials in the choice of shapes that improve this visual quality [38].

Finally, environmental criterion (ENV) is subdivided in three subcriteria: waste and emissions impact (EMI), embodied energy (EBE) and operating energy (OPE). Life cycle assessment optimizes design solutions favorable to the environment by taking into account the impact throughout construction, operation and final disposal of the roof [39]. In order to study the environmental impact of the roof, material and energy consumption and the consequent pollution and waste are considered through the three sub-criteria [40]. EMI refers not only to those from extraction and production of materials, but also to the impacts of construction. The anthropogenic greenhouse effect caused by the emissions is expressed in terms of their Global Warming Potential calculated as carbon dioxide equivalent. EBE is the energy utilized during the construction phase. It is the energy content of all the materials used in the building. Energy content of materials refers to the energy used to acquire raw materials, manufacture and transport them to a building site and energy incurred at the time of construction of the roof [41,42]. OPE subcriterion considers the necessary energy to heat and cool a building as a key factor in the operating energy, and therefore, in the building’s life cycle energy demand [43]. The energy efficiency of a building depends not only on the thermal properties and heat capacity of the materials used, but also on its shape. The geometry has the strongest effect on the demand for energy of the buildings, because it influences the thermal inertia and energy losses [44]. Taking into account all these requirements and following the initial step of AHP [45], the analysis goal is decomposed into a hierarchy structure shown in Figure 2. Saaty and Ozdemir [46] have observed that an individual cannot simultaneously compare more than seven items (plus or minus two) without becoming confused. This study does not exceed these limitations in the number of pairwise comparisons.

Figure 2. Hierarchy structure for selecting the roof assembly typology.

3. Obtaining Priorities for Criteria and Sub-Criteria

Continuing with the Delphi technique, experts assess different criteria in a second questionnaire. The Delphi process encourages interaction among the experts with anonymous feedback. The Delphi method helps to reduce the dispersion of the answers from the experts. AHP is used to break down a complex situation into its component parts. Table 1 shows particular questionnaires for evaluating criteria and sub-criteria with respect to the overall goal using a 9-point scale (see Table 2). Each expert performed a pairwise comparison to indicate his preference for each criterion. Pairwise comparison matrices for the criteria (A_i0) and sub-criteria (A_i1 to A_i3) are formed for the i-th expert using the values obtained from Table 3.

The principal eigenvector of each matrix A_ij is the priority vector ω_ij. Vector ω_i0 of A_i0 determine the weight of each criterion with respect to the analysis goal, while A_ij (j = 1 to 3) determine the weight of each subcriterion with respect to its criterion. To find these priority vectors, each linear system Aω = λω must be solved evaluating det [A − λ·I] = 0.

Table 1. Questionnaire implementing sustainable factors to assess main criteria and sub-criteria in the selection of roof typology.

**Table 1.** Questionnaire implementing sustainable factors to assess main criteria and sub-criteria in the selection of roof typology.
Criteria
QC1	How important are economic criteria (ECO) compared to social criteria (SOC)
QC2	How important are economic criteria (ECO) compared to environmental criteria (ENV)
QC3	How important are social criteria (SOC) compared to environmental criteria (ENV)
Sub-Criteria
QS1	How important is manufacture cost (MFC) compared to transport and assembly cost (TAC)
QS2	How important is manufacture cost (MFC) compared to roof maintenance cost (RMC)
QS3	How important is transport and assembly cost (TAC) compared to roof maintenance cost (RMC)
QS4	How important is satisfactory fireproofing (SFP) compared to use of local materials (ULM)
QS5	How important is satisfactory fireproofing (SFP) compared to aesthetic (AST)
QS6	How important is use of local materials (ULM) compared to aesthetic (AST)
QS7	How important is emissions impact (EMI) compared to embodied energy (EBE)
QS8	How important is emissions impact (EMI) compared to operating energy (OPE)
QS9	How important is embodied energy (EBE) compared to operating energy (OPE)

Table 2. 9-point scale for pairwise comparisons in AHP with linguistic terms.

**Table 2.** 9-point scale for pairwise comparisons in AHP with linguistic terms.
Notation	Meaning	Importance
EP	A criterion or alternative is extremely preferred to another	9
VP	A criterion or alternative is very strongly preferred to another	7
MP	A criterion or alternative is moderately preferred to another	5
SP	A criterion or alternative is slightly preferred to another	3
QP	A criterion or alternative is equally preferred to another	1
SN	A criterion or alternative is slightly non-preferred to another	1/3
MN	A criterion or alternative is moderately non-preferred to another	1/5
VN	A criterion or alternative is very strongly non-preferred to another	1/7
EN	A criterion or alternative is extremely non-preferred to another	1/9

One of AHP’s advantages is the possibility of measuring the consistency of the pairwise comparison matrix. The consistency ratio (CR) is used as the main indicator for ranking consistency. Maximum consistency ratio should be 5% for a 3 by 3 matrix, 9% for a 4 by 4 matrix, and 10% for a larger matrix [47]. Any higher score indicates that the judgments need re-examination. CR is determined by the ratio between the consistency index (CI) and the random consistency index (RCI). The RCI value is fixed and depends on the number of evaluated criteria. In order to calculate the CI, the largest eigenvalue (λ_max) of the normalized pairwise comparison matrix should be determined. Then the consistency index (CI) is calculated as follows:

C I = \frac{λ_{m a x} - n}{n - 1}

(1)

As an example, priority vector and consistency analysis for main criteria and sub-criteria for the first expert are shown in Table 4. Results of Consistency Ratio for the main criteria and sub-criteria for each expert are indicated in Table 5. The priority vectors for each sub-criterion with respect to the goal (ω_i) are obtained from priority vectors for criteria with respect to the goal and the subcriteria with respect to its criterion. This process is repeated for each expert and then information is aggregated and the priority vector for sub-criteria (ω) is obtained (see Table 6). The result is shown in Figure 3.

Table 3. Evaluation results of the main criteria and sub-criteria for each expert with respect to the overall goal.

**Table 3.** Evaluation results of the main criteria and sub-criteria for each expert with respect to the overall goal.
Pairwise Criteria			1st	2nd	3rd	4th	5th	6th	7th	8th	9th	10th
ECO	vs.	SOC	MP	VP	SP	SP	MP	SP	MP	SP	SP	SP
ECO	vs.	ENV	SP	QP	QP	MP	SP	MP	SP	MP	QP	SN
SOC	vs.	ENV	SN	MN	SN	SP	SN	SP	SN	SP	SN	MN
Pairwise Sub-Criteria
MFC	vs.	TAC	SP	SP	QP	MN	MP	QP	SP	QP	QP	SN
MFC	vs.	RMC	MP	MP	SN	SN	SP	MP	SN	MP	MP	MN
TAC	vs.	RMC	SP	SP	SN	SP	SN	MP	MN	MP	MN	SN
SFP	vs.	ULM	MN	SN	SN	QP	SN	SN	SP	SN	QP	SP
SFP	vs.	AST	EN	VN	MN	SN	EN	SN	SN	MN	MN	QP
ULM	vs.	AST	SN	SN	SN	SN	MN	QP	MN	SN	SN	MN
EMI	vs.	EBE	SN	MN	QP	MN	MP	QP	QP	QP	QP	MP
EMI	vs.	OPE	VN	EN	MN	MN	SP	MN	MN	SN	QP	SP
EBE	vs.	OPE	SN	SN	MN	QP	SN	SN	MN	SN	QP	SN

4. Evaluating Roof Assembly Typologies

The next step is to study the priority of typologies with respect to each subcriterion. Tangible subcriteria (MFC, TAC, EMI, EBE and OPE) only require direct measurement of an objective [48]. Values for priorities have been normalized for establishing a ranking [49]. If there are m typologies and n criteria, the j_th criterion can be expressed as Y_j = (y_1j, y_2j, …, y_ij, …, y_mj), where y_ij is the performance value of the j-th criterion in the i-th typology. The term Y_j can be translated into the comparability sequence X_j = (x_1j, x_2j, …, x_ij, …, x_mj) as follows. Performance values are scaled into (0,1) thereafter.

x_{i j} = \frac{M a x (y_{i j}, i = 1, 2, \dots, m) - y_{i j}}{M a x (y_{i j}, i = 1, 2, \dots, m) - M i n (y_{i j}, i = 1, 2, \dots, m)}

(2)

for i = 1,2,…,m and j = 1,2,…,n.

Table 4. Priority vector and consistency analysis of the pairwise comparison matrix for main criteria and sub-criteria for the first expert.

**Table 4.** Priority vector and consistency analysis of the pairwise comparison matrix for main criteria and sub-criteria for the first expert.
	ECO	SOC	ENV	Priority Vector
ECO	1	5	3	0.6370
SOC	1/5	1	1/3	0.1047
ENV	1/3	3	1	0.2583
λ_max = 3.0385, CI = 0.0193, CR = 0.0370 < 0.05 OK
	MFC	TAC	RMC	Priority Vector
MFC	1	3	5	0.6370
TAC	1/3	1	3	0.2583
RMC	1/5	1/3	1	0.1047
λ_max = 3.0385, CI = 0.0193, CR = 0.0370 < 0.05 OK
	SFP	ULM	AST	Priority Vector
SFP	1	1/5	1/9	0.0629
ULM	5	1	1/3	0.2654
AST	9	3	1	0.6716
λ_max = 3.0291, CI = 0.0145, CR = 0.0279 < 0.05 OK
	EMI	EBE	OPE	Priority Vector
EMI	1	1/3	1/7	0.0879
EBE	3	1	1/3	0.2426
OPE	7	3	1	0.6694
λ_max = 3.0070, CI = 0.0035, CR = 0.0068 < 0.05 OK

Table 5. Consistency ratio (CR) for main criteria and sub-criteria.

**Table 5.** Consistency ratio (CR) for main criteria and sub-criteria.
Expert	1st	2nd	3rd	4th	5th	6th	7th	8th	9th	10th
A₀	0.037	0.012	0.000	0.037	0.037	0.037	0.037	0.037	0.000	0.033
A₁	0.037	0.037	0.000	0.037	0.037	0.000	0.037	0.000	0.000	0.033
A₂	0.028	0.007	0.037	0.000	0.028	0.000	0.037	0.037	0.025	0.025
A₃	0.007	0.028	0.000	0.000	0.037	0.028	0.000	0.000	0.000	0.033

Table 6. Priority vector of sub-criteria.

**Table 6.** Priority vector of sub-criteria.
	MFC	TAC	RMC	SFP	ULM	AST	EMI	EBE	OPE
ω₁	0.4058	0.1645	0.0667	0.0066	0.0278	0.0703	0.0227	0.0627	0.1729
ω₂	0.3102	0.1258	0.0510	0.0068	0.0189	0.0521	0.0274	0.1155	0.2923
ω₃	0.0857	0.0857	0.2571	0.015	0.0369	0.091	0.0612	0.0612	0.3061
ω₄	0.0667	0.4058	0.1645	0.0517	0.0517	0.155	0.0095	0.0476	0.0476
ω₅	0.4058	0.0667	0.1645	0.0074	0.0187	0.0787	0.1645	0.0271	0.0667
ω₆	0.2895	0.2895	0.0579	0.0369	0.1107	0.1107	0.0164	0.0194	0.0690
ω₇	0.1645	0.0667	0.4058	0.0271	0.0110	0.0667	0.0369	0.0369	0.1845
ω₈	0.2895	0.2895	0.0579	0.0271	0.0667	0.1645	0.0209	0.0209	0.0628
ω₉	0.0612	0.0612	0.3061	0.0223	0.0265	0.0941	0.1429	0.1429	0.1429
ω₁₀	0.0271	0.0667	0.1645	0.0425	0.0119	0.0503	0.4058	0.0667	0.1645
ω	0.1969	0.1559	0.1896	0.0248	0.0348	0.0961	0.0723	0.0674	0.1621

Figure 3. Priority vector for sub-criteria.

Non-tangible subcriteria (RMC, SFP, ULM and AST) will be evaluated through a third questionnaire which is sent to the panel of experts using Delphi technique. To illustrate the proposed method, Table 7 shows the results obtained with respect to non-tangible sub-criteria. Then, a pairwise comparison matrix for the alternatives is obtained using judgments provided by each expert. As in previous steps, the eigenvector method had been applied to obtain the priority vector, and consistency analysis was performed for each case and expert. The results of the pairwise comparison of the alternatives with respect to the intangible sub-criteria for the first expert are shown in Table 8. A matrix of priority vectors for alternatives is formed linking tangible and intangible sub-criteria as shown in Table 9.

Table 7. Roof evaluation results for each expert with respect to non-tangible sub-criteria.

**Table 7.** Roof evaluation results for each expert with respect to non-tangible sub-criteria.
Expert	1st	2nd	3rd	4th	5th	6th	7th	8th	9th	10th
RMC
PCD vs. PSS	QP	QP	QP	SP	SP	MN	MP	SP	SN	MP
PCP vs. SLP	MP	MP	SN	SN	MP	QP	SP	VP	QP	SP
PCP vs. SSC	SN	MN	MN	MP	MP	SN	MP	SN	SN	MP
PCP vs. LWP	SP	SN	SN	MN	MP	SP	SP	MP	SP	QP
PSS vs. SLP	MP	MP	SN	MN	QP	MP	SN	MP	SP	SN
PSS vs. SSC	SN	MN	MN	SP	QP	SP	QP	MN	QP	SP
PSS vs. LWP	SP	SN	SN	MN	SP	MP	SN	MP	MP	SN
SLP vs. SSC	VN	EN	SN	MP	QP	MN	MP	VN	SN	SP
SLP vs. LWP	SN	VN	QP	QP	QP	MP	SP	SN	SP	SN
SSC vs. LWP	VP	SP	SP	MN	QP	MP	MN	VP	MP	MN
SFP
PCP vs. PSS	QP	QP	SP	MP	QP	SP	QP	SP	QP	VP
PCP vs. SLP	SP	MP	VP	EP	EP	EP	MP	MP	VP	EP
PCP vs. SSC	SP	MP	EP	EP	VP	VP	MP	VP	VP	EP
PCP vs. LWP	MP	VP	VP	SP	MP	MP	VP	MP	EP	VP
PSS vs. SLP	SP	MP	SP	VP	EP	MP	MP	SP	VP	MP
PSS vs. SSC	SP	MP	VP	VP	VP	SP	MP	MP	VP	MP
PSS vs. LWP	MP	VP	MP	QP	MP	SP	MP	SP	VP	QP
SLP vs. SSC	QP	QP	MP	SP	SN	SN	SP	SP	SP	SP
SLP vs. LWP	SP	SP	SP	MN	MN	QP	SP	QP	MP	SN
SSC vs. LWP	SP	SP	SN	VN	MN	QP	SP	MN	SP	MN
ULM
PCP vs. PSS	QP	SP	SP	SP	SP	QP	QP	QP	QP	MP
PCP vs. SLP	VP	MP	VP	MP	SP	SP	SP	MP	MP	SP
PCP vs. SSC	VP	VP	EP	VP	MP	SP	SP	MP	MP	VP
PCP vs. LWP	EP	EP	VP	MP	MP	MP	MP	EP	VP	VP
PSS vs. SLP	VP	SP	MP	SP	QP	SP	SP	MP	MP	QP
PSS vs. SSC	VP	MP	EP	SP	MP	SP	SP	MP	MP	SP
PSS vs. LWP	EP	VP	SP	SP	SP	MP	MP	EP	VP	SP
SLP vs. SSC	QP	SP	SP	SP	MP	QP	QP	QP	SP	MP
SLP vs. LWP	SP	MP	SN	QP	SP	SP	MP	MP	MP	SP
SSC vs. LWP	SP	SP	MN	MN	MN	SP	SP	SP	SP	SN
AST
PCP vs. PSS	MN	MN	VN	MN	QP	MN	SN	MN	SP	VN
PCP vs. SLP	SN	SN	MN	EN	MN	SN	QP	SN	SN	QP
PCP vs. SSC	VN	VN	EN	VN	MN	MN	MN	VN	QP	EN
PCP vs. LWP	EN	EN	MN	MN	VN	MN	VN	EN	MN	MN
PSS vs. SLP	SP	SP	MP	MN	MN	MP	SP	SP	MN	MP
PSS vs. SSC	SN	SN	SN	SN	MN	QP	MN	MN	SP	SN
PSS vs. LWP	MN	MN	SP	QP	VN	SP	VN	MN	VN	QP
SLP vs. SSC	MN	MN	EN	SP	QP	MN	MN	VN	MP	VN
SLP vs. LWP	VN	VN	SN	MP	MN	MN	VN	VN	MN	MN
SSC vs. LWP	SN	SN	MP	MP	MN	QP	MN	SN	EN	SP

Table 8. Priority vector and consistency analysis of the pairwise comparison matrix for the roof typologies, with respect to intangible sub-criteria for the first expert.

**Table 8.** Priority vector and consistency analysis of the pairwise comparison matrix for the roof typologies, with respect to intangible sub-criteria for the first expert.
RMC	PCP	PSS	SLP	SSC	LWP	Priority Vector
PCP	1	1	5	1/3	3	0.1951
PSS	1	1	5	1/3	3	0.1951
SLP	1/5	1/5	1	1/7	1/3	0.0422
SSC	3	3	7	1	7	0.4887
LWP	1/3	1/3	3	1/7	1	0.0790
λ_max = 5.1308, CI = 0.0327, CR = 0.0295 < 0.10 OK
SFP	PCP	PSS	SLP	SSC	LWP	Priority Vector
PCP	1	1	3	3	5	0.3435
PSS	1	1	3	3	5	0.3435
SLP	1/3	1/3	1	1	3	0.1290
SSC	1/3	1/3	1	1	3	0.1290
LWP	1/5	1/5	1/3	1/3	1	0.0551
λ_max = 5.0556, CI = 0.0139, CR = 0.0125 < 0.10 OK
ULM	PCP	PSS	SLP	SSC	LWP	Priority Vector
PCP	1	1	7	7	9	0.4129
PSS	1	1	7	7	9	0.4129
SLP	1/7	1/7	1	1	3	0.0703
SSC	1/7	1/7	1	1	3	0.0703
LWP	1/9	1/9	1/3	1/3	1	0.0337
λ_max = 5.1164, CI = 0.0291, CR = 0.0262 < 0.10 OK
AST	PCP	PSS	SLP	SSC	LWP	Priority Vector
PCP	1	1/5	1/3	1/7	1/9	0.0333
PSS	5	1	3	1/3	1/5	0.1290
SLP	3	1/3	1	1/5	1/7	0.0634
SSC	7	3	5	1	1/3	0.2615
LWP	9	5	7	3	1	0.5128
λ_max = 5.2375, CI = 0.0594, CR = 0.0535 < 0.10 OK

Table 9. Priority matrix for implementing sustainability criteria in the selection of a roof assembly.

**Table 9.** Priority matrix for implementing sustainability criteria in the selection of a roof assembly.
	MFC	TAC	RMC	SFP	ULM	AST	EMI	EBE	OPE
PCP	0.2463	0.0211	0.1938	0.4657	0.4388	0.0441	0.0000	0.1449	0.4099
PSS	0.2518	0.0000	0.1769	0.2969	0.2973	0.1522	0.2035	0.3947	0.1065
SLP	0.2927	0.4170	0.1198	0.0849	0.1251	0.1310	0.2059	0.1989	0.0587
SSC	0.2092	0.4378	0.3028	0.0638	0.0714	0.2856	0.2449	0.2615	0.4248
LWP	0.0000	0.1240	0.2067	0.0888	0.0676	0.3870	0.3457	0.0000	0.0000

5. Achieving Compromise Solution with VIKOR Method

The VIKOR method improves the proposed decision support tool by enabling to assess the stability and consensus of the roof assembly selected. In order to reach consensus among experts, VIKOR technique provides a compromise solution that is the closest to the ideal. VIKOR analyses the stability of the compromise solution and performs sensitivity analyses before accepting a solution as the optimal one [50]. The VIKOR method provides a maximum group utility for the majority and a minimum of individual regret for the opponent. The ranking of roof assembly typologies is obtained from comparison of alternatives according to each subcriterion [51,52].

For the j-th typology, the rating of the i-th criterion is denoted by f_ij. Development of the VIKOR method is started with the following form of L_p-metric:

L_{p j} = {\sum_{i = 1}^{9} {[ω_{i} (f_{i}^{*} - f_{i j}) / (f_{i}^{*} - f_{i}^{-})]}^{p}}^{1 / p} 1 \leq p \leq \infty; j = 1, 2, \dots, 5

(3)

Within the VIKOR method L_1j (S_j ) and L_∞j (R_j) are used to obtain ranking measures. The solution obtained by means of min S_j implies a maximum group utility (majority rule), and the solution obtained by means of min R_j corresponds to a minimum of individual regret for the opponent.

The compromise ranking algorithm of the VIKOR method has the following steps:

The best f_i^* and the worst values f_i⁻ of the nine subcriteria are computed using the equations f_i^* = max_j{f_ij}; f_i⁻ = min_j{f_ij}. S_j , R_j and Q_j values are calculated using the following equations:

$S_{j} = \sum_{i = 1}^{9} ω_{i} \frac{f_{i}^{*} - f_{i j}}{f_{i}^{*} - f_{i}^{-}}$

(4)

$R_{j} = m a x_{i} (ω_{i} \frac{f_{i}^{*} - f_{i j}}{f_{i}^{*} - f_{i}^{-}})$

(5)

$Q_{j} = υ \frac{S_{j} - S^{*}}{S^{-} - S^{*}} + (1 - υ) \frac{R_{j} - R^{*}}{R^{-} - R^{*}}$

(6)

where
- $S^{*} = m i n_{j} S_{j}$
- $S^{-} = m a x_{j} S_{j}$
- $R^{*} = m i n_{j} R_{j}$
- $R^{-} = m a x_{j} R_{j}$
and υ is the weight for the strategy of the majority of criteria or maximum group utility and (1 − υ) is the weight of the individual regret. To achieve consensus using VIKOR, the weight of decision making strategy υ will be set to 0.5, that is by consensus [53]. The results for the five studied typologies are shown in Table 10.
The roof assembly typologies are now ranked using the S, R and Q values in ascending order. Three ranking lists are obtained (see Table 11).
The SSC typology, which is the best ranked by means of the Q value (minimum), is proposed as a compromise solution if the following two conditions are satisfied:
- Condition 1: Acceptable advantage: The difference between the first and second positioned typologies in the ranking list by Q is greater than DQ, being DQ = 1/(J − 1), where J is the number of studied typologies. In this case, Q(PCP) − Q(SSC) = 0.64 > 0.25.
- Condition 2: Acceptable stability in decision making: The first typology in the ranking resulting from Q values is also the best ranked by means of S and R. In our case, this second condition is fulfilled as shown in Table 11.

Table 10. S_j, R_j and Q_j values for the five analyzed roof typologies.

**Table 10.** S_j, R_j and Q_j values for the five analyzed roof typologies.
	PCP	PSS	SLP	SSC	LWP
S_j	0.5093	0.5545	0.5241	0.1877	0.6958
R_j	0.1483	0.1559	0.1896	0.0561	0.1969
Q_j	0.6439	0.7150	0.8051	0.0000	1.0000

Table 11. Ranking obtained from VIKOR method for the five roof typologies.

**Table 11.** Ranking obtained from VIKOR method for the five roof typologies.
Position	1	2	3	4	5
S_j	SSC	PCP	SLP	PSS	LWP
R_j	SSC	PCP	PSS	SLP	LWP
Q_j	SSC	PCP	PSS	SLP	LWP

6. Discussion and Conclusions

The choice of roof assembly typology is one of the most important decisions with long-term consequences in medium span buildings. This selection must be made in terms of sustainability taking into account the triple bottom line that includes economic, social and environmental criteria. Industrialization, technological advances and innovation have allowed the development of alternatives with higher efficiency and less waste, but often such roof typologies are not applied because the construction industry does not have the ability to try before build and this is a sector that accepts innovations slowly. Therefore, the roof assembly selection is a complex problem due to the different factors that could be analyzed. In this research work, a hybrid decision support system based on Delphi, AHP and VIKOR methods has been applied to implement sustainability criteria.

In our case, a self-supporting curved system is the compromise solution to the selection problem. A self-supporting curved system is the alternative best ranked by the Q value and presents an acceptable advantage with respect to the one ranked second in the list by Q and an acceptable stability in decision making, because it also is the best ranked by S (majority rule) and R (minimum individual regret). As can be observed in Figure 4, the self-supporting curved system matches the ideal alternative when transport and assembly costs, roof maintenance costs and operating energy are considered. The manufacturing cost criterion has the greatest global weight but with the VIKOR method its importance is reduced because it has four alternatives with values near to the ideal one and the cost of the fifth alternative is much larger. Therefore, the factors considered previously are the most relevant ones and the main advantages of self-supporting curved system are its lightness and compactness. The next roof typology closest to the ideal solution is prefabricated concrete and purlins roof. Its value mainly results from clear prominence with respect to the other alternatives when fire resistance and the use of local materials are considered. Its greatest disadvantage is the transportation and assembly cost because of its high weight.

Figure 4. Comparison of roof tipologies with ideal F^* and compromise F^c solutions (PCP: Prefabricated concrete and purlin, PSS: Prefabricated concrete and self-supporting curved system. SLP: Steel lattice and purlin, SSC: Self-supporting curved system, LWP: Laminated wood and purlin).

Author Contributions

All the authors contributed equally to this research work.

Conflicts of Interest

The authors declare no conflict of interest.

References

European Union. Directive 2010/31/EU of the European Parliament and of the Council of 19 May 2010 on the energy performance of buildings (recast). Off. J. Eur. Union 2000, L153, 13–35. [Google Scholar]
United Nations 1998 Kyoto Protocol to the United Nations Framework Convention on Climate Change. Available online: http://unfccc.int/resource/docs/convkp/kpeng.pdf (accessed on 12 March 2015).
Canto-Perello, J.; Curiel-Esparza, J. Assessing governance issues of urban utility tunnels. Tunnel. Undergr. Space Technol. 2013, 33, 82–87. [Google Scholar] [CrossRef]
Martin-Utrillas, M.; Juan-Garcia, F.; Canto-Perello, J. Curiel-Esparza, J. Optimal infrastructure selection to boost regional sustainable economy. Int. J. Sustain. Dev. World Ecol. 2015, 22, 30–38. [Google Scholar]
Aguado, A.; del Caño, A.; de la Cruz, P.; Gómez, P.J.; Josa, A. Sustainability Assessment of Concrete Structures within the Spanish Structural Concrete Code. J. Constr. Eng. Manag. ASCE 2012, 138, 268–276. [Google Scholar] [CrossRef]
Ramesh, T. Prakash, R.; Shukla, K.K. Life cycle energy analysis of buildings: An overview. Energy Build. 2010, 42, 1592–1600. [Google Scholar] [CrossRef]
Reza, B.; Sadiq, R.; Hewage, K. Sustainability assessment of flooring systems in the city of Tehran: An AHP-based life cycle analysis. Constr. Build. Mater. 2011, 25, 2053–2066. [Google Scholar] [CrossRef]
Akiner, I.; Yitmen, I. International strategic alliances in construction: Performances of Turkish contracting firms. In Proceedings of the International Conference of Management and Innovation for a Sustainable Built Environment CIB, Amsterdam, The Netherlands, 20–23 June 2011.
Zadeh, S.M.; Hunt, D.V.L.; Lombardi, D.R.; Rogers, C.D.F. Shared Urban Greywater Recycling Systems: Water Resource Savings and Economic Investment. Sustainability 2013, 5, 2887–2912. [Google Scholar] [CrossRef]
Hunt, D.V.L.; Rogers, C.D.F. A benchmarking system for domestic water use. Sustainability 2014, 6, 2993–3018. [Google Scholar] [CrossRef]
Curiel-Esparza, J.; Canto-Perello, J. Understanding the major drivers for implementation of municipal sustainable policies in underground space. Int. J. Sustain. Dev. World Ecol. 2012, 19, 506–514. [Google Scholar] [CrossRef]
Collier, Z.A.; Wang, D.; Vogel, J.T.; Tatham, E.K.; Linkov, I. Sustainable Roofing Technology under Multiple Constraints: A Decision Analytic Approach. Environ. Syst. Decis. 2013, 33, 261–271. [Google Scholar] [CrossRef]
Ozdemir, M.S.; Saaty, T.L. The unknown in decision making, what to do about it. Eur. J. Oper. Res. 2006, 174, 349–359. [Google Scholar] [CrossRef]
Lee, G.K.L.; Chan, E.H.W. The analytic hierarchy process (AHP) approach for assessment of urban renewal proposals. Soc. Indic. Res. 2008, 89, 155–168. [Google Scholar] [CrossRef]
Syamsuddin, J.H. The use of AHP in security policy decision making: An open office calc application. J. Softw. 2010, 5, 1162–1169. [Google Scholar] [CrossRef]
Thapa, R.B.; Murayama, Y. Drivers of urban growth in the Kathmandu valley, Nepal: Examining the efficacy of the analytic hierarchy process. Appl. Geogr. 2010, 30, 70–83. [Google Scholar] [CrossRef]
Canto-Perello, J.; Curiel-Esparza, J.; Calvo, V. Criticality and threat analysis on utility tunnels for planning security policies of utilities in urban underground space. Expert Syst. Appl. 2013, 40, 4707–4714. [Google Scholar] [CrossRef]
Hsu, C.C.; Sandord, B.A. The Delphi technique: Making sense of consensus, Practical Assessment. Res. Eval. 2007, 12, 1–7. [Google Scholar]
Roubelat, F. The Delphi method as a ritual: Inquiring the Delphic Oracle. Technol. Forecast. Soc. Chang. 2011, 78, 1491–1499. [Google Scholar] [CrossRef]
Gracht, H.A. Consensus measurement in Delphi studies, review and implications for future quality assurance. Technol. Forecast. Soc. Chang. 2012, 79, 1525–1536. [Google Scholar] [CrossRef]
Curiel-Esparza, J.; Canto-Perello, J. Selecting utilities placement techniques in urban underground engineering. Arch. Civil Mech. Eng. 2013, 13, 276–285. [Google Scholar] [CrossRef]
Mela, K.; Tiainen, T.; Heinisuo, M. Comparative study of multiple criteria decision making methods for building design. Adv. Eng. Inform. 2012, 26, 716–726. [Google Scholar] [CrossRef]
San Cristobal, J. Contractor Selection Using Multicriteria Decision-Making Methods. J. Constr. Eng. Manag. 2012, 138, 751–758. [Google Scholar] [CrossRef]
Lee, W.S. Merger and acquisition evaluation and decision making model. Serv. Ind. J. 2013, 33, 1473–1494. [Google Scholar] [CrossRef]
Martin-Utrillas, M.; Azorin-Carrion, A.; Canto-Perello, J.; Curiel-Esparza, J. Multi-criteria decision-making model for establishing the optimal typology for clinker storage silos. ZKG Int. 2015, 68, 50–58. [Google Scholar]
Fouladgar, M.M.; Yazdani-Chamzini, A.; Zavadskas, E.K.; Yakhchali, S.H.; Ghasempourabadi, M.H. Project Portfolio Selection Using Fuzzy AHP and VIKOR Techniques. Transform. Bus. Econ. 2013, 11, 213–231. [Google Scholar]
Rostamzadeh, R.; Ismail, K.; Zavadskas, E.K. Multi criteria decision making for assisting business angels in investments. Technol. Econ. Dev. Econ. 2014, 20, 696–720. [Google Scholar] [CrossRef]
Tsai, P.H.; Chang, S.C. Comparing the Apple iPad and non-Apple camp tablet PCs: A multicriteria decision analysis. Technol. Econ. Dev. Econ. 2013, 19 (Suppl. 1), S256–S284. [Google Scholar] [CrossRef]
European Union. Directive 2008/98/EC of the European Parliament and of the Council of 19 November 2008 on waste and repealing certain Directives. Off. J. Eur. Union 2008, L312, 3–30. [Google Scholar]
San-José Lombera, J.T.; Garrucho, I.; Losada, R.; Cuadrado, J. A proposal for environmental indicators towards industrial building sustainable assessment. Int. J. Sustain. Dev. World Ecol. 2007, 14, 160–173. [Google Scholar] [CrossRef]
San-José, J.T.; Garrucho, I; Cuadrado, J. The first sustainable industrial building projects. Proc. Inst. Civil Eng.: Munic. Eng. 2006, 159, 147–153. [Google Scholar]
Martin-Utrillas, M.; Reyes-Medina, M.; Canto-Perello, J.; Curiel-Esparza, J. Hybrid method for selection of the optimal process of leachate treatment in waste treatment and valorization plants or landfills. Clean Technol. Environ. Policy 2015, 17, 873–885. [Google Scholar] [CrossRef]
Lowinska-Kluge, A.; Blaszczynski, T. The influence of internal corrosion on the durability of concrete. Arch. Civil Mech. Eng. 2012, 12, 219–227. [Google Scholar] [CrossRef]
Khosrowshahi, F.; Alanib, A. Visualisation of impact of time on the internal lighting of a building. Autom. Constr. 2011, 20, 145–154. [Google Scholar] [CrossRef]
Kim, S.; Kim, G.H.; Lee, Y.D. Sustainability Life Cycle Cost Analysis of Roof Waterproofing Methods Considering LCCO₂. Sustainability 2014, 6, 158–174. [Google Scholar] [CrossRef]
Lo, S.M.; Zhao, C.M.; Liu, M.; Coping, A. A simulation model for studying the implementation of performance-based fire safety design in buildings. Autom. Constr. 2008, 17, 852–863. [Google Scholar] [CrossRef]
Markelj, J.; Kuzman, M.K.; Groselj, P.; Zbasnik-Senegacnik, M. A Simplified Method for Evaluating Building Sustainability in the Early Design Phase for Architects. Sustainability 2014, 6, 8775–8795. [Google Scholar] [CrossRef]
Alwaer, H.; Clements-Croome, D.J. Key performance indicators (KPIs) and priority setting in using the multi-attribute approach for assessing sustainable intelligent buildings. Build. Environ. 2010, 45, 799–807. [Google Scholar] [CrossRef]
Malmqvist, T.; Glaumann, M.; Scarpellini, S.; Zabalza, I.; Aranda, A.; Llera, E.; Díaz, S. Life cycle assessment in buildings: The ENSLIC simplified method and guideline. Energy 2011, 36, 1900–1907. [Google Scholar] [CrossRef]
Shao, L.; Chen, G.Q.; Chen, Z.M.; Guo, S.; Han, M.Y.; Zhang, B.; Hayat, T.; Alsaedi, A.; Ahmad, B. Systems accounting for energy consumption and carbon emission by building. Commun. Nonlinear Sci. Numer. Simul. 2014, 19, 1859–1873. [Google Scholar] [CrossRef]
Zabalza Bribian, I.; Valero Capilla, A.; Aranda Uson, A. Life cycle assessment of building materials: Comparative analysis of energy and environmental impacts and evaluation of the eco-efficiency improvement potential. Build. Environ. 2011, 46, 1133–1140. [Google Scholar] [CrossRef]
Goggins, J.; Keane, T.; Kelly, A. The assessment of embodied energy in typical reinforced concrete building structures in Ireland. Energy Build. 2010, 42, 735–744. [Google Scholar] [CrossRef]
Broun, R.; Babaizadeh, H.; Zakersalehi, A.; Menzies, G.F. Integrated Life Cycle Energy and Greenhouse Gas Analysis of Exterior Wall Systems for Residential Buildings. Sustainability 2014, 6, 8592–8603. [Google Scholar] [CrossRef]
Parasonis, J.; Keizikas, A.; Kalibatiene, D. The relationship between the shape of a building and its energy performance. Archit. Eng. Des. Manag. 2012, 8, 246–256. [Google Scholar] [CrossRef]
Saaty, T.L. Decision making with the analytic hierarchy process. Int. J. Serv. Sci. 2008, 1, 83–98. [Google Scholar]
Saaty, T.L.; Ozdemir, M. Why the Magic Number Seven Plus or Minus Two. Math. Comput. Model. 2003, 38, 233–244. [Google Scholar] [CrossRef]
Saaty, T.L. Decision Making for Leaders. In The Analytic Hierarchy Process for Decisions in a Complex World, 3rd ed.; University of Pittsburgh: Pittsburgh, PA, USA, 2012. [Google Scholar]
Tatham, E.K.; Eisenberg, D.A.; Linkov, I. Sustainable Urban Systems: A Review of How Sustainability Indicators Inform Decisions. In Sustainable Cities and Military Installations; Linkov, I., Ed.; Springer: Amsterdam, The Netherlands, 2014. [Google Scholar]
Kuo, Y.; Yang, T.; Huang, G.W. The use of grey relational analysis in solving multiple attribute decision-making problems. Comput. Ind. Eng. 2008, 55, 80–93. [Google Scholar] [CrossRef]
Opricovic, S.; Tzeng, G.H. Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS. Eur. J. Oper. Res. 2004, 156, 445–455. [Google Scholar] [CrossRef]
Curiel-Esparza, J.; Cuenca-Ruiz, M.A.; Martin-Utrillas, M.; Canto-Perello, J. Selecting a Sustainable Disinfection Technique for Wastewater Reuse Projects. Water 2014, 6, 2732–2747. [Google Scholar] [CrossRef]
Sayadi, M.K.; Heydari, M.; Shahanaghi, K. Extension of VIKOR method for decision making problem with interval numbers. Appl. Math. Model. 2009, 33, 2257–2262. [Google Scholar] [CrossRef]
Opricovic, S.; Tzeng, G.H. Extended VIKOR method in comparison with outranking methods. Eur. J. Oper. Rses. 2007, 178, 514–529. [Google Scholar] [CrossRef]

© 2015 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/4.0/).

Share and Cite

MDPI and ACS Style

Canto-Perello, J.; Martinez-Garcia, M.P.; Curiel-Esparza, J.; Martin-Utrillas, M. Implementing Sustainability Criteria for Selecting a Roof Assembly Typology in Medium Span Buildings. Sustainability 2015, 7, 6854-6871. https://doi.org/10.3390/su7066854

AMA Style

Canto-Perello J, Martinez-Garcia MP, Curiel-Esparza J, Martin-Utrillas M. Implementing Sustainability Criteria for Selecting a Roof Assembly Typology in Medium Span Buildings. Sustainability. 2015; 7(6):6854-6871. https://doi.org/10.3390/su7066854

Chicago/Turabian Style

Canto-Perello, Julian, Maria P. Martinez-Garcia, Jorge Curiel-Esparza, and Manuel Martin-Utrillas. 2015. "Implementing Sustainability Criteria for Selecting a Roof Assembly Typology in Medium Span Buildings" Sustainability 7, no. 6: 6854-6871. https://doi.org/10.3390/su7066854

Article Menu

Implementing Sustainability Criteria for Selecting a Roof Assembly Typology in Medium Span Buildings

Abstract

1. Introduction

2. Setting Hierarchy Structure in Medium Span Roofs

3. Obtaining Priorities for Criteria and Sub-Criteria

4. Evaluating Roof Assembly Typologies

5. Achieving Compromise Solution with VIKOR Method

6. Discussion and Conclusions

Author Contributions

Conflicts of Interest

References

Share and Cite

Article Metrics

Article Access Statistics

Further Information

Guidelines

MDPI Initiatives

Follow MDPI