4.1. Sustainability Indicator Identification
The selection of evaluation indicators in this study was guided by the following principles. The first principle is comprehensiveness and purposefulness. Indicators must cover the entire lifecycle of public building energy retrofit projects, from the initial design phase to demolition. This includes reflecting cost-benefit aspects during operation, as well as technology choices, construction, and usage phases. The focus is on relevance and specificity to the evaluation goals rather than the sheer number of indicators. The second principle is comparability. Indicators should be quantitatively comparable to ensure an objective assessment of retrofit projects. They need to align with those used in past assessments to maintain consistency. For example, if greenhouse gas emissions were previously used, this study should also include similar environmental quality monitoring indicators. The third principle is practicality. Selected indicators should be practical and feasible, effectively reflecting various dimensions of the retrofit projects. They must be clearly defined and support the collection of necessary data to ensure the evaluation is operational and actionable. The fourth principle is universality. To enable comparisons across different regions and building types, indicators should have strong universality and be widely used. Indicators specific to a few projects should be limited or avoided to ensure broad applicability and relevance.
The indicators for evaluating the sustainability of building energy efficiency retrofits encompassed nine areas: people, policy, energy and resources, technology, society, materials and facilities, program management, environmental impacts, and economic impacts. The first step in selecting these indicators was to define the study’s scope, which covered the entire life cycle of a building from cradle to grave. This included the design phase, involving the initial planning, material selection, and energy efficiency design; the construction phase, focusing on practices such as waste management and resource use; the use phase, which assesses the building’s performance including daily energy and water consumption and maintenance costs; and the end phase, which covers demolition or renovation including the demolition process and material recycling. A summary of impact indicators based on a synthesis of relevant literature is shown in
Table 1.
The four phases of a building’s life cycle—design, construction, use, and demolition—support and influence each other due to the need for quality control, craftsmanship, and optimized design. Energy-saving retrofit impact indicators can be attributed to four aspects, which are the key personnel, programs, resources and technologies, and the supervision and regulations. The indicators for evaluating the life cycle sustainability of BER are shown in
Table 2.
The key personnel aspect included investment units, design units, construction units, users, facility management teams, maintenance personnel, demolition units, waste disposal personnel, and stakeholders. While investors and constructors focus on the initial costs and efficiency, users and facility managers prioritize functionality and comfort. Demolition units and waste handlers impact the end-of-life phase. Designers, stakeholders, and maintenance staff are crucial for energy efficiency, with designers directly affecting sustainability, stakeholders shaping project goals, and maintenance staff ensuring operational efficiency.
The program aspect included space planning, building design, construction, operation structure, energy management, maintenance, demolition, waste management, and resource recovery plans. Key elements impacting energy efficiency include the building design program, construction program, and energy management plan. These elements ensure the appropriate sustainable materials selection, construction practices, and long-term energy strategies. The demolition and resource recovery plans focus on eco-friendly demolition and material reuse.
The resources and technologies aspect included the use of materials, equipment, and green technologies that directly affect a building’s energy efficiency. Sustainable materials and energy-efficient equipment can significantly reduce energy consumption. The development and application of green technologies are vital for improving energy efficiency, reducing greenhouse gas emissions, and lowering operating costs.
The supervision and regulation aspect included the specific supervision and regulation needed to manage the numerous units involved in retrofit projects and to ensure energy efficiency. This helps prevent deviations and maintains the project’s sustainability goals.
4.2. Judgment Matrix
For the indicators in the same level, the judgment matrix of the evaluation indicators was constructed sequentially by comparing the degree of importance of each indicator to a factor in the previous level in two by two, denoted as P.
Assuming that the evaluation target is A, the evaluation indicators and F = {f1, f2, f3, …, fn}, then the judgment matrix P is constructed as Equation (1) shows
where fij denotes the relative importance value of the factor where i = 1, 2,...n; j = 1, 2,...n). Based on a two-by-two judgment of the indicators at the criterion level, obtained using Santy’s 1–9 scaling method, as shown in
Table 3.
To build a hierarchical structure model in the AHP, start by defining the overall goal at the top. Identify the key criteria that influence the decision and break these down into sub-criteria. List the alternatives at the bottom of the hierarchy. Arrange these elements in a clear, logical structure to guide the decision-making process. This paper took the whole life cycle sustainability evaluation of building energy retrofit as the overall objective A. This objective served as the foundation for the assessment, guiding the analysis of various factors that influence sustainability outcomes throughout the entire life cycle of the retrofit process. The whole life cycle included the design, construction, use, and end-of-life phases. This study evaluated how the relative importance of different elements (denoted as F1, F2, F3, and F4) with respect to the overall objective were assessed through expert judgment. A scoring table, as shown in
Table 4, was created based on this expert evaluation.
4.3. Weight Vector Determination
Using a hierarchical single sort on the previous layer of an element will reveal the elements in this layer. For the order of importance, the specific calculations can be based on the judgment matrix A, and the calculations must ensure that they comply with the conditions of the eigenroot and the eigenvector of Aω = λmaxω. Here, the largest eigenroot of A was λmax, the regularized eigenvector corresponding to λmax was ω, and ωi was the component of ω, which referred to the weight value and corresponded to the single ordering of its corresponding elements. The judgment matrix was used to calculate the weights (weight coefficients) of each factor aij on the target layer. The calculation steps (square root method or sum method) for the weight vector (ω) and the maximum feature (λmax) are shown in the following:
- (1)
Multiply the product of each row’s judgment matrix score by nth power, as shown in Equation (2).
- (2)
The weight vector is obtained after normalization, as shown in Equation (3). The data were normalized even if the sum of the elements in the vector was equal to 1; the elements of A were found for the same level of factors as for the previous level, and for the relative importance of a factor depending on the ranking weight value.
- (3)
Determine the largest characteristic root of the matrix, as shown in Equation (4).
4.4. Consistency Check
In the AHP method, the consistency check is a crucial step for ensuring the relative importance scores provided by the experts are logically consistent. To ensure consistency in the decision-makers’ judgments about the relative importance of the entries in the pairwise comparison matrices at all levels, a consistency test should be conducted [
52]. This study used the following consistency index CI to test the consistency index of judgment, where CI = 0 indicated that the judgment matrix was completely consistent, and the larger the CI was, the more serious the degree of inconsistency of the judgment matrix was. The random consistency index (RI) is a value obtained from randomly generated matrices, and it varies depending on the size of the matrix. The consistency ratio (CR) was used for measuring the consistency of the judgment matrix. The calculations of CI and CR are shown in Equations (5) and (6), respectively.
The CI was the consistency check index, and n was the order of the judgment matrix. The CR was the test coefficient. The RI was derived from simulations performed by Saaty, which involved generating 1000 simulations of random pairwise comparison matrices [
53,
54,
55,
56]. This process helps in establishing a benchmark for what constitutes a random level of consistency in a matrix. The values obtained from these simulations were then used to create the RI table, which provided the expected consistency indices for matrices of different sizes.
Table 5 displays these RI values for various matrix orders.
If CR < 0.1, it indicated that the degree of consistency of judgment matrix A was considered to be within the tolerance range; at this time, the eigenvectors of A could be used to carry out the calculation of the weight vector. If CR ≥ 0.1, it was considered that the judgment matrix A failed to pass the test, and could not be used as a fraction of the components in ω [
57]. At this time, consideration was given to the correction of the judgment matrix A until it could meet the consistency required.
4.5. Results
A clear hierarchical framework was finalized. This framework categorized the indicators into multiple tiers: primary sustainability goals, critical assessment criteria, and specific indicators. The framework was intended to provide a comprehensive and balanced perspective that considers building sustainability’s economic, social, and environmental dimensions. The goal level is a system of life cycle sustainability indicators for BER, the guideline level is the four stages of a building’s full life cycle, and the program level is the corresponding evaluation indicators for each stage.
Table 6 reflects the final evaluation indicator weights, with the data arranged in descending order to illustrate the level of importance of the indicators more clearly. The ranking of the weights of the four stage intermediate levels for the decision objectives was determined. The weights of the design and occupancy phases were much larger than those of the construction and end-of-use phases, indicating that the design and occupancy phases are considered more important than the construction and end-of-use phases for building energy retrofit projects in this statistic.
The weighting of the decision objectives at the program level was ranked as shown in
Table 7. Material and equipment selection has the highest weighted program, with a weight of 0.1551, indicating that selecting appropriate materials and equipment is the most critical consideration in building energy efficiency retrofit programs. The energy management plan ranked second with a weight of 0.1241, reflecting how important it is for programs to manage energy use and optimize the energy efficiency in the overall program. The application of new technology and energy efficiency occupy the third and fourth positions, with weights of 0.1009 and 0.0871, respectively, indicating that using technology to improve energy efficiency is a priority. On the other hand, maintenance personnel and public scrutiny and advice had lower weights of 0.0125 and 0.0104, respectively, but were still regarded as components of sustainability assessment despite their relatively low weights.
Based on the results of the pairwise comparisons, the Consistency Ratio (CR) was calculated to be less than 0.1. The CR was calculated using Equation (5), with the results for each stage shown in
Table 8,
Table 9,
Table 10 and
Table 11.
Table 12 shows the weighting for each phase and the consistency check results. The calculations were made with the help of Microsoft Excel, thus simplifying the AHP calculation process.