Evaluating the Efficiency of Industrialization Process in Prefabricated Residential Buildings Using a Fuzzy Multicriteria Decision-Making Method

To alleviate the housing pressure and achieve a sustainable society, prefabricated residential building (PRB) has witnessed rapid growth in recent years. The usage of prefabricated components in the building represents a significant indicator that is traditionally used to differentiate the PRB from the traditional building. However, it cannot provide details on the efficiency of the industrialization process in the PRB.The main goal of this paper is to develop a composite index to measure the multidimensional concept of industrialization efficiency. Fuzzy Analytic Hierarchy Process (fuzzy AHP) and fuzzy Technique for Order Preference by Similarity to Ideal Solution (fuzzy TOPSIS) are applied to combine the hierarchical structure of indicators into one overall index. Finally, the industrialization efficiency assessment of three PRBs is chosen as a case to illustrate the effectiveness of the method. It can effectively quantify experts’ linguistic expressions on the performance of the PRB in different established indicators. This research can provide a decision support tool to assess and continuously promote the improvement of industrialization production in the housing industry.


Introduction
Prefabrication has been widely used and considered as a potential approach for performance improvements in the housing industry [1,2].Distinct from conventional cast-in situ construction, prefabrication involves a set of construction technologies and processes, through which building components are manufactured in a controlled environment, transported, and assembled on the job-site in order to minimize site works [3,4].A variety of interchangeable terms are associated with housing that uses the prefabrication technology, such as off-site construction [5], modular housing [6], industrialized building [3,7], modern methods of construction [8], and prefabrication housing [9].In this study, "prefabricated residential building (PRB)" is used to represent residential buildings that use prefabrication technologies [10].By contrast, "conventional residential building" refers to the buildings involving cast-in situ technologies [11].
In contrast with traditional buildings, the production of PRB involves many potential benefits, such as enhanced productivity and quality, shortened construction schedule, improved health and safety conditions, and sustainability in terms of environmental, energy, and ecological aspects [12,13].However, the uptake of PRB has been found to be sluggish, especially in some developing countries, such as China, India, and Malaysia [4,10,14].A major reason is that contractors lack experience in using prefabrication and they do not know how to adopt the PRB to their projects effectively [15].Current industrialized activities in many PRB projects are far from ideal [16].The production processes suffer from deficiencies in various aspects, such as low level of mechanization, automation, and information technologies.Therefore, it is imperative to develop an integrated decision tool for contractors to assess the efficiency of their PRB practices, through which they can select the most effective production strategies.

Mathematical Problems in Engineering
In the following section, the literature concerning PRBrelated practices, definitions, and assessment was reviewed.Then, the methodologies based on both fuzzy Analytic Hierarchy Process (fuzzy AHP) and fuzzy Technique for Order Preference by Similarity to Ideal Solution (fuzzy TOPSIS) were proposed and demonstrated using three PRBs located in the northeast China.The final section offered the conclusions and limitations.

Literature Review
2.1.PRB-Related Practices and Definitions.PRB has been adopted in housing projects for centuries [17].Prefabrication has contributed significantly to the efficiency improvement and environmental conservation in the housing industry [10].Prefabricated and standardized technologies were widely used in reconstruction projects in Asian and European countries during 1950s and the 1960s after World War II [18].France, for example, was one of the world's earliest countries to implement mass production of housing using prefabrication, whereas Japan was the first country in Asian area in 1965 [19].In the early 1970s, the American government also introduced several prefabricated building systems, which covered the aspects of prefabrication, standardization, production, and quality control [20].Hong Kong and Singapore began to adopt prefabrication approaches in housing projects in the 1980s [4,21].According to the developing processes of PRB in different countries, the production characteristics of PRB have shifted from the mass-production approach to the latter mass-customized approach, which had improved the customer orientation and integration of production processes [19].
Various frameworks were used in previous literature to categorize the PRB based on their off-site work.Tam et al. identified three categories of PRB in Hong Kong: semiprefabricated nonstructural components, such as windows and partition walls; comprehensive prefabricated units, such as columns and beams; and modular buildings which are manufactured wholly off-site [22].Goodier and Gibb classified the PRB into four levels in the UK, including component manufacture and subassembly, nonvolumetric preassembly, volumetric preassembly, and modular buildings [23].Similarly, In Australia, Blismas and Wakefield defined the off-site system from three categories: nonvolumetric preassembly, volumetric preassembly, and modular building [24].
Industrialization is an essential part of wide modernization process through development of innovative technologies and manufacturing methods [25].With regard to house building, industrialization of construction primarily refers to the rationalization of construction process through prefabrication in order to achieve the cost efficiency and improved productivity and quality [26].Six major characteristics of industrialized house building existed in current relevant definitions, including industrialization in transportation, production, and assembly, mass production, on-site fabrication, standardization and structured planning, and process integration [27].In addition, improved production performance can be achieved through prefabrication, including economic, social, and environmental aspects [28,29].Thus, compared with conventional buildings, PRB is the building that can bring significantly rationalized production process and improved production performance.

PRB Assessment Research.
Recently, building assessment is widely used to offer a standard approach to assessing new or existing buildings.Leadership in Energy and Environmental Design (LEED) developed by the American Green Building Council is a voluntary national standard in the USA to promote green buildings [30].Building Research Establishment Environmental Assessment Method (BREERAM) in the UK is developed to rank the environmental performance of buildings [30].Intelligent Building Index System is developed by the Asian Institute of Intelligent Building to assess the performance of intelligent building [31].Meanwhile, the industrialized buildings are also assessed according to the efficiency of their production process.In China, as an illustration, Standard for Assessment of Industrialized Building (SAIB) has been issued in May 2016, which included 99 specific items categorized in four-dimension design, manufacture, management, and benefits for assessing the efficiency of PRB implementation [32].
Various criteria or indicators were used to assess the PRB in terms of the efficiency of their production process in previous studies, such as prefabricated ratio or degree of off-site production [23,33]; degree of product standardization [34]; extent of mechanization and automation [26]; integration of supply chain management in production [35].Therefore, the assessment of industrialization efficiency of PRB is a multicriteria decision-making (MCDM) problem, which involves multiple, usually conflicting, decision criteria [31].De Barba et al. applied a MCDM technique to compare the industrialized and traditional building systems from three aspects of sustainability: environmental, economic, and social aspects [12].Alinaitwe et al. recommended twelve indicators of measurement to determine the efficiency of industrialization process in the PRB [26].Lessing et al. established a categorization model for the efficiency of PRB production based on eight indicators [35].
As two most known MCDM techniques, AHP and TOPSIS have been widely used in building performance evaluation, such as intelligent building [31], building energy conservation [36], building day-lighting and tradition continuity [37], and green building [38].Based on the theory of fuzzy sets proposed by Zadeh [39], fuzzy MCDM is developed to deal with qualitative, imprecise, and ill-structured information during the decision process [40].However, the fuzzy AHP and TOPSIS have not been applied to assess the efficiency of PRB.The assessment of PRB, as a MCDM problem, is related to vague criteria and subjective opinions of decision-makers.To overcome these limitations, this study proposed a fuzzy AHP-TOPSIS approach to assessing the industrialization efficiency of PRB.

Methodologies
This study proposed a fuzzy AHP-TOPSIS approach to assessing the PRB in terms of their industrialization efficiency for promoting the industrialization practices in the housing industry.The research process consisted of three stages: (1) critical measurement indicators were identified.At this stage, influential criteria and measurement indicators were determined through PRB-related literature and expert opinions.
(2) The fuzzy AHP method was utilized to determine the importance weights of the criteria and indicators.(3) The fuzzy TOPSIS method was employed to condense multilayer indicators into a composite index to present the efficiency of PRB's industrialization practices.The specific research procedure was shown as Figure 1.

Determining the Assessment Indicator System.
As mentioned earlier, the major characteristics of PRB involve two dimensions: industrialized production process and improved production performance.Therefore, industrialization efficiency of PRB is assessed from the two aspects.A comprehensive review of previous literature related to the PRB was conducted to identify the factors that have significant impacts on the industrialization efficiency of PRB [12, 13, 23, 26, 28, 29, 31-33, 35, 41-43].Finally, five criteria regarding the industrialized production process were identified, including standardized design, off-site manufacture, on-site construction, component transportation, and collaboration management.One criterion, sustainability, was identified to interpret improved production performance.Then, these six criteria were further measured by relevant subcriteria (indicators), and a preliminary draft of indicator system was determined subsequently.Six domain experts, including four scholar researchers and two practitioners, were invited to provide the qualitative validation of the measurements.Their average working experience was fifteen years in the industrialized building field.Several modifications were performed through simplifying, rephrasing, and eliminating relevant items three times.Finally, the initial indicator system was obtained, including six criteria and twenty three subcriteria (indicators), as shown in Table 1.

Fuzzy AHP.
AHP is developed to address complex MCDM problems, involving multiple quantitative and qualitative criteria [44].Considering the vagueness of experts' judgments, several fuzzy AHP methods which integrate fuzzy set theory and basic AHP have been proposed in recent years [31].In fuzzy AHP, the pairwise comparisons of indicators are conducted using linguistic variables, which are represented

Modular coordination (F11)
The design shall have good coordination of dimension and space, in which the building and its components are dimensioned and positioned based on a basic unit or module.
The design shall comply with relevant national or international modular coordination standards, such as the Modular Coordination Standard for the Building (GB/T50002) in China.
Degree of prefabrication (F12) The degree that prefabricated components account for the volume of concrete products used in the whole building.
Degree of preassembly (F13) The degree that nonvolumetric and volumetric preassembly account for the volume of prefabricated components used in the whole building.
Integrated design of main structure, equipment and decoration (F14) The design shall integrate the prefabricated structural wall, insulation layer and exterior decoration.
The design shall integrate the main structure, equipment and interior decoration.The design shall integrate the pipeline system of the mechanical and electrical equipment.
Off-site manufacture (F2) Qualification of manufacturer (F21) The manufacturer shall have relevant production technologies and equipment, and adopt the quality management system.
Prefabrication standard and guide (F22) The prefabrication process shall comply with relevant technical standards and operational codes.

Prefabrication quality control measures (F23)
The supervisors shall monitor the production process in the factory, which shall have the documents of all quality acceptance records.The quality of components shall comply with the requirements of design.
On-site construction (F3) Qualification of contractor (F31) The project is delivered using the general contractor management mode.
The construction process is implemented by a specialized construction team.

Mechanized construction (F32)
The construction mechanization is adopted to ease the work of labor and improve the productivity.
Construction management planning (F33) Construction management planning shall contain the organization of construction schedule, site layout, material, people, and machines.
Construction management planning shall provide measures regarding quality, environmental, and safety issues.
Prefabricated component assembly planning (F34) Assembly planning of components shall contain various measures and technologies regarding components' protection, storage, turning, lifting, positioning, stabilization, and connection.
Construction standard and guide (F35) Construction process shall adopt relevant prefabricated construction technical standards and codes.
Assembly quality testing (F36) Physical sampling inspections shall be conducted for critical zones and connecting parts, and testing results shall comply with the design requirements.Quality acceptance activities shall be conducted according to prefabricated-building-related standards.Quality testing results shall comply with the requirements of relevant standards and codes.
Integrated construction of main structure, equipment installment and decoration (F37) The construction and manufacture of main structural components shall be integrated and coordinated with equipment installation and decoration.
Component transportation (F4) Component transportation planning (F41) Component transportation planning shall include the organization of schedule, order, route lines of transportation, other measures related to components' protection.
Component stacking and storage management (F42) Component stacking and storage should be coordinated with the construction process in order to avoid retransportation and on-site stacking.
Component quality and safety control measures (F43) Transportation and temporary storage shall have special measures to ensure quality and safety of components.developing (F51) The information management system shall be developed, which can dynamically, quantitatively and systematically control and coordinate the whole production process.
Information management professionals (F52) All project participants shall appoint information management professionals, who are responsible for the maintenance of the information system.
Information collecting, sharing and transferring (F53) The building information modeling (BIM) shall be developed at the design stage, and be subsequently updated with the manufacture of components and the construction process, in order to ensure the information sharing and transferring, and collaboration.

Sustainability (F6)
Economical benefits (F61) The project shall achieve significant lower overall construction cost, and shortened durability compared with similar traditional buildings.
Social effects (F62) The project shall develop a specialized construction team, have a significantly improved health and safety performance, and contribute to the continuous improvement of industrialization technologies.
Environmental effects (F63) The project has the significantly reduced energy and water consumption, environmental emissions and construction site waste, compared with similar traditional buildings.by triangular numbers [45].In this study, Buckley' fuzzy AHP method was used [46].The steps of fuzzy AHP are illustrated as follows [31,47].
Experts compare the criteria or subcriteria using the linguistic terms that are shown in Table 2 [47].The pairwise comparison matrix can be expressed in matrix form as in where c is a linguistic term representing the importance of a criterion over the other one.C is the pairwise comparison matrix obtained from the expert   ,  = 1, 2, 3, . . ., .The expert opinions are aggregated using the geometric mean method (GMM), which is more consistent with the meanings of judgments in AHP [48].
Step 2 (calculating the fuzzy weights).The fuzzy weight matrix is calculated as where r represents the geometric mean of fuzzy comparison values of each criterion.w = (  ,   ,   ) is the fuzzy weight of the criterion .
Step 3 (defuzzification).The fuzzy weights are converted into a crisp value using the defuzzification process.The center of gravity defuzzification [49] was used in this study, which is calculated using Step 4 (determining the normalized weights).The weight value   should be normalized using

Fuzzy TOPSIS.
The TOPSIS method was first developed by Hwang et al. [50], for solving the MCDM problems based on the priority that the chosen alternative should have the shortest distance from the positive ideal solution (PIS) and the farthest distance from the negative ideal solution (NIS) [51].Considering the MCDM problems often involve vague criteria and subjective opinions of experts, the TOPSIS has been extended in the fuzzy environment, where the ratings of alternatives were described by linguistic assessments quantified with triangular fuzzy numbers [52].The linguistic variable is a special variable whose value is a linguistic term such as "low, very low, and so forth."The linguistic variable is useful to describe qualitative and vague information [51].
In this research, the fuzzy TOPSIS was used to assess the industrialization efficiency of PRB.Triangular fuzzy numbers were used to quantify the linguistic value, as set forth in Table 3.The steps of fuzzy TOPSIS are described as follows [51].
Step 5 (constructing the fuzzy decision matrix).The fuzzy decision matrix is constructed as shown in (5).
denotes  indicators involved in the assessment process;   is the triangular fuzzy number ( ()  ,  ()  ,  ()  ) for PRB   with respect to factor   , which is determined through the linguistic assessment according to Table 3.The ratings of group judgments are aggregated using (6), where  is the number of experts and    represents the rating by the th expert.

S = [s
Step 8 (determining the fuzzy positive idea solution (FPIS) and fuzzy negative idea solution (FNIS)).According to the weighted normalized matrix, FPIS and FNIS are defined as (11) and ( 12) [54].In other words, each value of an element in FNIS is equal to (0, 0, 0), and the value of element s+  in FPIS is equal to (  ,   ,   ), where   is the weight of criterion   .

FPIS: 𝐴
where Step 9 (calculating the distance of the alternative sequence s = [s 1 , s2 , . . ., s ] to FPIS and FNIS).The calculation process is shown as ( 13) and (14). where Step 10 (calculating the closeness coefficient   ).The closeness coefficient   for each alternative sequence with respect to FPIS is calculated as Step 11 (determining the industrialization efficiency and prioritizing alternatives).The closeness coefficient   is in the interval of (0, 1).Generally, the higher the closeness coefficient   of alternative s , the closer the alternative to the FPIS( + ).Thus,   is regarded as the industrialization efficiency of PRB   because FPIS represents the optimal status of PRB production process.According to   , the ranking order of alternatives can be determined according to the value of industrialization efficiency.

Empirical Study
With the rapid development of the national economy, increasing labor costs, and growing requirements for sustainable society, the usage of PRB in China has expanded since the middle 2000s [4].In this study, three PRB buildings located in northeast China, denoted by PRB-A, PRB-B, and PRB-C, were selected to validate the proposed approach.Specifically, PRB-A is a 15-story residential building with a prefabrication ratio of 85% and construction area of 10280.58m 2 ; PRB-B is a 12-story residential building with a prefabrication ratio of 60% and construction area of 11795.23 m 2 ; PRB-C is a 15-story residential building with a prefabrication ratio of 55% and construction area of 14321.56m 2 .Note that the prefabrication ratio represents the degree of prefabrication in each PRB.To collect relevant data for industrialization efficiency assessment, documents and records regarding the production processes of three PRBs were examined.
In order to determine the importance weights of 23 indicators and the corresponding 6 criteria, a questionnaire survey was conducted.The questionnaire consisted of seven pairwise comparison matrices: six used to determine the relative importance of each indicator in comparison with the other indicator in terms of one criterion and one overall matrix used to determine the relative importance between two criteria in terms of overall goal.Five-level linguistic scales were used to reflect the relative importance value between two indicators or criteria (shown as Table 2).The questionnaire was associated with a presentation letter, which informed the respondents about the research aim and method.Finally, the questionnaire was sent via email to 40 Then, regarding the performance of 3 target PRBs, nine experts were further invited to review production-related documents and data records according to the established indicators depicted in Table 1.The average working experience of 9 experts related to industrialized building was 12 years.The performance of alternatives with respect to each indicator was assessed using a seven-level linguistic scale (shown as Table 3).

Determining the Weights of Indicators.
A total of 21 valid questionnaires were recovered.These 21 respondents were formed of 9 research scholars, 7 practitioners, and 5 regulators, with an overall response rate of 52.5% and subgroup response rates of 45%, 70%, and 50%, respectively.The diversity of the respondents was a guarantee of obtaining reliable assessment results.The geometric means method was employed to aggregate the group judgments.Based on the seven pairwise comparison matrices of main criteria and indicators, priority weights of indicators were calculated based on the fuzzy AHP as mentioned earlier.The local and global weights of each indicator were shown in Table 4.The weighted ranking of six criteria from high to low are as follows: standardized design (0.36), on-site construction (0.25), integrated information management (0.12), off-site manufacture (0.11), component transportation (0.08), and sustainability (0.08).As for the global weights of indicators under each criterion, degree of prefabrication is the most influential indicator for the industrialization efficiency of the PRB, with a global weight of 0.216.For the criterion of standardized design, degree of prefabrication is the most important with a local weight of 0.60; for off-site manufacture, qualification of manufacturer is top one indicator, with a weight of 0.72; for on-site construction, construction management planning is the critical indicator, with a weight of 0.39; for component transportation, component transportation planning is the critical indicator (0.71); for integrated information management, information collecting, sharing, and transferring are the critical indicator (0.58); for sustainability, economical benefits are the critical indicator (0.51).

4.2.
Determining the Industrialization Efficiency.Linguistic assessments were conducted to assess performance of three PRBs according to established indicators in Table 1 and the seven-level linguistic scale listed in Table 3.The ratings of nine experts were aggregated using (5) and (6).The industrialization efficiency of PRB-A, PRB-B, and PRB-C was determined using the fuzzy TOPSIS [51].The FPIS and FNIS were obtained using (11) and (12).The distances of individual indicators from the FPIS and FNIS were calculated  using ( 13) and ( 14).The FPIS and FNIS distances for three alternatives were demonstrated in Table 5. Next, the closeness coefficient was calculated using (15).The closeness coefficient represented the efficiency of each PRB in the industrialization production, namely, the industrialization efficiency.Thus, the overall ranking of three PRBs in terms of industrialization efficiency was determined: PRB-A, PRB-B, and PRB-C (shown as Table 6).The rankings by six specific criteria were obtained accordingly, which were also presented in Table 6.
The layout of the industrialization efficiency of three PRBs under the overall performance and five different criteria is shown in Figure 2   results, the contractors, as producers of three PRBs, can make positive adjustments to promote the effectiveness of identified problem areas during the future industrialization practices of PRBs.

Conclusion
PRB has attracted increasing attentions from both researchers and practitioners due to its potentials to enhance productivity and meet the requirements for achieving a sustainable society.However, there is still lack of a reliable assessment tool for assessing the efficiency of the industrialization production.One significant contribution in this study is the proposed PRB assessment model, which allows contractors to track the performance of their PRB practices and identify effective strategies.Based on the extensive literature review and expert opinions, the industrialization efficiency of PRB was depicted using six criteria, including standardized design, off-site manufacture, on-site construction, component transportation, integrated information management, and sustainability.Six criteria, representing both production process and performance, were further interpreted using twentythree indicators.The PRB assessment tool can provide more comprehensive information on the status of industrialization production.The fuzzy AHP and TOPSIS were applied to combine multilayer indicators into one overall industrialization index.In addition, this approach took into account the vagueness of expert's opinions and could effectively handle experts' linguistic expressions.The study provided a set of criteria and indicators for extracting information on the industrialization efficiency of PRB.Based on the importance weights, this study found that standardized design and on-site construction were two most influential criteria for improving the industrialization performance.The critical indicators under each criterion were further determined, including degree of prefabrication, qualification of manufacturer, construction management planning, component transportation planning, information collecting, sharing, and transferring, and economical benefits.Both contractors and policy makers should pay more attentions to the critical factors for promoting the industrialized building.In addition, the proposed model can be used as decision support systems.The policy makers can assess the performance of industrialization production and make incentive measures for the PRBs in accord with their industrialization efficiency.The contractors can use this model as a benchmark with others and detect the deficiencies in their industrialization practices.Thus, the proposed model can continuously promote the improvement of the efficiency of industrialization production in the housing industry.
It was also worth noting that this study focused on the industrialization efficiency assessment of buildings at the individual project level, rather than the industry.Thus, macrocriteria, such as supply chain management, and operationrelated criteria were not considered in the assessment process.Another limitation of this study was that the indicators and associated weights were determined by the experts in the Chinese housing industry, which were expected to be affected by the industrialization development in the region.governance engineering (nos.HGZL/KY-17 and HGZL/KY-03).The work described in this paper was also funded by the National Key Research & Development Program (no.2016YFC0701606).

Figure 1 :
Figure 1: Main process of assessing the efficiency of industrialization process in the PRB.

FPIS: fuzzy positive
ideal solution; FNIS: fuzzy negative ideal solution; (s +  , s ) is the distance between factor  in the alternative sequence and the FPIS, and (s −  , s ) is the distance between factor  in the alternative sequence and the FNIS;  +  is the sum of distance for (s +  , s ), and  −  is the sum of distance for (s −  , s ).

Figure 2 :
Figure 2: The distribution of industrialization efficiency of three PRBs.

Table 1 :
Definitions of the industrialization efficiency assessment indicators.

Table 2 :
Linguistic scale for the pairwise matrix.

Table 3 :
Triangular fuzzy number for each linguistic value in the research.

Table 4 :
Local and global importance weights of 6 criteria and 23 indicators.

Table 5 :
The distances of three PRBs from FPIS and FNIS.

Table 6 :
The ranking of PRBs by the industrialization efficiency and individual criteria.