The Supplier Selection of Prefabricated Component Production Line: A Lean-Based AHP–Improved VIKOR Framework

Abstract

Prefabrication is increasingly recognized as a sustainable construction practice, with the efficiency of prefabricated component (PC) production lines playing a critical role in its success. However, supplier selection for PC production lines has become more complex due to evolving industrial demands, uncertain supply chain conditions, and operational complexities. This study addresses this gap by developing a lean-based AHP–improved VIKOR decision-making framework to enhance the supplier selection for PC production lines. The framework integrates advanced lean principles with universal and specific evaluation criteria, identified through a comprehensive literature review and expert interviews. Its validity was tested via a real-world case study with Yizhong Construction Co., Ltd., Tianjin, China. The results show that the three suppliers are ranked as Zhongjian > Tianyi > Xindadi, where Zhongjian is the best supplier in this case study, with a VIKOR index of 0.156. The findings show that the developed framework can improve the supplier selection efficiency by aligning with lean principles and enhancing the performance of PC production lines. By addressing the challenges of PC supplier selection, this study provides a practical tool to advance the adoption of prefabrication in construction. Furthermore, it contributes to the development of the PC industry by offering a robust method for the selection of suitable suppliers, which can help to optimize the production efficiency and support sustainable practices in construction.

1. Introduction

The construction industry is considered a major driver of economic and social development in our society [1,2]. However, conventional construction has faced criticism in recent years for its high energy consumption, excessive resource waste, and substantial carbon emissions [3]. In this context, prefabricated construction has emerged as an alternative, shifting from traditional to sustainable construction practice [4,5,6]. Potential advantages, like fast installation, high quality, reduced labor, and enhanced environmental protection, have been proven in numerous studies, like Mao, et al. [7], Wu, et al. [8], Chippagiri, et al. [9], Gao and Tian [10], Liu, et al. [11], and Luo, et al. [12]. Hence, this technology has been adopted in many developed countries and areas, e.g., Australia, the U.K., Singapore, and Hong Kong [7]. In the US, for instance, Plant Prefab has announced that the firm raised up to USD 42 million to boost manufacturing capabilities [13]. Moreover, developing countries, like China and Malaysia, have embraced prefabrication as an efficient vehicle for achieving sustainability in the construction industry [6,14].

Along with its growing popularity, the evaluation and selection of suppliers for prefabricated component (PC) production lines require significant attention. Evidence for this can be derived from Zhao, et al. [15], who stated that supplier selection directly influences the performance of prefabricated projects, as the purchase of PCs accounts for nearly 70% of the total cost. Similarly, Liang, et al. [16] argue that the selection of a supplier is critical to the success of prefabrication. This is because PC production lines act as the cornerstone of prefabrication, with its unique requirements and production rules, such as the mold arrangement, fixed-size platforms, and other facets, significantly influencing the efficiency of the prefabrication implementation [17,18,19]. However, selecting suppliers has become increasingly challenging due to the evolving, uncertain demands and complexity in production processes, especially in developing countries, where there is an anticipated surge in PC facilities. In fact, many PC producers are still facing the dilemma of how to evaluate and select suitable suppliers. Especially, according to the report by the China Construction Association Certification Center [20], most PC production lines are established by construction firms that lack experience in PC production. Therefore, the evaluation and selection of suppliers to address the client’s demands for PC production lines has become more pressing.

Satisfactory supplier selection makes a significant difference to a firm’s future, which can reduce the operational costs and improve the quality of products, and can allow for rapid responses to the customers’ demands [16,21,22]. One of the most important components of supplier evaluation and selection is criteria formulation. In such a process for selection, [23] stated that firms should have pursued the ‘‘lean’’ thinking paradigm to construct lean evaluation criteria, where the supplier attributes involve low cost, high quality, efficiency, and flexibility. This is more important for firms without professional experience in solving PC production problems, particularly during the development stage of prefabrication. Notably, the lean principle is effective for improving the operational management and boosting the quality and efficiency of production processes in prefabrication [24,25,26]. When evaluating PC production lines, it is necessary to implement all-round, multi-level lean principles [27]. This includes the process flow, equipment performance, personnel arrangement, production line layout, and platform configuration [28]. Several studies have concentrated on supplier selection based on lean criteria. For example, Rashidi, et al. [29] determined seven lean manufacturing evaluation criteria for supplier selection. Although these studies have provided valuable support for lean-based supplier selection, there is limited focus on supplier selection in the PC context. Additionally, lean supplier evaluation metrics should be selectively tailored from a wide range of criteria to align with the uniqueness of PC production and industry demands. Thus, lean evaluation criteria should consist not only of universal standards to reflect suppliers’ common features, but also specific standards, reflecting their own unique attributes.

Considering that PC supplier evaluation and selection is a multi-criteria decision-making (MCDM) problem [30], various quantitative models have been adopted in the MCDM area, including the Analytic Hierarchy Process (AHP), Analytic Network Process, Linear Programming, TOPSIS, Data Envelopment Analysis, and VIKOR [29,31,32,33,34,35,36,37]. Among of them, VIKOR is considered as particularly effective, as it can obtain a compromise solution that is closer to the ideal [38]. Moreover, to differentiate evaluation criteria, including universal and specific criteria, the VIKOR method can be modified to a group-based decision matrix that differs between different alternatives and different criteria [38]. Meanwhile, a hybrid model integrating the AHP into the VIKOR method was proposed, where the AHP was used to determine the weights of the evaluation criteria, and to improve the reliability and validity of the VIKOR model [39].

Building on this, this study develops a new, quantitative lean-based AHP–improved VIKOR framework to support the producer in selecting suppliers of PC production lines. The AHP is introduced to identify the weights of lean principles, including both the universal and specific criteria, to consider the multiple aspects of such decisions. After the weights are obtained, alterative suppliers are ranked by the improved VIKOR method for balancing conflicting and non-commensurable criteria. This offers a flexible system that not only ensures the lean aspects but also accounts for the distinctive characteristics of each PC production line. This framework reveals that it is important to consider both universal and specific evaluation criteria that highlight the advantages of each alternative supplier so to avoid focusing solely on one aspect.

2. Literature Review

Supplier selection is a critical element of the prefabrication production process and has been deeply investigated in the literature. This study closely reviews the following three streams to identify the gaps involved in supplier selection for PC production lines in prefabricated projects: (1) the lean principle, (2) supplier selection in PC production, and (3) MCDM methods for supplier selection. An in-depth review of these three streams in the literature is presented in the following sections.

2.1. Lean Principle

The “lean principle” began in the manufacturing environment and is known by a variety of synonyms, like lean manufacturing, lean production, the Toyota Production System, etc. [40]. It is mainly aimed at eliminating waste in process activities to reduce process cycles, improve the quality, and increase the efficiency, which is converted to a suitable form for use in construction [27,41]. Particularly, the rapid development of prefabricated construction has significantly increased the demand for PC production lines [42]. Concurrently, there is a growing trend towards adopting a lean culture and its principles in the construction sector [27,43,44,45]. Elmalky, et al. [46] and Rosli, Muhammad Tamyez and Zahari [44] discussed lean principles on construction waste to improve construction performance. Refocusing on prefabrication, it necessitates the specific molds, which are carried via various processing units to complete the entire production cycle [18]. This production process shares several characteristics, like modular production and sequential workflows, yet it also exhibits unique requirements and operational protocols [47]. With this in mind, Du, Xue, Sugumaran, Hu and Dong [25] shed light on the lean production scheduling of PCs using an improved biogeography-based optimization algorithm. In their study, lean principles, like value-based management and just-in-time, are incorporated into the production process of PCs. Similarly, Shabeen and Krishnan [48] employed value stream mapping in PC manufacturing to demonstrate lean principles so to increase production in a PC manufacturing unit. Moreover, the interactions of robotic systems and the lean principle were addressed in Gusmao Brissi, Wong Chong, Debs and Zhang [45], as well as the integration with the BIM [24,49,50]. However, most studies regarding lean principles focus on tackling phenomenal delays and budget over-runs [51]. The current lean research focus on production line evaluation and supplier selection remains limited.

2.2. Supplier Selection in PC Production

Notably, meticulous attention to production line evaluation and supplier selection is crucial for achieving PC production, not only because of cost-effectiveness, but also due to the higher quality and efficiency it ensures [15,52,53]. However, the multitude of diverse criteria must be considered. Among these, lean principles should have been prioritized [25,54,55].

The importance of evaluation in construction projects, which has been already highlighted by Yang, et al. [56], is that it builds the parameters to quantify the efficiency and effectiveness of the actions, and to reach the desired results. When introduced to PC production line evaluation, existing studies shed light on its supplier selection through various perspectives, like the BIM-based AHP method [15], sustainable development [53,57], the fuzzy TOPSIS model [16], and the neural network model [58]. In contrast to these studies, this paper introduces lean principles, which have been proven to be effective in industrial production processes and operations, to enhance the efficiency [59]. This becomes particularly imperative when selecting a PC production line, especially when facing challenges like low production efficiency, disorganized production processes, and poor production balance [42] at the initial stage of prefabrication development.

Though most studies regarding lean principles focus on tackling phenomenal delays and budget over-runs [51], several studies have concentrated on supplier selection based on lean principles. For instance, Rashidi, Noorizadeh, Kannan and Cullinane [29] determined seven lean manufacturing evaluation criteria for supplier selection, including the quality, cost, flexibility, customer service, just-in-time (JIT) performance, operational leanness, and labor leanness. Tsai [60] identified seven evaluation criteria based on lean concepts in the supplier selection model, i.e., reliability, capability, quality, distance, property, service, and economy. All the studies provided supportive and valuable information for evaluation and supplier selection through the lens of lean principles. However, specific selection criteria must be established based on practical considerations, including the context, the nature of the product, and the type of market [23,61]. In the context of PC production, there is a noted need for lean supplier evaluation metrics. These metrics should be selectively tailored from a wide range of criteria to specifically align with the uniqueness of PC production and industry perspective, reflecting the current state of prefabrication development.

2.3. MCDM Methods for Supplier Selection

PC production line evaluation and supplier selection is a problem of multi-criteria decision making (MCDM), wherein criteria such as cost, quality, and service will significantly influence the decision-makers’ preferences regarding potential suppliers [30]. In this context, a series of methods associated with MCDM has been used for supplier selection [37]. These can be based on a single method and/or based on integration techniques.

The single methods include the Analytic Hierarchy Process (AHP), Analytic Network Process, Linear Programming, TOPSIS, Data Envelopment Analysis, and VIKOR [29,31,32,33,34,35,36,37,62]. For example, Pamucar, et al. [63] proposed a fuzzy decision-making approach for supplier selection. Among these single methods, VIKOR emerged as a particularly effective approach for addressing MCDM problems [64]. The reason is that VIKOR can identify a compromise solution for supplier selection that is the closest to the ideal [38]. Particularly, this method seeks to maximum group utility while minimizing individual regret [65]. To this end, Amiri, Hashemi-Tabatabaei, Ghahremanloo, Keshavarz-Ghorabaee, Zavadskas and Banaitis [38] developed an improved VIKOR decision-making method, which necessitates a group-based decision matrix that varies across different alternatives and norms, thereby broadening the applicability of this VIKOR method. Moreover, the improved VIKOR method facilitates the development of supplier selection in lean management [66]. This method integrates both universal criteria and the specific criteria of features, thereby establishing the groundwork for a decision-making model focused on the lean-based evaluation and selection of suppliers. However, it should be noted that the single method for supplier selection lacks flexibility, and has conflicting and incommensurable aspects, for instance, quality criteria conflicts with those centered on cost reduction [1].

As a result, integration techniques have become popular, like the AHP + Fuzzy-VIKOR. Compared to single methods, the integrated techniques provide a more comprehensive analysis by leveraging the strengths of different MCDM methods [37]. Considering the benefits of the improved VIKOR, the integrated AHP–improved VIKOR is adapted in this study as an effective and easy-going method [67,68]. The benefit is that the AHP can be used to determine the weight of criteria, while the improved VIKOR method can be applied to rank the alternatives, considering both universal and specific criteria, to offer a detailed and multi-faceted view of the decision problem [69,70]. This can be further attributed to the fact that the assigned weights significantly influence the accuracy of the results calculated using the improved VIKOR method [71]. While there is no evidence specifically showcasing the use of the AHP–improved VIKOR in our proposed context, the advantages of integrating the AHP with VIKOR can be found in Soner, et al. [72], Awasthi, et al. [73], and Luthra, et al. [74], who have applied this integrated method to optimize the selection process in ship construction and supply chains. This study develops the AHP–improved VIKOR method based on AHP-VIKOR, with a unique focus on evaluating PC production lines and supplier selection. This adaptation not only addresses a significant gap in the literature but enhances the methodological framework to better suit the unique challenges of this sector.

In summary, most single MCDM methods fail to provide balanced results, and some integrated techniques do not adequately consider the weights of criteria, which often involve a mix of subjective and objective conditions. Considering the shortcomings of the existing methods, the plurality of criteria, and the inherent uncertainty in PCs, this paper develops a lean-based AHP–improved VIKOR framework to address production line evaluation and supplier selection problems.

3. Lean-Based AHP–Improved VIKOR Evaluation Framework

The developed AHP–improved VIKOR framework can be considered as a three-phase MCDM model, which includes the identification of the lean criteria system, the weighting of lean criteria, and the selection of the supplier, as shown in Figure 1.

3.1. Identifying the Universal Lean Evaluation Criteria

Evaluating a PC production line from a lean perspective necessitates the application of lean principles, alongside universal evaluation standards, to determine the line’s efficiency, resilience, and emergency responsiveness. However, applying a uniform set of evaluation criteria across diverse production lines poses challenges, as each line not only shares common features but also possesses its own unique attributes. Consequently, the evaluation of production line suppliers must incorporate both universal and specific criteria. Universal lean evaluation criteria constitute a foundational system for assessing PC production lines, encompassing the following five key aspects: standardization, quality, time, cost, and flexibility [75,76]. The universal second-level criteria of the five key aspects were identified by a literature review and interviews of experts.

Firstly, a systematic literature review was undertaken to identify a list of preliminary evaluation criteria. This study searched journal articles in Web of Science and Google Scholar with the following combination of keywords: “supplier selection and evaluation”, “lean” and “production line”, etc. The journal articles were further examined for whether they referred to the five aspects or not. Then, in-depth interviews were conducted with twenty experts (five lean experts, ten managers, and five PC experts) to validate the rationality and comprehensiveness of the preliminary criteria. These experts mainly had at least five years of experience in PC production lines. Based on their practical experiences, each criterion was reviewed, and suggestions were provided on whether certain preliminary criteria should be adjusted, added, or deleted. Based on these, the fourteen universal criteria of the five key aspects were identified, as shown in

Table 1. The universal lean evaluation criteria of PC production lines.

1st-Level Criteria	2nd-Level Criteria	Main Sources
A1: Standardization	Z1: Production process standardization degree	[77]
	Z2: Customized standard process design level	[78]
	Z3: The comprehensiveness of differentiated standard operating systems	[77]
	Z4: Standard operation level	[76]
A2: Quality	Z5: Total productive maintenance level	[17]
	Z6: Product quality and reliability level	[79]
	Z7: Equipment reliability or failure rate	[80]
A3: Time	Z8: Production Takt and turnround time	[81]
	Z9: Just-in-time and pull level	[82]
	Z10: Equipment utilization level	[77]
A4: Cost	Z11: Buying price	[83]
	Z12: Use and maintenance cost level	[84]
	Z13: Unit production cost	[83]
A5: Flexibility	Z14: Mass customization production level of the quick response to customers’ demands	[85]

. Furthermore, the specific lean evaluation criteria, focusing on the unique advantages and capabilities of each PC production line, should be determined to build the holistic lean evaluation criteria.

3.2. Weight Criteria Based on AHP

The AHP method is used to calculate the criterion weights, i.e., $W_i$. The calculation process of the AHP consists of the following four steps [31]: (1) constructing the pairwise comparison matrix, (2) calculating the priority vectors, (3) checking for consistency, and (4) determining the criterion weights.

3.2.1. Constructing Pairwise Comparison Matrices

Constructing a pairwise comparison matrix based on the relative importance scores among the criteria collected from experts is an important process for calculating the weights. The relative importance scores were evaluated by integrating the experts’ evaluations of each pair of criteria $i$ and j with the mean method [33], as shown in

Table 2. Relative importance scale of the criteria.

Score	Relative Importance
1	Criteria i and j are of equal importance.
3	Criteria i is weakly more important than j.
5	Criteria i is strongly more important than j.
7	Criteria i is very strongly more important than j.
9	Criteria i is absolutely more important than j.

Note: 2, 4, 6, and 8 are intermediate values.

.

$A$ pairwise comparison matrix A can be created based on the relative importance scores, shown as Equation (1). Each element $a_{ij}$ of the matrix represents the result of comparing element $i$ to element j in terms of their relative importance towards the upper hierarchy of the criteria.

$$A={\left(a_{\mathfrak{i}\mathfrak{j}}\right)}_{\mathfrak{n}\times \mathfrak{n}}$$

(1)

3.2.2. Calculating Priority Vectors

The priority vector, which means the relative weights of the elements being compared, is calculated from the pairwise comparison matrix $A$. The eigenvector method was used [86], where the priority vector W corresponds to the normalized principal eigenvector of the comparison matrix $A$. For the consistent reciprocal matrix, the largest eigenvalue $\lambda max$ is equal to the number of comparisons, or $\lambda max=n$.

$$AW={\lambda }_{max}W$$

(2)

The step to approximate $W$ involves normalizing each column of $A$ and then averaging across rows to obtain each criterion of $W$.

3.2.3. Checking for Consistency

To check the consistency of the pairwise comparisons, the Consistency Index ($CI$) and Consistency Ratio ($CR$) are calculated in Equations (3) and (4), as follows:

$$CI={\displaystyle \frac{{\lambda }_{max}-n}{n-1}}$$

(3)

$$CR={\displaystyle \frac{CI}{RI}}$$

(4)

where $n$ is the number of elements being compared and $RI$ is the Random Index, which is an average $CI$ for randomly generated pairwise comparison matrices of the same size $n$. The values of the $RI$ vary with n and are tabulated based on simulations. If $CR<0.10$, the judgments are considered acceptably consistent. If $CR\ge 0.10$, the judgments need to be reviewed.

3.2.4. Determining Criterion Weights

When determining the weights of the evaluation criteria corresponding to the upper hierarchy of criteria $W_i$, the lower hierarchy of the criteria corresponding to the evaluation goal can be finally calculated by Equation (5), where $i$ is the number of hierarchies of the evaluation criteria, as follows:

$$W_{final}=w_1\times w_2\times ···\times w_i$$

(5)

3.3. Supplier Evaluation and Selection Based on Improved VIKOR Method

After determining the weights and scores for each criterion, the suppliers of PC production lines can be evaluated and selected. Using the steps of the improved VIKOR method, which requires modifications when deciding among suppliers, we can evaluate the suppliers based on both universal and specific criteria [66,87,88]. This approach leverages the strengths of the VIKOR method to ensure a comprehensive assessment. The steps of the improved VIKOR method are as shown below:

Step 1: Construct and aggregate the evaluation matrix.

We calculate the evaluation value $f_{ij}$ of the group decision matrix $D_i$ based on each alternative and each evaluation criteria belonging to the alternative, because each alternative has its own evaluation criteria. Every expert from the group of decision-makers makes a separate evaluation matrix, which consists of the evaluation of alternatives compared to the corresponding criteria, with a scale of 1–5 [66]. Then, we average the separated evaluation matrices by each expert into one decision matrix D, which is formed as in

Table 3. Group decision matrix.

	Z1	Z2	Z3	$\cdots$	Zn
$S_1$	$f_{11}$	$f_{12}$	$f_{13}$	$\cdots$	$f_{1n}$
$S_2$	$f_{21}$	$f_{22}$	$f_{23}$	$\cdots$	$f_{2n}$
$S_3$	$f_{31}$	$f_{32}$	$f_{33}$	$\cdots$	$f_{3n}$
$⋮$	$⋮$	$⋮$	$⋮$	$\ddots$	$⋮$
$S_m$	$f_{m1}$	$f_{m2}$	$f_{m3}$	$\cdots$	$f_{mn}$

.

Step 2: Select the best value and the worst value of each sub-criterion.

We then set $f_j^{\ast }$, which represents the optimal evaluation value, and $f_j^{-}$, which represents the worst value. Universally, $f_j^{\ast }$ and $f_j^{-}$ can be separately determined by the largest and smallest ranking values $f_{ij}$ in the decision matrix, or the theoretically largest and smallest evaluation values. Considering the sub-criteria $Z_j$, if $Z_j$ belongs to the type of efficiency criteria

$$f_j^{\ast }=\begin{array}{c}max\\ i\end{array}\left(f_{ij}, j=\mathrm{1,2}\dots , n\right)$$

(6)

$$f_j^{-}=\begin{array}{c}min\\ i\end{array}\left(f_{ij}, j=\mathrm{1,2}\dots , n\right)$$

(7)

If ${\mathrm{Z}}_{\mathrm{j}}$ belongs to the type of cost criteria

$$f_j^{\ast }=\begin{array}{c}min\\ i\end{array}\left(f_{ij}, j=\mathrm{1,2}\dots , n\right)$$

(8)

$$f_j^{-}=\begin{array}{c}max\\ i\end{array}\left(f_{ij}, j=\mathrm{1,2}\dots , n\right)$$

(9)

Step 3: Calculate the values of $Q_i$ and $G_i$.

$Q_i$ and $G_i$ represent the group utility and individual loss utility. $Q_i$ means the difference between the overall solution and the optimal solution in the ideal state. $G_i$ is the difference between the actual value of a single criterion for the suppliers and its optimal value in each supplier. The group utility $Q_i$ and individual utility $G_i$ of the alternatives based on the corresponding evaluation criteria of every alternative are determined as follows:

$$Q_i=\sum _{j=1}^n{\displaystyle \frac{W_j\left(f_j^{\ast }-f_{ij} \right)}{f_j^{\ast }-f_j^{-}}}$$

(10)

$$G_i=\begin{array}{c}max\\ i\end{array}\left[{\displaystyle \frac{W_j\left(f_j^{\ast }-f_{ij} \right)}{f_j^{\ast }-f_j^{-}}}\right]$$

(11)

From the above, $Q^{\ast }=\begin{array}{c}min\\ i\end{array}{Q}_i$, $Q^{-}=\begin{array}{c}max\\ i\end{array}{Q}_i$, $G^{\ast }=\begin{array}{c}min\\ i\end{array}{G}_i$, $G^{-}=\begin{array}{c}max\\ i\end{array}{G}_i$. $Q^{\ast }$, and $G^{\ast }$ are, respectively, the smallest values of the utility cost. The total utility of a supplier of PC production lines is the combination of both group optimal utility and individual loss utility.

Step 4: Computation of VIKOR index $U_i$.

$U_i(i=\mathrm{1,2},\dots ,m)$ represents the total utility of an alternative supplier of PC production lines, $r$ means the weight of the group utility, and $1-r$ is the weight of the individual loss utility $(0\le r\le 1)$; therefore, $r$ shows the decision-making mechanism coefficient of alternative suppliers, as follows:

$$U_i=r\left[{\displaystyle \frac{Q^{\ast }-Q_i }{Q^{\ast }-{Q }^{-}}}\right]+\left(1-r\right)\left[{\displaystyle \frac{G^{\ast }-G_i}{G^{\ast }-{G }^{–}}}\right]$$

(12)

It can be seen from the $U_i$ formula that the comprehensive utility loss of the scheme considers the comprehensiveness of the whole and the uniqueness of one, the weights of which are variable. The decision-makers can reach a consensus through negotiation. If $r<0.5$, then minimizing the individual loss utility plays a dominant role in the evaluation mechanism; if $r=0.5$, then minimizing the individual regret utility plays the same role as maximizing the group utility, and decision-makers reach consensus through consultation; if $r>0.5$, then maximizing the group utility plays a dominant role in the evaluation mechanism.

Universally, minimizing the individual loss utility is considered as equally important as maximizing the group utility, where $U_i$ represents the expression of the total utility of decision making when using the improved VIKOR method to make decisions, upon which decision-makers reach agreement through discussion. The decision-making mechanism coefficient is 0.5 according to Valipour Parkouhi and Safaei Ghadikolaei [69], Anvari, Zulkifli and Arghish [70], Prasad, et al. [89], Chang [90].

Step 5: Rank the order of preference.

An alternative based on the calculation results is prioritized and the following sequence is formed according to the value of $U_i$ from small to large: ${\mathrm{S}}^{\left(1\right)},{\mathrm{S}}^{\left(2\right)},\dots ,{\mathrm{S}}^{\left(\mathrm{m}\right)}$. The following two conditions must be satisfied before the alternative in the first position in the $U_i$ ranking is suggested as the adjustment’s solutions:

I.

Acceptable advantage:

$$U\left(S^{\left(2\right)}\right)-U\left(S^{\left(1\right)}\right)\ge {\displaystyle \frac{1}{m-1}}$$

(13)

In which m is the number of alternative suppliers in the problem and S₂ in the $U$ ranking list means the alternative with the second position.

II.

Acceptable stability:

The alternative S ⁽¹⁾ must also be the best in the $Q$ or $G$ ranking list. Go to the extra phase to obtain the compromise solution if either condition is not satisfied. When condition I is not satisfied, then the compromise solution is ${\mathrm{S}}^{\left(1\right)},{\mathrm{S}}^{\left(2\right)},\dots ,{\mathrm{S}}^{\left(\mathrm{m}\right)}$, and the maximum values of $m$ need to be searched with the following relationship:

$$U\left(S^{\left(m\right)}\right)-U\left(S^{\left(1\right)}\right)<{\displaystyle \frac{1}{m-1}}$$

(14)

When condition II is not satisfied, then both S ⁽¹⁾ and S ⁽²⁾ are adjustment solutions. So, condition I refers to the optimal terms of the acceptable alternative, and condition II is accepted as a stable decision-making alternative.

4. Case Study

4.1. Case Description

Yizhong Construction firm is a leading universal contractor in Tianjin, China. In response to China’s PC development policy, this firm proactively embraced PC production and construction. This initiative included establishing PC factories for production to bolster industrialized construction capabilities. It also formed a collaborative partnership with PC experts for the evaluation and selection of PC suppliers. They emphasized the production line’s critical role in determining the quality, efficiency, and cost of PCs. Meanwhile, they provided the valuable lean insights of selecting the supplier of PC production lines through the analysis of the site selection, factory, and workshop layout. The experts were selected and invited via the following snow sampling principle: (1) at least 5 years of related PC knowledge; (2) having undertaken important tasks in PC production; (3) holding senior positions in production teams [91]. These principles can ensure that the selected experts are qualified to answer questions pertaining to the supplier of PC production lines so to ensure the validity and accuracy. This expert group, comprised of professional individuals from Yizhong, Tianjin University, Yuanda, and other PC factories, included five lean experts, ten managers, and five PC experts, totaling twenty members. The detailed information of these twenty experts is shown in

Table 4. Expert profiles.

No. Expert	Stakeholder Group	No.	Main Position	Education Level	Experience
1	Tianjin University	3	Professor	Master’s	5≤
2	Tianjin University	2	Senior scholar	Bachelor’s	5≤
3	Yizhong	1	Universal manager	Master’s	5≤
4	Yizhong	4	Vice-Universal manager	Master’s	5≤
5	Yizhong	5	Project manager	Bachelor’s	5≤
6	Yuanda Factory	2	Factory director	Master’s	5≤
7	Other Factories	3	Universal manager	Master’s	5≤

.

In this case context, the following three suppliers participated in the survey: Tianyi, Zhongjian, and Xindadi. The PC production lines of each presented unique strengths and weaknesses. The experts conducted on-site studies and interviews with the three suppliers, summarizing their respective strengths and weaknesses, and extracting their key characteristics, as detailed in

Table A1. The description of the suppliers.

Suppliers	The Main Description of the Production Line	Special Characteristic
Zhongjian	Automated production line with state-of-the-art automated equipment; requires little manual labor; simple equipment operation without the need for technical training; a high level of craftsmanship; strong expandability; extensive visual monitoring means of process control.	High level of automation and digitalization
Tianyi	Semi-automatic production line with partial automatic machinery, like a curing kiln and material feeder; well-designed logistics; free technical training provided; a variety of matching mold types, thereby improving the responsiveness to customer demands.	High level of mold utilization and optimization
Xindadi	Manual production line with less automatic equipment, with most of the operations carried out manually by workers; minimal fixed asset investment, using natural curing methods, requiring relatively more workers; the common solution without the need for specific criteria.	-

.

4.2. Data Analysis

4.2.1. Establishing Specific Lean Evaluation Criteria

In contrast, the specific lean evaluation criteria focus on the unique advantages and the capabilities particular to each PC production line, necessitating individual industrial considerations. For example, Zhongjian’s production line is distinguished by its advanced digital technology and capabilities, while Tianyi excels in the layout efficiency and turnaround rate. The specific second-level criteria were determined by the twenty experts based the alternative suppliers of Zhongjian, Xindadi, and Tianyi. Then, in-depth interviews with the twenty experts were conducted to identify the specific lean evaluation criteria of three alternative suppliers so to construct the holistic lean evaluation criteria. First, the experts were invited by telephone or face-to-face to discuss whether the universal criteria identified from the literature exist or not in a real-world PC production situation. Additional criteria were also proposed and explained based on their experiences. Secondly, they identified the specific evaluation criteria based the character of alternative suppliers. Each interview lasted 1–2 h so to confirm the reliability of the identified criteria. When disagreements among interviewees existed, these experts were contacted for further discussion. After three rounds of discussion, the experts reached agreement for all the questions. The final evaluation criteria, combing universal and specific criteria, are detailed in

Table A2. The lean evaluation criteria of PC production lines with specific criteria.

1st-Level Criteria	2nd-Level Criteria	Suppliers
		ZJ	Y	DD
A1: Standard	Z1: Production process standardization degree	✓	✓	✓
	Z2: Customized standard process design level	✓	✓	✓
	Z3: The comprehensiveness of differentiated standard operating systems	✓	✓	✓
	Z4: Standard operation level	✓	✓	✓
A2: Quality	Z5: Total productive maintained level	✓	✓	✓
	Z6: Product quality and reliability level	✓	✓	✓
	Z7: Equipment reliability or failure rate	✓	✓	✓
	Z8: * Automated monitoring level of quality and reliability	✓	-	-
A3: Time	Z9: Production Takt and turnround time	✓	✓	✓
	Z10: Just-in-time and pull level	✓	✓	✓
	Z11: Equipment utilization level	✓	✓	✓
	Z12: * One-piece flow level and line balance level	✓	-	-
	Z13: * Mold optimization level for improving the operation efficiency	-	✓	-
A4: Cost	Z14: Buying price	✓	✓	✓
	Z15: Use and maintenance cost level	✓	✓	✓
	Z16: Unit production cost	✓	✓	✓
	Z17: * Mold utilizing operation	-	✓	-
A5: Flexibility	Z18: Mass customization production level of the quick response to customers’ demands	✓	✓	✓

Note: “*” indicates the specific evaluation criteria of a certain production line; “✓” indicates a certain production line has corresponding characteristics; “-” indicates a production line does not have corresponding characteristics.

.

4.2.2. Calculating Weights of Criteria

The weights of first-level criteria (standard, quality, time, cost, and flexibility) corresponding to the lean evaluation goals, WA1, WA2, WA3, WA4, and WA5, were calculated. The relative importance scores among the five criteria were determined by the twenty experts, according to Table 2, to construct a pairwise comparison matrix, as shown in

Table 5. The pairwise comparison matrix of five first-level criteria.

1st-Level Criteria	A1	A2	A3	A4	A5
A1	1	1/3	1	1/5	3
A2	3	1	3	1/3	5
A3	1	1/3	1	1/5	3
A4	5	3	5	1	7
A5	1/3	1/5	1/3	1/7	1

.

The weights were calculated by Equations (1)–(4), based on the average scores of twenty experts, and are as follows:

$\mathit{W}=\left[\mathit{W}\mathit{A}\mathbf{1},\mathit{W}\mathit{A}\mathbf{2},\mathit{W}\mathit{A}\mathbf{3},\mathit{W}\mathit{A}\mathbf{4},\mathit{W}\mathit{A}\mathbf{5}\right]=[0.102,0.245,0.102,0.504,0.046]$, $\mathit{C}\mathit{I}=0.0317\mathit{C}\mathit{R}=0.0283<0.1$; thus, the judgments are considered acceptably consistent.

Then, the weights of the second-level criteria, corresponding to five first-level criteria, were calculated. Since the lean evaluation criteria of each supplier of a PC production line were different, which is shown in Table A2, the weights of the second-level criteria were calculated for each supplier in Zhongjian, Tianyi, and Xindadi. The calculating processes were the same as the calculations of the weights of the five first-level criteria. The weights of the second-level criteria, corresponding to five first-level criteria of Zhongjian, Tianyi, and Xindadi, are shown in

Table A3. The lean evaluation criteria of PC production lines.

The Evaluation Goal	1st-Level Criteria	Weights of 1st-Level Criteria	2nd-Level Criteria	Weights Corresponding to 1st-Level Criteria			Weights Corresponding to the Evaluation Goal
				ZJ	TY	XDD	ZJ	TY	XDD
The lean evaluation and selection of suppliers	A1	0.102	Z1	0.125	0.125	0.125	0.013	0.013	0.013
			Z2	0.375	0.375	0.375	0.038	0.038	0.038
			Z3	0.375	0.375	0.375	0.038	0.038	0.038
			Z4	0.125	0.125	0.125	0.013	0.013	0.013
	A2	0.245	Z5	0.390	0.637	0.637	0.096	0.156	0.156
			Z6	0.068	0.105	0.105	0.017	0.026	0.026
			Z7	0.152	0.258	0.258	0.037	0.063	0.063
			Z8	0.390	-	-	0.096	-	-
	A3	0.102	Z9	0.113	0.168	0.637	0.012	0.017	0.065
			Z10	0.064	0.075	0.258	0.007	0.008	0.026
			Z11	0.411	0.570	0.105	0.042	0.058	0.011
			Z12	0.411	-	-	0.042	-	-
			Z13	-	0.187	-	-	0.019	-
	A4	0.504	Z14	0.637	0.522	0.637	0.321	0.263	0.321
			Z15	0.258	0.200	0.258	0.130	0.101	0.130
			Z16	0.105	0.078	0.105	0.053	0.039	0.053
			Z17	-	0.200	-	-	0.101	-
	A5	0.046	Z18	1	1	1	0.046	0.046	0.046

Note: “-” means irrelevant evaluation criteria of PC production lines.

. Then, the weights of the second-level criteria, corresponding to the lean evaluation goals, were further calculated with Equation (5).

4.2.3. Selecting Suppliers

After determining the weights of the evaluation criteria for each supplier, we used the improved VIKOR method to evaluate and select the supplier of the PC production line according to the steps shown in Section 3.3.

Step 1: The aforementioned experts from the set of twenty experts produced the evaluation value $f_{ij}$ of the evaluation matrix through the comparison of three alternatives of PC production lines relative to each criteria by using a scale of 1–5 [66]. In the scale, one signifies ‘tiny or extremely difficult’, two denotes ‘lesser or difficult’, three represents ‘medium’, four indicates ‘big or easy’, and five corresponds to ‘giant or very easy’. Then, we averaged every evaluation matrix by each expert into one decision matrix D, which was formed as shown below in

Table A4. The aggregation decision matrix of experts’ opinions for alternatives.

	Z1	Z2	Z3	Z4	Z5	Z6	Z7	Z8	Z9	Z10	Z11	Z12	Z13	Z14	Z15	Z16	Z17	Z18
Zhongjian	4.50	3.83	4.67	3.33	3.83	3.50	3.33	4.33	4.00	3.83	3.50	4.50	-	4.83	2.67	3.83	-	3.50
Tianyi	4.00	3.67	4.17	4.00	4.33	3.50	3.50	-	4.33	4.17	4.33	-	4.33	4.00	3.50	3.83	4.00	4.17
Xindadi	3.67	3.00	3.83	4.00	4.67	3.50	4.17	-	3.67	3.50	2.83	-	-	2.33	4.00	4.33	-	3.50

.

Step 2: The next step was to select the best value $f_j^{\ast }$ and the worst value $f_j^{-}$ of each sub-criterion according to Equations (6) and (7). Considering that the criteria $Z_j$ is the efficiency criteria, we set five as the highest-ranking value $f_j^{\ast }$ and one as lowest-ranking value $f_j^{-}$.

Step 3: We then calculated the values of $Q_i$ and $G_i$ for the alternatives based on the corresponding evaluation criteria of every alternative using Equations (10) and (11), as shown in

Table A5. Results of the selection process based on the improved VIKOR.

	${\mathit{Z}}_{\mathit{j}}$	${\mathit{f}}_{\mathit{i}\mathit{j}}^{-}$	${\mathit{f}}_{\mathit{i}\mathit{j}}^{\mathbf{\ast }}$	${\mathit{f}}_{\mathit{i}\mathit{j}}$	${\mathit{R}}_{\mathit{i}\mathit{j}}$	${\mathit{W}}_{\mathit{i}\mathit{j}}$	${\mathit{W}}_{\mathit{i}\mathit{j}}\mathbf{ \ast }{\mathit{R}}_{\mathit{i}\mathit{j}}$	${\mathit{G}}_{\mathit{i}}$	${\mathit{Q}}_{\mathit{i}}$	${\mathit{U}}_{\mathit{i}}$	Rank
Zhongjian	Z1	1	5	4.50	0.125	0.013	0.002	0.066	0.235	0.156	1
	Z2	1	5	3.83	0.293	0.038	0.011
	Z3	1	5	4.67	0.083	0.038	0.003
	Z4	1	5	3.33	0.418	0.013	0.005
	Z5	1	5	3.83	0.293	0.096	0.028
	Z6	1	5	3.50	0.375	0.017	0.006
	Z7	1	5	3.33	0.418	0.037	0.016
	Z8	1	5	4.33	0.168	0.096	0.016
	Z9	1	5	4.00	0.250	0.012	0.003
	Z10	1	5	3.83	0.293	0.007	0.002
	Z11	1	5	3.50	0.375	0.042	0.016
	Z12	1	5	4.50	0.125	0.042	0.005
	Z14	1	5	4.83	0.043	0.321	0.014
	Z15	1	5	2.67	0.583	0.130	0.076
	Z16	1	5	3.83	0.293	0.053	0.015
	Z18	1	5	3.50	0.375	0.046	0.017
Tianyi	Z1	1	5	4.00	0.25	0.013	0.003	0.076	0.254	0.160	2
	Z2	1	5	3.67	0.333	0.038	0.013
	Z3	1	5	4.17	0.208	0.038	0.008
	Z4	1	5	4.00	0.250	0.013	0.003
	Z5	1	5	4.33	0.168	0.156	0.026
	Z6	1	5	3.5	0.375	0.026	0.010
	Z7	1	5	3.5	0.375	0.063	0.024
	Z8	1	5	4.33	0.168	0.017	0.003
	Z9	1	5	4.17	0.208	0.008	0.002
	Z10	1	5	4.33	0.168	0.058	0.010
	Z11	1	5	4.33	0.168	0.019	0.003
	Z12	1	5	4.00	0.250	0.263	0.066
	Z14	1	5	3.50	0.375	0.101	0.038
	Z15	1	5	3.83	0.293	0.039	0.012
	Z16	1	5	4.00	0.250	0.101	0.025
	Z18	1	5	4.17	0.208	0.046	0.010
Xindadi	Z1	1	5	3.67	0.333	0.013	0.004	0.214	0.384	0.299	3
	Z2	1	5	3.00	0.50	0.038	0.019
	Z3	1	5	3.83	0.293	0.038	0.011
	Z4	1	5	4.00	0.250	0.013	0.003
	Z5	1	5	4.67	0.083	0.156	0.013
	Z6	1	5	3.50	0.375	0.026	0.010
	Z7	1	5	4.17	0.208	0.063	0.013
	Z8	1	5	3.67	0.333	0.065	0.022
	Z9	1	5	3.50	0.375	0.026	0.010
	Z10	1	5	2.83	0.543	0.011	0.006
	Z11	1	5	2.33	0.668	0.321	0.214
	Z12	1	5	4.00	0.250	0.130	0.033
	Z14	1	5	4.33	0.168	0.053	0.009
	Z15	1	5	3.50	0.375	0.046	0.017

.

Step 4: This step included the calculation of the VIKOR index $U_i$, which represents the total utility of an alternative supplier of three PC production lines according to Equation (12). Here, the decision-making mechanism coefficient $r$ was 0.5, according to Valipour Parkouhi and Safaei Ghadikolaei [69], Anvari, Zulkifli and Arghish [70], Prasad, Prasad, Rao and Patro [89], Chang [90]. Furthermore, the twenty experts were invited to evaluate the importance of minimizing the individual regret utility and maximizing the group utility. The experts thought that they played the same role, meaning that r was also 0.5. The results of $U_i$ for Zhongjian, Tianyi, and Xindadi are shown in Table A5.

Step 5: We then ranked the order of three alternative suppliers of PC production lines based on the value of $U_i$ from small to large. Originally, the ranking results of $U_i$ were $U_1<U_2<U_3$, leading to the ranking results of S ^(1), S ⁽²⁾, and S ⁽³⁾ as Zhongjian, Tianyi, and Xindadi. According to Equations (13) and (14), two conditions should be further satisfied before the alternative supplier in the first position in the Ui ranking. Condition I: $U\left({\mathrm{S}}^{\left(2\right)}\right)-U\left({\mathrm{S}}^{\left(1\right)}\right)\ge {\displaystyle \frac{1}{m-1}}$, in which $\mathit{U}\left({\mathrm{S}}^{\left(2\right)}\right)-U\left({\mathrm{S}}^{\left(1\right)}\right)$ = 0.160 − 0.156 = 0.04, ${\displaystyle \frac{1}{m-1}}$ = ${\displaystyle \frac{1}{3-1}}$ = 0.5. Therefore, condition I is not satisfied. For condition II, the first-order value of $U_1$ is the first-order value of $Q$ and of $G$. The ranking of the $Q$ values from small to large is as follows: $Q_1<Q_2<Q_3$. The ranking of the $G$ values from small to large is as follows: $G_1<G_2<G_3$. Therefore, the compromise solution is S ⁽¹⁾, S ⁽²⁾, and S ⁽³⁾. Additionally, if condition I is not satisfied, the maximum values of m need to be searched with the relationship $\mathit{U}\left({\mathrm{S}}^{\left(\mathbf{m}\right)}\right)-\mathit{U}\left({\mathrm{S}}^{\left(\mathbf{1}\right)}\right)<{\displaystyle \frac{1}{\mathit{m}-1}}$, in which $U\left({\mathrm{S}}^{\left(3\right)}\right)-U\left({\mathrm{S}}^{\left(1\right)}\right)$ = 0.299 − 0.156 = 0.143 < 0.5. Hence, the final ranking of the three alternatives, S ⁽¹⁾, S ⁽²⁾, and S ⁽³⁾, is Zhongjian, Tianyi, and Xindadi, as shown in Table A5.

4.3. Case Result

The result means that the three suppliers are ranked as Zhongjian > Tianyi > Xindadi, where Zhongjian is the best supplier in this case study. The PC production line of Zhongjian offers significant advantages, including cost efficiency, ease of operation, balanced production, and the comprehensive management of information in practical scenarios. Furthermore, its proximity to the Yizhong Construction Co., Ltd. facilitates convenient services such as equipment installation, debugging, production guidance, and maintenance. As Yizhong Construction Co., Ltd. is currently undergoing a transition period, partnering with Zhongjian could lead to savings in investment and production costs while enhancing the production operability.

5. Discussion and Conclusions

This study examined the evaluation of production lines and supplier selection for prefabricated construction projects through the lens of lean principles. Unlike the existing selection models, like TOPSIS [53,57], the developed framework integrated the AHP [92] to assign weights to the lean criteria and employed the improved VIKOR method [93] to rank alternative suppliers, which was designed to facilitate the selection of suppliers for PC production lines, especially in developing countries.

To demonstrate the practical applicability the lean-based AHP–improved VIKOR evaluation framework, a case study was conducted in collaboration with experts from Tianjin University and three leading PC factories. The case study identified Zhongjian as the optimal supplier for the PC production line based on its superior performance in various lean-oriented criteria, such as cost efficiency, operational simplicity, and the effective management of information systems. These lean criteria are critical for fostering lean thinking in PC production and for optimizing prefabrication outcomes.

To be more specific, this study expands the scope beyond the limitations observed in the works by Abdollahi, Arvan and Razmi [23] by fully integrating these lean criteria into a comprehensive MCDM framework that includes both universal and specific criteria [15,66]. Notably, while the single methods, such as the AHP, DEA, VIKOR, and TOPSIS, have been explored in the literature, the integrated AHP–improved VIKOR method distinguishes itself by combining the weighted dimensions to synthesize diverse criteria into a coherent evaluation and ranking system [72]. This approach acknowledges the multifaceted nature of supplier selection, which aligns with the holistic objective of lean operations in prefabrication, thereby offering an advancement over traditional construction.

The contribution of this study is twofold. From a theoretical view, it expands the existing body of knowledge for the evaluation of production lines for PCs via a lean-based AHP–improved VIKOR framework, facilitating a deeper understanding of the combination of both universal and specific criteria in supplier selection. This developed framework enriches the project management practices of prefabrication development from an efficient procurement perspective. From a practical view, it provides the following actionable insights:

• For suppliers of PC production lines, it is vital to enhance and develop lean operation capabilities and management strategies based on the evaluation criteria so to improve the efficiency and success of PC production lines.
• For producers of PCs, they should consider the level of automaticity and information technology, and lean production requirements, while selecting the production line.
• For policymakers, it is necessary to formulate industry standards and conduct relevant activities, like adding lean principles into policies for PC development, so to improve the awareness of lean-based PC production lines.

6. Limitations and Future Directions

While the lean-based AHP–improved VIKOR framework provides a robust tool for supplier selection in prefabricated component (PC) production lines, this study has certain limitations. Firstly, the framework relies on comprehensive, high-quality data for accurate decision making, which can be difficult to obtain in resource-constrained environments. Future research could focus on adapting the framework specifically for suppliers operating under such constraints. Additionally, scalability remains a challenge, as adapting the framework to suppliers of varying sizes and operational complexities can be demanding. Future studies could aim to simplify the framework so to enhance the accessibility and to incorporate real-time data analysis tools for improved usability. Lastly, to adapt to the dynamic supply chain environment, a feedback mechanism, like the long-term performance evaluation of the framework, could be established. This would enable regular updates and refinements, ensuring that the criteria align with the current demands and requirements of the PC supply chain.