A New Model of Emergency Supply Management for Swift Transition from Peacetime to Emergency Considering Demand Urgency and Supplier Evaluation

Abstract

In recent years, the increasing complexity of natural disasters has highlighted the limitations of existing emergency material assistance systems. To address these challenges, this study proposes a collaborative adaptation mechanism for “peacetime and emergency integration” and develops a supplier evaluation framework. The framework incorporates multi-dimensional indicators such as profit, business credit, regional advantages, and emergency capability. Using a DEMATEL-ANP-based model, supplier L2 is identified as the optimal choice with a weight of 0.285. A fuzzy comprehensive assessment approach is applied to classify emergency materials based on demand urgency, identifying drinking water, rescue tools, medical supplies, and other critical items as priority resources. The evaluation vectors for these materials range from 0.1540 to 0.9909. This study enhances emergency material management through improved information systems, a better control of critical processes, and a unified assurance strategy. It provides theoretical support and practical guidance for more scientific and standardized disaster management practices.

1. Introduction

In recent years, various disasters have occurred on a regular basis; extreme weather disasters have become more intense, and the risk of natural and man-made disasters, like earthquakes and epidemics, has increased, with their sudden onset, large damage surface, long time span, chain reaction, complex environment, and other characteristics causing massive losses to the country and its people. On 18 December 2023, an MS6.2 earthquake occurred in Jishishan County, Linxia Prefecture, Gansu Province. As of 31 December 2023, the earthquake has caused 151 deaths and 979 injuries. In this short period of time, there was a need for medical supplies, as well as water and food, to meet survival needs [1]. From 10 to 21 February 2024, a total of 221 forest fires occurred in Guizhou Province. Due to strong winds and the rapid fire spread in the early stage, local government departments actively organized emergency forces to rush to the scene to fight and rescue, and a total of more than 9200 people and nearly 40,000 units of equipment participated in the fighting of the forest fire [2]. Since early 2020, Japan has reported severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) transmission, with approximately 27.0 million cumulative COVID-19 cases reported as of mid-December 2022. Routine public health reporting may underestimate true numbers of infections because mild or asymptomatic cases may not be tested and are likely to remain unidentified [3]. As China’s social economy continues to expand, various catastrophes occur on a regular basis, and the types, scales, and characteristics of these emergencies have evolved significantly [4]. The traditional emergency material support system has failed to fulfill the demands of reacting to emergencies.

During the epidemic, the demand for emergency supplies skyrockets, pharmacies run out of stock, production costs rise, prices rise, and demand outpaces supply. Currently, there are issues such as the lack of effective supply, variable quality, and difficulty in ensuring suppliers’ reputations [5]. The COVID-19 epidemic has highlighted the need for emergency supplies [6]. Traditional emergency material management has shortcomings in the form of material shortages, an inadequate reserve system and an inflexible distribution mechanism. Currently, the emergency material management system cannot handle the outbreak. Earthquakes, typhoons, and wildfires present an increasing need to quickly adapt emergency material management from peacetime to emergency situations, while epidemics require faster provider response [7]. These issues have not only resulted in the wasting of emergency resources and the slowing of rescue efforts, but they also had a significant influence on people’s lives and societal stability. Consequently, it is imperative to tackle the pressing matter of coordinated stockpiling and swift conversion during public emergencies while enhancing the effectiveness of emergency supply usage and expediting supplier assessment.

In this study, DEMATEL technology and ANP are utilized to create an evaluation index system for emergency material providers with four levels of indicators as follows: profit, business credit, regional advantage, and emergency capacity. The significance of suppliers’ time efficiency, supply quality, and other system variables is assessed. Based on the evaluation results, we developed a flexible supplier supply plan to ensure a reasonable material reserve. Simultaneously, AHP and fuzzy comprehensive evaluation methods are used to convert the qualitative evaluation of the urgency of emergency materials into quantitative evaluation, and a fuzzy comprehensive evaluation index system is built to comprehensively evaluate the urgency of emergency material demand, providing a strong support for emergency material management and scheduling. The DEMATEL-ANP methodology is used to evaluate solutions for rapidly adapting emergency supplies in both routine and crisis scenarios while taking into consideration the inherent constraints of each approach [8]. The model’s design makes it suitable for measuring the urgency of emergency materials in public health emergencies. This technique aids in the sensible selection of emergency supply suppliers, as well as the speedy transition between normal reserves and emergency deployment, hence optimizing resource utilization and improving the overall emergency supply management system.

The main innovation points are reflected in the following aspects. First, the development of a digital management system is based on the “emergency integration” collaborative adaptation mechanism in order to improve the intelligent and efficient management level of emergency warehousing and achieve a rapid response mechanism. Second, a complete evaluation index system is built using the four factors of profit, business credit, regional advantage, and emergency capacity to comprehensively and accurately analyze all of the elements of emergency storage management. Finally, this work innovatively blends DEMATEL, ANP, and the fuzzy comprehensive evaluation method, providing a strong theoretical support and practical assistance for emergency material management and optimization.

The abstract of this paper provides a concise overview of the whole content. Section 1 outlines the idea, present status, issues, and innovative solutions related to emergency supplies. Section 2 involves the integration of findings from both national and international research to provide a concise overview. Section 3 outlines the methodology for constructing the DEMATEL-ANP model while Section 4 clarifies the fuzzy comprehensive assessment strategy and the associated data analysis. Section 5 concludes the paper. The most recent aggregation of references is presented after that. The research concepts and research material of this work are depicted in Figure 1 below.

2. Literature Review

After the COVID-19 epidemic, emergencies such as public health problems, natural disasters and geopolitical conflicts have become more common, and it is necessary for countries to increase their emergency supplies reserves. The reserve of emergency materials is essential for the effective response to unexpected natural disasters and timely rescue operations. In emergency situations, adequate supplies allow for the efficient and rapid allocation of resources, significantly improving the effectiveness of relief efforts and protecting the population. In normal times, a sufficient stock of resources can effectively meet people’s needs for necessities, such as medical supplies, water, and food. Therefore, the research of this paper focuses on the scientific management of emergency materials, and the relevant research is mainly concentrated in the following three aspects.

2.1. Current Situation of Emergency Logistics and Supply Chain Management

Emergency logistics is crucial to providing disaster relief assistance, and its importance in daily life cannot be underestimated. In order to cope with increasingly complex emergencies, the use of systematic and efficient methods helps to improve the emergency transformation capacity of emergency logistics systems. Medical supplies are an important resource in the fight against major infectious diseases. Therefore, the strategic arrangement and rational distribution of emergency medical supplies are essential to reduce deaths and losses in disaster areas and improve the efficiency of relief operations. Wang and Zhu developed a multi-objective optimization model for coordinating the distribution of emergency medical supplies across many locations, including the differences in material storage and regional supply imbalances. Their research results show that considering regional differences in the process of emergency resource allocation can greatly improve the effectiveness of cooperative material allocation [9].

Zhang et al. used the DEA method to construct an evaluation model and successfully implemented it in reality, improving the timeliness and equality of material distribution [10]. In addition, Guan et al. combined the entropy method and TOPSIS to evaluate the effectiveness of his model by taking the Wenchuan earthquake as a case study [11]. Still, these studies tend to focus on a single category of commodities and ignore the inherent complexities in the distribution of various emergency supplies. Infectious diseases are a worldwide public health threat exacerbated by the difficulties in resource allocation [12]. Emergency response often encounters supply–demand imbalances, which makes the strategic use of emergency resources critical to reducing costs and improving response efficiency. These findings highlight the need for more flexible and comprehensive emergency logistics systems to adapt to the changing environmental and resource demands [13].

Ran et al. used the DEMATEL method to evaluate the emergency response probability of the supply network under complete information symmetry, partial information symmetry and information asymmetry. This approach provides a novel framework for emergency management and enhances the organization’s ability to deal with crises [14]. However, it fails to accurately depict the relative significance of the various components involved in emergency logistics management. Büyüközkan et al. optimized the decision-making process by using IF-DEMATEL and IF-ANP models in real industrial applications. Despite their effectiveness, the complexity of these models requires constant optimization to adapt to changing market conditions and logistics needs [15]. Pagano et al. have conducted research on emergency drinking water, developed decision support systems using the Analytic Hierarchy Process (AHP), studied the difficulties of prioritizing drinking water to solve public health emergencies and highlighted the importance of drinking water in emergency rescue and drinking water supply systems. They also provide guidelines for setting up emergency supply levels. However, their research failed to fully consider emergency logistics management, which hindered the optimization of emergency supply management [16]. Post-disaster emergency logistics needs to ensure fairness in the distribution of emergency materials. Another study adopts a multi-phase model to distribute emergency materials to disaster-affected areas and explains the impact of distribution fairness on disaster response, which optimizes the emergency supply distribution model [17]. Wang et al.’s analysis of rescue time and the priority of emergency supplies, a study that uses two-tier planning and rigorous optimization to demonstrate unforeseen emergencies, is critical for maritime emergency logistics [18].

2.2. Optimization Model and Decision-Making Method of Emergency Material Distribution

Efficient emergency resource allocation depends on a strong optimization model and decision framework. Kundu et al. proposed an organizational response system for emergency logistics management that provides an intelligent and comprehensive framework to improve operational efficiency before and during disasters [19]. Ge et al. developed an indicator system using TOPSIS to evaluate the ecological responsibility of resource-based enterprises and provided suggestions for improving the resilience of emergency supply networks [20]. Xu et al. integrated ANP with Pythagorean fuzzy VIKOR to create the ANP-PF-VIKOR model, which was used to evaluate emergency response strategies during the catastrophic flood in Zhengzhou in 2021. This technology shows that inter-organizational collaboration has a significant impact on the effectiveness of emergency supply chains and provides relevant references for supplier selection [21]. Zhang et al. evaluated the suitability of water resources for emergency rescue operations but failed to address the dynamics of resource allocation and management during the integrated crisis transition [22]. Guo and Wu combined a fuzzy comprehensive evaluation with AHP-DEMATEL-VIKOR to establish the index of a social sustainable supply chain [23]. Although this research was creative, it did not adequately address upstream and downstream suppliers, resulting in a flawed approach to emergency material management.

Huang and Song proposed an emergency logistics distribution model, which solved the problem of uncertainty and insufficient data, finally improved the emergency logistics system, and provided a basis for strengthening management [24]. Balcik and Ak used scenario-based techniques to address procurement cost and demand uncertainty and created a model to effectively reconcile these factors. These studies emphasize the necessity of integrating modern methods into emergency logistics to achieve the dynamic optimization of resource allocation [25]. Wu and Shelfer used a solution model to assess the corresponding distributive “parity” risk and to analyze the effectiveness of various risk management measures. Situational sensitivity requires different risk management strategies to mitigate conflicts among stakeholders. Proactive risk management and allocation can significantly reduce conflicts between parties in disaster areas [26]. Liu et al. used a fuzzy symmetric ideal solution to evaluate the performance of emergency logistics using multi-granularity language data. The article introduces, in detail, the management suggestions of emergency logistics, which are helpful to assess the urgency of emergency materials, but they ignore the priority order of goods in emergency logistics [27]. Jin and Zhang developed a similar DEMATEL approach to supplement the missing values and identify important success factors in emergency information response systems. It clarifies the urgency ranking of various decision-making situations, reduces selection bias, improves the accuracy of decision-making results, and puts forward an emergency plan that is crucial to emergency management, which provides the direction for the research focus of this paper [28]. However, the reliability of this strategy requires more scrutiny and reflection.

In addition, Jiang et al. developed a new decision framework using the Delphi method to evaluate ELSR and constructed a mixed multi-attribute decision-making (MADM) model, D-ANP, based on DEMATEL and ANP to determine the key factors affecting ELSR and to further select emergency material suppliers rationally. This literature study demonstrates the causal relationship between several evaluation indicators and their roles in emergency material rescue systems [29]. This study aims to provide a systematic and focused allocation of emergency supplies while strengthening the management of the transformation of emergency supplies. He et al. enhanced the NSGA-II method to achieve multi-objective optimization by effectively allocating 3D materials while considering device variability and resource diversity. In addition, this study also addresses the difficulty of adjusting the supply and demand of emergency resources in unexpected public health emergencies [30]. Jiang et al. used quantitative analysis principles and models based on the concept of distributing emergency supplies from many regions to various crisis areas. This model has high timeliness and can achieve almost real-time decision-making. It can dynamically evaluate simulated environments during unexpected public health crises and accurately, timely, and effectively coordinate the allocation of emergency supplies [31].

Table 1. Comparison of research methods.

Authors	Research	Players	ANP	DEMATEL	AHP	TOPSIS	FUZZY	CASE	DEA
Wang et al., 2022 [9]	Medical Science	2						√
Zhang et al., 2019 [10]	Marine Transit Network	3							√
Guan etc., 2020 [11]	Engineering	4						√
Liang, H. etc., 2004 [12]	Public Health	2						√
Zhao, Y. et al., 2022 [13]	Urban Emergency Logistics	2						√
Ran W. etc., 2021 [14]	Supply Chain	3				√	√	√
Büyüközkan, Gülçin et al., 2017 [15]	Enterprise Operation	3	√	√				√
Pagano, A. etc., 2021 [16]	Drinking Water Supply Systems	3			√
Wang etc., 2019 [17]	Emergency Material Allocation	3		√	√		√
Kundu, T. etc., 2022 [19]	Logistics Management	3						√
Ge, X. et al., 2020 [20]	Logistics Supply Chain	4				√
Xu, W. et al., 2023 [21]	Humanitarian Supply Chain	4	√				√
Zhang, Q. etc., 2021 [22]	GIS	8			√
Guo, R. et al., 2023 [23]	Supply chain management	2		√	√		√
Huang et al., 2016 [24]	Logistics Distribution	2						√
Wu etc., 2009 [26]	Allocation Management	2							√
Liu, Y. etc., 2020 [27]	Emergency Logistics	4						√
Jin etc., 2023 [28]	EIRS	2		√			√
Jiang et al., 2020 [29]	Emergency Logistics System	5	√	√			√
Wu etc., 2016 [32]	Supply Chain	2	√
This research	Emergency supply chain	3	√	√	√		√	√

compares the research methods of related studies.

2.3. Supplier Selection and Resource Prioritization

The selection of suppliers is crucial in emergency logistics as the rational selection of emergency materials ensures the effectiveness and reliability of rescue operations. Wang et al. introduced a hybrid ANP (H-ANP) method that improves the weight allocation of emergency material supplier selection indicators, providing a solution for achieving multi-criteria decision-making [33]. In addition, Lei et al. analyzed the factors that affect the production, assembly, and distribution of emergency supplies and further improved emergency supply transportation planning and inventory allocation based on linear programming principles [34]. Ju et al. proposed a hybrid model that combines fuzzy AHP with binary organizational fuzzy language, emphasizing that predictive ability, emergency assistance, and post-disaster management should be key evaluation criteria when selecting emergency material suppliers [35]. Ortiz-Barrios et al. improved multi-criteria decision-making by using target priority to enhance decision accuracy [36]. These technologies collectively provide a wealth of insights for evaluating suppliers based on timeliness, resource diversity, and cost efficiency. In addition, Jana et al. achieved the maximum speed and minimum cost in emergency supply transportation through the metaheuristic differential evolution method, emphasizing the importance of emergency material demand [37]. Xing proposed an improved particle swarm optimization algorithm for the dynamic allocation of emergency supplies, thereby optimizing their transportation time and cost. Therefore, these models can achieve the effective allocation of resources while minimizing costs [38]. Wu and Barnes established a model for identifying eco-friendly partners and establishing supply chains by combining the Analytic Network Process (ANP) with Multi-Objective Programming (MOP) methods. This method is widely recognized in the industry as a powerful and practical framework [32]. However, the accuracy of the prediction is not precise enough. Olanrewaju et al. conducted a sensitivity analysis on costs and studied the differences attributed to expenses between suppliers and rescue agencies, which is crucial for reducing the default risk of emergency supplies suppliers [39].

2.4. Research Gap

In reviewing the relevant research on emergency material management and reserves, we identified that the existing studies mainly focus on evaluating the selection and reserve models of emergency material suppliers. There is a lack of comprehensive consideration for the combination of emergency material management and reserves, and the methods and frameworks related to this topic have not been widely studied. The insufficient research on the combination of emergency material management and collaborative reserves in various countries hinders the efficient utilization of emergency resources. Therefore, it is necessary to conduct a comprehensive evaluation of emergency material management and improve the material reserve system. The reality shows that the implementation and strengthening of government emergency measures provide better support and comply with certain standards. During the rescue operation, it is necessary to conduct a comprehensive review of management strategies and develop a powerful and efficient emergency material storage framework to effectively manage and reserve emergency materials.

Table 2. Literature comparison.

Authors	Research	Players	Schedule Time	Production Costs	Production Quality	Route Allocation	Transport Cost
Balcik, B. et al., 2013 [25]	Supplier selection	2		√	√
He, J. et al., 2021 [30]	Supply and demand relationship	4	√	√
Jiang, J. et al., 2017 [31]	Vehicle scheduling	4	√			√
Wang, C. et al., 2023 [33]	Sea delivery	3	√			√
Lei, L. et al., 2016 [34]	Multi-level production	3	√			√
Ju, Y. et al., 2012 [35]	Emergency response capability	3	√			√	√
Jana, R.K et al., 2021 [37]	Material demand	3	√			√	√
Xing, H. etc., 2016 [38]	Collecting network	1	√	√		√	√
Olanrewaju, O.G et al., 2020 [39]	Planning and management	3	√	√	√
This research	Emergency supply chain	3	√	√	√	√	√

reviews previous studies and shows the gap between this study and previous research.

This study summarizes five criteria for supplier selection: quality, efficiency, business credit, regional advantage, and emergency capability. And it includes 14 sub-indicators, including qualification rate, quality assurance, batch purchase time of materials, material storage and scrap time, supplier delivery punctuality rate, equipment level, degree of informatization, financial condition, traffic location condition, policy advantages, regional stability, emergency management capability, emergency transportation risk and fast production line conversion capability. This study dynamically evaluates the rational selection of emergency material suppliers based on the current research literature and provides a more comprehensive and systematic indicator system.

3. Method and Results

3.1. Methods Introduction

Two approaches, DEMATEL and ANP, are adopted in this paper, which are particularly introduced as indicated in Figure 2 below.

3.2. Hypothesis for Research

(1)

Causal links exist across supplier assessment variables, which may be clearly articulated via quantitative analysis.

(2)

The supplier assessment index is both autonomous and characterized by a complex dependency and feedback connection; for instance, a modification in one index may directly or indirectly influence other indicators.

(3)

The causal matrix derived from the DEMATEL approach accurately represents the influence among indicators and offers a dependable input for future ANP weight computation.

(4)

The fuzzy comprehensive assessment approach may convert qualitative issues, such as demand urgency, into quantitative analytical results, offering a foundation for prioritizing material distribution.

(5)

The composite score derived from the DEMATEL, ANP, and fuzzy comprehensive assessment may precisely represent the supplier’s priority and address real emergency requirements.

3.3. DEMATEL

3.3.1. DEMATEL for Causal Indicator Relations

The Decision Testing and Evaluation Laboratory (DEMATEL), known as the laboratory method, offers a more empirical and reasonable methodology compared to the Analytic Network Process (ANP). It evaluates both the direct and indirect relationships between indicators, the latter of which is difficult to measure. The laboratory method improves its effectiveness in evaluating the comprehensive impact connection among indicators with this approach. This article employs the DEMATEL approach to ascertain the entire effect connections of assessment indicators for emergency material suppliers. It aims to create a comprehensive impact matrix, identify the causal links among components and determine the position of each component within the system.

3.3.2. An Overview of the DEMATEL Method

(1) Create a direct impact matrix $M$.

This paper aims to enhance the logical selection of providers for emergency goods and facilitate the efficient transformation of these items into a complete emergency supply. An extensive evaluation system is created for emergency material providers, consisting of four essential dimensions: profit, business credit, regional advantage, and emergency capacity. The system consists of a total of 14 primary indicators, as shown in

Table 3. Presentation of the evaluation indicators that are used to assess emergency material suppliers.

Criteria for Evaluation Using the BOCR Model	Set of Elements	Principal Indicator (Element)	Symbolic Representations Denoting Fundamental Indicators
Profit	QualityA1	Qualification rate Quality assurance	Q1 Q2
	EfficiencyA2	Batch purchase time of materials Material storage and scrap time Supplier delivery punctuality rate	S1 S2 S3
Business credit	B	Equipment level Degree of informatization Financial condition	B1 B2 B3
Regional advantage	R	Traffic location condition Policy advantage Regional stability	R1 R2 R3
Emergency capacity	E	Emergency management capacity Emergency transportation risk Fast production line conversion capability	E1 E2 E3

. In order to obtain a more accurate comprehension of the relationships between various indicators, it is important to further quantify them and produce a matrix that directly represents their effects, as exemplified in

Table 4. Matrix illustrating direct impacts.

	Q1	Q2	S1	S2	S3	B1	B2	B3	R1	R2	R3	E1	E2	E3
Q1	0	6	0	3	0	3	5	4	0	0	0	0	0	0
Q2	5	0	0	3	0	2	6	3	0	0	0	0	0	0
S1	0	0	0	7	5	3	5	0	2	5	4	0	0	0
S2	3	7	3	0	6	2	0	0	1	0	0	0	0	0
S3	0	0	8	5	0	0	0	0	3	5	2	7	1	4
B1	4	2	6	4	0	0	5	4	0	0	0	0	0	0
B2	2	3	3	0	0	5	0	7	0	0	0	0	0	0
B3	5	7	0	0	0	2	4	0	0	0	0	3	7	9
R1	0	0	3	5	4	0	0	0	0	3	6	5	8	3
R2	0	0	2	0	5	0	0	0	2	0	4	0	0	0
R3	0	0	6	0	7	0	0	0	2	6	0	4	7	4
E1	0	0	0	0	4	0	0	4	9	0	6	0	3	4
E2	0	0	0	0	6	0	0	5	8	0	7	3	0	5
E3	0	0	0	0	5	0	0	3	8	0	5	2	6	0

. The article uses the variable $M_{ij}$ to denote the extent of reciprocal influence between indicators. The strength of this relationship is comprehensively and accurately assessed using a scientific and systematic 10-point measurement technique, which is carefully set on a scale of 0 to 9 to provide a clear, comparable quantitative benchmark for the strength of the relationship between suppliers. A score of 0 represents little to no connection or influence, while a score of 9 represents an extremely close and strong relationship. In order to construct this evaluation system, we first conducted an in-depth literature review and extensively collected and analyzed the domestic and foreign research on supplier relationship strength evaluation. By systematically combing the theoretical framework, evaluation model, and empirical results of these studies, we carefully extracted a series of core factors that affect the strength of supplier relationships and built a comprehensive evaluation standard framework on this basis. Secondly, in order to ensure the objectivity and authority of the evaluation results, we invited a number of senior experts from the relevant fields to participate in the evaluation process. These experts not only have deep professional knowledge backgrounds but also have accumulated rich practical experience in practical work. According to the criteria under the framework of comprehensive evaluation standards, combined with their deep understanding of the industry and intuitive feelings about suppliers, they conducted a detailed evaluation of suppliers. In the evaluation process, the experts fully consider the performance of suppliers in different dimensions and adopt a combination of quantitative analysis and qualitative judgment, striving to produce evaluation results that are both scientific and accurate. Through this evaluation process, we can not only obtain the specific score of supplier relationship strength but also clearly identify the strengths and weaknesses of suppliers in various dimensions so as to provide strong decision support for the subsequent supplier selection, relationship maintenance and strategic cooperation.

(2) Create a uniform and standardized direct impact matrix $N$.

Create a standardized direct impact matrix by normalizing the original relationship matrix to create the standardized direct impact matrix. Normalization is a regular procedure used to standardize objects. Here, $n$ represents the total number of influencing factors in the evaluation system. In this study, $n$ = 14. The direct effect matrix $M$ is represented by the value $a_{ij}$, as stated in Formula (1):

$$M={{\displaystyle \left({{\displaystyle a}}_{ij}\right)}}_{\mathrm{n}\times \mathrm{n}}$$

(1)

Compute the sum of each row in the matrix and determine the highest value among these sums, as indicated by Formula (2):

$$\mathrm{M}axv\mathrm{ar}=\max \left({\displaystyle \sum _{j=1}^n{{\displaystyle a}}_{ij}}\right)$$

(2)

Next, apply the process of standardizing the direct matrix, as depicted in Formula (3):

$$N={{\displaystyle \left(\frac{{{\displaystyle a}}_{ij}}{Max\mathrm{var}}\right)}}_{n\times n}$$

(3)

Lastly,

Table 5. Presentation of the direct impact matrix specifications.

	Q1	Q2	S1	S2	S3	B1	B2	B3	R1	R2	R3	E1	E2	E3
Q1	0.000	0.162	0.000	0.081	0.000	0.081	0.135	0.108	0.000	0.000	0.000	0.000	0.000	0.000
Q2	0.135	0.000	0.000	0.081	0.000	0.054	0.162	0.081	0.000	0.000	0.000	0.000	0.000	0.000
S1	0.000	0.000	0.000	0.189	0.135	0.081	0.135	0.000	0.054	0.135	0.108	0.000	0.000	0.000
S2	0.081	0.189	0.081	0.000	0.162	0.054	0.000	0.000	0.027	0.000	0.000	0.000	0.000	0.000
S3	0.000	0.000	0.216	0.135	0.000	0.000	0.000	0.000	0.081	0.135	0.054	0.189	0.027	0.108
B1	0.108	0.054	0.162	0.108	0.000	0.000	0.135	0.108	0.000	0.000	0.000	0.000	0.000	0.000
B2	0.054	0.081	0.081	0.000	0.000	0.135	0.000	0.189	0.000	0.000	0.000	0.000	0.000	0.000
B3	0.135	0.189	0.000	0.000	0.000	0.054	0.108	0.000	0.000	0.000	0.000	0.081	0.189	0.243
R1	0.000	0.000	0.081	0.135	0.108	0.000	0.000	0.000	0.000	0.081	0.162	0.135	0.216	0.081
R2	0.000	0.000	0.054	0.000	0.135	0.000	0.000	0.000	0.054	0.000	0.108	0.000	0.000	0.000
R3	0.000	0.000	0.162	0.000	0.189	0.000	0.000	0.000	0.054	0.162	0.000	0.108	0.189	0.108
E1	0.000	0.000	0.000	0.000	0.108	0.000	0.000	0.108	0.243	0.000	0.162	0.000	0.081	0.108
E2	0.000	0.000	0.000	0.000	0.162	0.000	0.000	0.135	0.216	0.000	0.189	0.081	0.000	0.135
E3	0.000	0.000	0.000	0.000	0.135	0.000	0.000	0.081	0.216	0.000	0.135	0.054	0.162	0.000

is derived.

(3) Create a comprehensive impact matrix $T$.

The norm directly influences the convergence of the matrix when it undergoes repeated multiplication with itself. During this procedure, all of the elements of the matrix will progressively converge towards zero, ultimately yielding a matrix consisting entirely of zeros, as exemplified by Formula (4):

$$0=\underset{k\to \infty }{\lim }{{\displaystyle N}}^{\mathrm{k}}$$

(4)

The indirect impact is obtained by considering the cumulative secondary effects through higher-order powers of the direct impact matrix. By taking into account all of the secondary and higher-order consequences, the resulting comprehensive impact matrix $T$ is computed as follows:

$$T=N{\left(I-N\right)}^{-1}$$

(5)

where $T$ represents the comprehensive impact matrix, $N$ represents the normalized direct impact matrix and $I$ is the identity matrix. Here, ${\left(I-N\right)}^{-1}$ accounts for the accumulation of all indirect impacts.

Lastly,

Table 6. Comprehensive impact matrix.

	Q1	Q2	S1	S2	S3	B1	B2	B3	R1	R2	R3	E1	E2	E3
Q1	0.122	0.296	0.119	0.187	0.126	0.176	0.266	0.249	0.100	0.056	0.093	0.083	0.116	0.117
Q2	0.228	0.141	0.108	0.174	0.113	0.147	0.273	0.215	0.089	0.050	0.082	0.073	0.101	0.102
S1	0.107	0.151	0.279	0.385	0.462	0.184	0.254	0.161	0.295	0.316	0.348	0.207	0.222	0.203
S2	0.173	0.291	0.246	0.169	0.339	0.138	0.136	0.125	0.175	0.118	0.150	0.132	0.131	0.129
S3	0.097	0.144	0.516	0.395	0.487	0.108	0.142	0.192	0.482	0.383	0.454	0.462	0.368	0.395
B1	0.223	0.219	0.309	0.261	0.196	0.122	0.287	0.261	0.143	0.103	0.143	0.112	0.145	0.143
B2	0.171	0.220	0.210	0.134	0.156	0.223	0.152	0.323	0.130	0.081	0.127	0.107	0.151	0.152
B3	0.278	0.366	0.259	0.229	0.401	0.185	0.296	0.287	0.394	0.180	0.360	0.344	0.522	0.535
R1	0.106	0.157	0.451	0.412	0.674	0.108	0.141	0.236	0.496	0.375	0.627	0.491	0.619	0.456
R2	0.034	0.050	0.219	0.128	0.340	0.041	0.056	0.071	0.219	0.137	0.273	0.149	0.156	0.139
R3	0.090	0.129	0.512	0.294	0.715	0.102	0.140	0.220	0.529	0.447	0.470	0.454	0.565	0.458
E1	0.100	0.142	0.345	0.268	0.609	0.093	0.129	0.313	0.670	0.279	0.593	0.363	0.521	0.478
E2	0.114	0.161	0.387	0.297	0.710	0.105	0.147	0.362	0.696	0.312	0.660	0.479	0.490	0.546
E3	0.094	0.134	0.339	0.263	0.624	0.089	0.123	0.287	0.641	0.274	0.564	0.409	0.572	0.372

is derived.

(4) Ascertain the IISC of each element.

From the value $t_{ij}$ in the comprehensive impact matrix $T$, we obtain the influence degree, affected degree, centrality and causality degree of each factor. The value $t_{ij}$ represents the degree of direct and indirect impact between factors, i.e., the comprehensive influence degree generated. Here, $n$ represents the total number of influencing factors in the evaluation system. In this study, $n$ = 14.

The impact degree is the total sum of the values in each row of matrix $T$. The matrix reflects the overall influence value of each element on all other elements. The set of influence degrees is represented by the symbol $D$, as indicated in Formula (6):

$$D=\left(D_1,D_2,D_3,\dots ,D_{\mathrm{n}}\right)$$

(6)

The set of influence degrees, $D=\left(D_1, D_2,D_3,\dots ,D_n\right)$, represents the total influence exerted by each element, as indicated in Equation (6). To quantify each $D_i$, Equation (7) provides a detailed formula, where $D_i$ is calculated as the sum of all $t_{ij}$ values corresponding to row $i$ in matrix $T$.

$${{\displaystyle D}}_i={\displaystyle \sum _{j=1}^n{{\displaystyle t}}_{ij,}}(i=1,2,3,\dots ,n)$$

(7)

Compute the sum of the elements in each row of matrix $T$ to determine the influence degree of the corresponding factor and compute the sum of the elements in each column of matrix $T$ to determine the influence degree of the corresponding factor. The set of influence degrees is represented by the symbol $C$, as indicated in Formula (8):

$$C=\left(C_1,C_2,C_3,\dots ,C_{\mathrm{n}}\right)$$

(8)

The following is included in the group:

$${{\displaystyle C}}_i={\displaystyle \sum _{j=1}^n{{\displaystyle t}}_{ij,}}(i=1,2,3,\dots ,n)$$

(9)

The combined value of the degree of influence and the degree of influence is referred to as centrality, symbolized as $M_i$. The value illustrates the extent of influence exerted by the factor within the system. The distinction between the degree of influence and the degree of influence is referred to as the causal degree, symbolized as $R_i$, which signifies the causal connection between the factor and other elements in the system. If the causal degree is over 0, it signifies that the component has a substantial influence on other factors and is referred to as the causal factor. Conversely, it is referred to as the outcome factor. The calculation formulas matching to (10) and (11) are displayed:

$$M_i=D_i+C_i$$

(10)

$$R_i=D_i-C_i$$

(11)

Lastly,

Table 7. The comprehensive impact index of the influencing factors of the evaluation index of emergency material suppliers.

Key Factors	Level of Impact	Scope of Influence	Centrality	Causality Degree
Profit
A1 Quality
Q1 Qualification rate	2.107	1.937	4.044	0.170
Q2 Quality assurance	1.896	2.599	4.495	−0.703
A2 Efficiency
S1 Batch purchase time of materials	3.574	4.298	7.872	−0.724
S2 Material storage and scrap time	2.453	3.595	6.048	−1.143
S3 Supplier delivery punctuality rate	4.626	5.950	10.575	−1.324
Business credit
B1 Equipment level	2.667	1.822	4.489	0.845
B2 Degree of informatization	2.335	2.543	4.878	−0.208
B3 Financial condition	4.636	3.302	7.938	1.334
Regional advantage
R1 Traffic location condition	5.348	5.059	10.407	0.289
R2 Policy advantage	2.013	3.110	5.123	−1.098
R3 Regional stability	5.125	4.945	10.070	0.179
Emergency capacity
E1 Emergency management capacity	4.904	3.868	8.772	1.036
E2 Emergency transportation risk	5.466	4.679	10.144	0.787
E3 Fast production line conversion capability	4.785	4.225	9.010	0.559

is derived.

(5) Create a DEMATEL causality diagram.

Using Python 3.11, generate Cartesian plots to visually demonstrate the influence of various characteristics on the evaluation of emergency material suppliers. Depict the centrality and causality on the x-axis and y-axis, respectively, as seen in Figure 3.

(6) Evaluation of the result.

To analyze the direct causal link between components in a rating system for suppliers of emergency materials, this paper employs the DEMATEL approach. The process involves creating a direct effect matrix for four layers of interconnected components and then calculating a full impact matrix to assess the degree of influence, degree of affectedness, centrality and causation degree of each factor. Refer to Figure 3. If $Q_1$, $B_1$, $B_3$, $R_1$, $R_3$, $E_1$, $E_2$ and $E_3$ have values greater than 0, they are considered causal factors. This means that they have a significant influence on other factors and are the main factors that affect the evaluation indicators of emergency material suppliers. Factors with values below 0 are classified as outcome factors and are heavily influenced by other factors. The evaluation of emergency material providers is mostly influenced by these outcome elements, which are the most direct ones.

3.4. DEMATEL-ANP

3.4.1. Overview of the DEMATEL-ANP Method

The DEMATEL model’s data validation enables the assessment of impact degree, susceptibility degree, centrality and causation among many components via a comprehensive impact matrix. However, the DEMATEL model has numerous shortcomings. Nevertheless, the D-ANP model mitigates these limitations by including the temporal delay in the interactions among components. Figure 4 illustrates the DEMATEL-ANP model. D-ANP is a flexible and powerful decision-making tool that allows us to consider the interactions and dependencies between factors. In our study, we first identified 14 key factors through expert interviews and a literature review. We then use the D-ANP method to build a network model where each factor is a node and the lines between nodes represent the interactions between the factors. In constructing the network model, we consider the direct and indirect relationships between factors, as well as possible causal relationships. By calculating the relative importance of each factor (usually using a hypermatrix and a limiting hypermatrix), we are able to arrive at a comprehensive assessment that reflects the combined impact of all factors on the selection of a particular supplier. Thus, although the 14 factors have different correlations and possible causation, the D-ANP method allows us to aggregate them in a systematic way, resulting in a clear and comprehensive decision outcome. The DEMATEL-ANP methodology offers a comprehensive framework for addressing complex decision-making scenarios. By scientifically and methodically demonstrating the interconnection of components, it considers multiple criteria in a holistic manner. In catastrophic calamities impacting the society, government and corporations, this methodology provides vital guidance for decision-making. Utilizing the DEMATEL comprehensive impact matrix, the D-ANP model constructs a network diagram that visually represents relationships and dependencies. The resulting limit super matrix quantifies the relative importance of factors, helping to identify and prioritize suitable emergency material sources.

3.4.2. Steps of the DEMATEL-ANP Principle

(1) Establish the objectives and standards.

A thorough description of the decision issue is essential, including the objectives, criteria, sub-objectives, players and their aims, as well as the possible outcomes of the decision problem. A supplier evaluation system may be established by a standardized performance assessment based on the four criteria of benefit, opportunity, cost, and risk (BOCR criterion), as illustrated in Figure 5 below.

(2) Create an obj-criteria network.

The ANP network consists of two elements: the control layer, referred to as the target/criterion layer, and the network layer. The network layer is built atop the criteria layer and illustrates the interactions among individual components and groups of elements within the network based on the criterion. ANP has the capability to generate subnets based on various factors. A subnet consists of clusters of elements that represent the relevant control needs. L stands for multiple suppliers; specifically, in our case, L1, L2, L3, and L4 refer to four different suppliers. These suppliers are evaluated according to the evaluation criteria we established in previous tiers. Through a layer-by-layer analysis and comparison, we can score and rank each supplier according to these criteria. Ultimately, based on these detailed evaluations, we can determine which supplier (i.e., L1, L2, L3, or L4) best meets our needs and select the best supplier source. It is important to note that the ‘4L’ here is only a concrete case or example of how our proposed framework works in practical applications. In fact, the framework is highly configurable and can be adapted to different application scenarios and needs, as illustrated in Figure 6 below.

(3) Create a metamaterial without considering weight.

For each control criterion, an unweighted hypermatrix $W_S$ is created using the pairwise comparison method to compare elements. Initially, the established criteria $ABCD$ are utilized as the major criteria. Furthermore, the element $Q_i$ (where $i=1, 2,\dots , n$) within a specific element group $A_i$ (where $i=1, 2,\dots , n$) in the criteria layer is designated as a subordinate criterion. The $A_i$ judgment matrix is created by assessing the extent to which $Q_i$ in element group A influences other elements, and then obtaining the normalized eigenvector $W_T$. By employing 14 major indicators and four suppliers, the article simulates the model to identify the optimal supplier.

Table 8. Unweighted hypermatrix.

	Q1	Q2	S1	S2	S3	B1	B2	B3	R1	R2	R3	E1	E2	E3	L1	L2	L3	L4
Q1	0.000	1.000	0.000	0.659	0.000	1.000	0.399	0.333	0.000	0.000	0.000	0.000	0.000	0.000	0.800	0.750	0.667	0.800
Q2	1.000	0.000	0.000	0.341	0.000	0.000	0.601	0.667	0.000	0.000	0.000	0.000	0.000	0.000	0.200	0.250	0.333	0.200
S1	0.000	0.000	0.428	0.357	0.115	1.000	1.000	0.000	0.409	0.393	0.357	0.663	0.554	0.285	0.070	0.051	0.067	0.073
S2	1.000	1.000	0.372	0.000	0.470	0.000	0.000	0.000	0.260	0.000	0.000	0.000	0.000	0.000	0.743	0.752	0.715	0.701
S3	0.000	0.000	0.200	0.643	0.416	0.000	0.000	1.000	0.332	0.607	0.643	0.337	0.446	0.715	0.187	0.197	0.218	0.226
B1	0.391	0.488	0.365	0.794	0.432	0.000	0.168	0.377	0.000	0.000	0.000	0.000	0.000	0.000	0.547	0.547	0.540	0.483
B2	0.413	0.130	0.448	0.000	0.000	0.593	0.000	0.241	0.000	0.000	0.000	0.000	0.000	0.000	0.190	0.263	0.297	0.349
B3	0.196	0.382	0.187	0.206	0.568	0.407	0.832	0.382	1.000	1.000	1.000	1.000	1.000	1.000	0.263	0.190	0.163	0.168
R1	0.000	0.000	0.670	0.520	0.705	0.000	0.000	0.574	0.060	0.287	0.303	0.574	0.311	0.738	0.540	0.467	0.631	0.452
R2	0.000	0.000	0.276	0.000	0.204	0.000	0.000	0.000	0.457	0.000	0.476	0.000	0.000	0.000	0.163	0.333	0.152	0.250
R3	0.000	0.000	0.054	0.480	0.090	0.000	0.000	0.426	0.483	0.713	0.221	0.426	0.689	0.262	0.297	0.200	0.218	0.298
E1	0.000	0.000	0.385	0.145	0.418	0.000	0.000	0.214	0.313	0.317	0.265	0.670	0.216	0.193	0.321	0.062	0.402	0.238
E2	0.000	0.000	0.450	0.222	0.442	0.000	0.000	0.408	0.284	0.402	0.369	0.146	0.295	0.321	0.439	0.624	0.123	0.198
E3	0.000	0.000	0.165	0.633	0.141	0.000	0.000	0.378	0.403	0.281	0.365	0.183	0.489	0.486	0.240	0.314	0.475	0.563
L1	0.351	0.285	0.010	0.171	0.189	0.220	0.147	0.155	0.320	0.269	0.241	0.351	0.202	0.242	0.000	0.000	0.000	0.000
L2	0.293	0.082	0.264	0.402	0.304	0.236	0.280	0.479	0.095	0.164	0.359	0.137	0.432	0.335	0.000	0.000	0.000	0.000
L3	0.200	0.218	0.379	0.204	0.347	0.226	0.443	0.223	0.125	0.108	0.354	0.161	0.315	0.099	0.000	0.000	0.000	0.000
L4	0.156	0.553	0.348	0.223	0.161	0.318	0.122	0.121	0.511	0.472	0.047	0.351	0.051	0.325	0.000	0.000	0.000	0.000

displays the unweighted super matrix.

(4) Creating a weight hypermatrix.

The main criterion for comparison is $ABCD$, with element group $A_i$ serving as the supplementary criterion. Pairwise comparisons are conducted between element groups to create a judgment matrix $aj$. The matrix is subsequently normalized to produce a standardized feature vector ${\left(aj\right)}_T$.

Therefore, a weight matrix $A_s$ can be derived to represent the connections between groups of elements based on a specific criterion.

The weight super matrix, denoted as $W_s^w$, is created by multiplying the weight matrix $A_s$ with the unweighted super matrix $W_s$, as indicated in Formula (12). The weight super matrix is given in

Table 9. Weight hypermatrix.

	Q1	Q2	S1	S2	S3	B1	B2	B3	R1	R2	R3	E1	E2	E3	L1	L2	L3	L4
Q1	0.000	0.480	0.000	0.316	0.000	0.480	0.192	0.160	0.000	0.000	0.000	0.000	0.000	0.000	0.384	0.360	0.320	0.384
Q2	0.480	0.000	0.000	0.164	0.000	0.000	0.288	0.320	0.000	0.000	0.000	0.000	0.000	0.000	0.096	0.120	0.160	0.096
S1	0.000	0.000	0.206	0.171	0.055	0.480	0.480	0.000	0.196	0.189	0.171	0.318	0.266	0.137	0.034	0.024	0.032	0.035
S2	0.480	0.480	0.178	0.000	0.226	0.000	0.000	0.000	0.125	0.000	0.000	0.000	0.000	0.000	0.357	0.361	0.343	0.337
S3	0.000	0.000	0.096	0.309	0.200	0.000	0.000	0.480	0.159	0.291	0.309	0.162	0.214	0.343	0.090	0.095	0.105	0.109
B1	0.060	0.075	0.056	0.122	0.066	0.000	0.026	0.058	0.000	0.000	0.000	0.000	0.000	0.000	0.084	0.084	0.083	0.074
B2	0.063	0.020	0.069	0.000	0.000	0.091	0.000	0.037	0.000	0.000	0.000	0.000	0.000	0.000	0.029	0.040	0.046	0.054
B3	0.030	0.059	0.029	0.032	0.087	0.062	0.127	0.059	0.153	0.153	0.153	0.153	0.153	0.153	0.040	0.029	0.025	0.026
R1	0.000	0.000	0.024	0.019	0.026	0.000	0.000	0.021	0.002	0.010	0.011	0.021	0.011	0.027	0.020	0.017	0.023	0.016
R2	0.000	0.000	0.010	0.000	0.007	0.000	0.000	0.000	0.017	0.000	0.017	0.000	0.000	0.000	0.006	0.012	0.006	0.009
R3	0.000	0.000	0.002	0.017	0.003	0.000	0.000	0.016	0.018	0.026	0.008	0.016	0.025	0.010	0.011	0.007	0.008	0.011
E1	0.000	0.000	0.035	0.013	0.038	0.000	0.000	0.019	0.028	0.029	0.024	0.061	0.019	0.017	0.029	0.006	0.036	0.022
E2	0.000	0.000	0.041	0.020	0.040	0.000	0.000	0.037	0.026	0.036	0.033	0.013	0.027	0.029	0.040	0.056	0.011	0.018
E3	0.000	0.000	0.015	0.057	0.013	0.000	0.000	0.034	0.036	0.025	0.033	0.017	0.044	0.044	0.022	0.028	0.043	0.051
L1	0.084	0.068	0.002	0.041	0.045	0.053	0.035	0.037	0.077	0.064	0.058	0.084	0.048	0.058	0.000	0.000	0.000	0.000
L2	0.070	0.020	0.063	0.096	0.073	0.057	0.067	0.115	0.023	0.039	0.086	0.033	0.104	0.080	0.000	0.000	0.000	0.000
L3	0.048	0.052	0.091	0.049	0.083	0.054	0.106	0.053	0.030	0.026	0.085	0.039	0.076	0.024	0.000	0.000	0.000	0.000
L4	0.037	0.133	0.083	0.053	0.038	0.076	0.029	0.029	0.122	0.113	0.011	0.084	0.012	0.078	0.000	0.000	0.000	0.000

of this article.

$$W_S^W=A_{\mathrm{i}}{W}_{\mathrm{s}}$$

(12)

(5) Calculate the supremum matrix limit.

To address the interdependence of elements in the ANP technique, it is essential to determine the stable priority of each element using the limit super matrix approach, as shown in Formula (13). The limit hypermatrices in this paper are displayed in

Table 10. Bound hypermatrix.

	Q1	Q2	S1	S2	S3	B1	B2	B3	R1	R2	R3	E1	E2	E3	L1	L2	L3	L4
Q1	0.149	0.149	0.149	0.149	0.149	0.149	0.149	0.149	0.149	0.149	0.149	0.149	0.149	0.149	0.149	0.149	0.149	0.149
Q2	0.104	0.104	0.104	0.104	0.104	0.104	0.104	0.104	0.104	0.104	0.104	0.104	0.104	0.104	0.104	0.104	0.104	0.104
S1	0.094	0.094	0.094	0.094	0.094	0.094	0.094	0.094	0.094	0.094	0.094	0.094	0.094	0.094	0.094	0.094	0.094	0.094
S2	0.179	0.179	0.179	0.179	0.179	0.179	0.179	0.179	0.179	0.179	0.179	0.179	0.179	0.179	0.179	0.179	0.179	0.179
S3	0.114	0.114	0.114	0.114	0.114	0.114	0.114	0.114	0.114	0.114	0.114	0.114	0.114	0.114	0.114	0.114	0.114	0.114
B1	0.053	0.053	0.053	0.053	0.053	0.053	0.053	0.053	0.053	0.053	0.053	0.053	0.053	0.053	0.053	0.053	0.053	0.053
B2	0.025	0.025	0.025	0.025	0.025	0.025	0.025	0.025	0.025	0.025	0.025	0.025	0.025	0.025	0.025	0.025	0.025	0.025
B3	0.046	0.046	0.046	0.046	0.046	0.046	0.046	0.046	0.046	0.046	0.046	0.046	0.046	0.046	0.046	0.046	0.046	0.046
R1	0.012	0.012	0.012	0.012	0.012	0.012	0.012	0.012	0.012	0.012	0.012	0.012	0.012	0.012	0.012	0.012	0.012	0.012
R2	0.003	0.003	0.003	0.003	0.003	0.003	0.003	0.003	0.003	0.003	0.003	0.003	0.003	0.003	0.003	0.003	0.003	0.003
R3	0.006	0.006	0.006	0.006	0.006	0.006	0.006	0.006	0.006	0.006	0.006	0.006	0.006	0.006	0.006	0.006	0.006	0.006
E1	0.015	0.015	0.015	0.015	0.015	0.015	0.015	0.015	0.015	0.015	0.015	0.015	0.015	0.015	0.015	0.015	0.015	0.015
E2	0.018	0.018	0.018	0.018	0.018	0.018	0.018	0.018	0.018	0.018	0.018	0.018	0.018	0.018	0.018	0.018	0.018	0.018
E3	0.018	0.018	0.018	0.018	0.018	0.018	0.018	0.018	0.018	0.018	0.018	0.018	0.018	0.018	0.018	0.018	0.018	0.018
L1	0.033	0.033	0.033	0.033	0.033	0.033	0.033	0.033	0.033	0.033	0.033	0.033	0.033	0.033	0.033	0.033	0.033	0.033
L2	0.047	0.047	0.047	0.047	0.047	0.047	0.047	0.047	0.047	0.047	0.047	0.047	0.047	0.047	0.047	0.047	0.047	0.047
L3	0.042	0.042	0.042	0.042	0.042	0.042	0.042	0.042	0.042	0.042	0.042	0.042	0.042	0.042	0.042	0.042	0.042	0.042
L4	0.042	0.042	0.042	0.042	0.042	0.042	0.042	0.042	0.042	0.042	0.042	0.042	0.042	0.042	0.042	0.042	0.042	0.042

.

$$W_s^i=\underset{k\to \infty }{\lim }{W}^k$$

(13)

(6) The options are sorted.

Compute the sum of the limit vectors for each control criterion, taking into account their separate weights. Then, sort them in descending order based on the weight values of each potential solution to identify the optimal selection scheme. By performing computational analysis, it may be deduced that $L2$ has the highest magnitude. After considering several signs, it can be concluded that $L2$ aligns more closely with the requirements, making it the most suitable provider, as stated in

Table 11. Supplier weights.

Supplier	Weight
L1	0.202
L2	0.285
L3	0.257
L4	0.255

below.

4. Discussion

4.1. Fuzzy Comprehensive Evaluation

Fuzzy Evaluation for Material Urgency Level

Unanticipated public health crises are characterized by significant ambiguity about their location, timing, and extent of impact. Emergency supplies are essential for establishing a strong foundation and instilling confidence to carry out a successful rescue operation. Emergency supply suppliers must respond promptly. Possessing the necessary emergency supplies would enhance the effectiveness of rescue operations and save lives and properties.

Emergency supply vendors must strive to provide emergency supplies in a focused and well-organized way to address the urgent need for these materials amid unforeseen public health emergencies. In the course of the rescue effort, several levels of urgency for emergency supplies exist. The research included three criteria to assess the urgency of emergency provisions: the danger to human life from insufficient supplies, the degree of lack, and the need for material resources. Thus, we used the fuzzy comprehensive evaluation approach to evaluate the urgency of material requirements.

The study uses the fuzzy comprehensive assessment approach, a well-recognized analytical tool, to examine and provide informed conclusions on many complicated topics. This strategy involves breaking down the issue into several components and then using fuzzy logic for a thorough assessment, leading to the final evaluative result.

4.2. The Fuzzy Comprehensive Evaluation Method Follows These Steps

(1) Calculate the evaluation metric.

Evaluation indicators serve as benchmarks for assessing various facets of the situation. This article conducts its analysis using the degree of life risk from insufficient supply, the immediacy of material scarcity, and the irreplaceability of resources as evaluative criteria.

(2) Ascertain the evaluation grade.

The evaluation grade assesses the quality or excellence of the index, often represented by numerical values or descriptive terms. This research categorizes the assessment grade into three tiers: urgent, severe, and general.

(3) Construct a fuzzy evaluation matrix.

The fuzzy evaluation matrix is created by linking the evaluation index with the assessment grade to establish a matrix. The matrix is structured so that each row denotes an assessment index and each column signifies an evaluation level. The matrix entries indicate the degree of membership of each index across various assessment levels. The degree of membership signifies the extent to which an assessment index corresponds with a certain evaluation grade. A fuzzy evaluation matrix is established using three assessment indices: the degree of life danger due to insufficient supply, the intensity of emergency material shortages and the degree of material irreplaceability. The matrix is organized into three assessment categories: emergency, severe, and general, shown in rows.

(4) Calculate the weight.

The purpose of determining the weight is to assess the impact of each evaluation criterion on the final assessment outcome. This research used a hierarchical analytic method to determine the weight value of the contributing factors.

(5) Determine the comprehensive evaluation score.

The complete evaluation value is obtained by calculating the fuzzy evaluation index and its associated weight, leading to the final assessment result. This research utilizes the weighted average approach of the multiplication-bounded sum operator to generate the fuzzy evaluation index and its associated weight. The ultimate assessment outcome is subsequently established.

4.3. Illustrative Examination

In the occurrence of a natural disaster, it is essential to possess emergency supplies, including communication devices, potable water, insulated clothing, food, lifting equipment, search and rescue tools, shelters, fuel, medical supplies, rescue gear and protective equipment for health maintenance. To improve the efficacy of emergency material distribution, it is essential to classify and prioritize high-priority materials for distribution, given the limited transport capacity. Emergency specialists have discovered three elements that affect the immediate need for emergency supplies: the magnitude of life-threatening danger resulting from inadequate supply, the severity of material scarcity, and the degree of material irreplaceability. Matrix S was introduced as a judgment matrix to evaluate the urgency of emergency material demand. By using a judgment matrix in

Table 12. Urgency judgment matrix for emergency supplies.

Urgent Demand for Emergency Materials	Degree of Life Hazard Due to Insufficient Supply	Degree of Shortage of Emergency Supplies	Irreplaceable Degree of Materials	Weight
Degree of life hazard due to insufficient supply	1	2	4	0.5714
Degree of shortage of emergency supplies	1/2	1	2	0.2857
Irreplaceable degree of materials	1/4	1/2	1	0.1429

, the matrix ${\lambda }_{max}\left(S\right)=3$, $CI=0$, $RI=0.52$, $CR=CI / RI=0<0.1$. Therefore, the judgment matrix is consistent, and the weight of each factor $w=\left(0.5714, 0.2857, 0.1429\right)$ is obtained.

The evaluation vector of each kind of emergency material is obtained by combining the single factor evaluation matrix with the weight of each factor. Urgency materials refer to those that are most urgently needed and have the greatest impact on rescue operations in an emergency. The critical category refers to those whose need is less urgent, but whose shortage or delay will have a significant negative impact on the effectiveness of relief; general goods are those whose needs are less urgent and can be replaced or delayed to some extent [40,41]. According to the Chinese national standard Classification and Coding of Emergency Supplies, we classify communication equipment, drinking water, food, rescue tools, power fuel, medical supplies, rescue equipment and health protection equipment as emergency items [42]. These materials are identified as essential for ensuring basic survival, facilitating rescue operations, and supporting disaster response efforts. This classification is consistent with international frameworks such as the Sendai Framework for Disaster Risk Reduction (2015–2030), which emphasizes the prioritization of resources critical for life-saving and disaster recovery [43]. Cotton-padded garments, tents, and lifting hooks are classified as serious items. Let us assume that the decision-maker assigns emergency ratings of 30 for the three urgent levels, 20 for the severity level, and 10 for the general level. After calculation, the demand and urgency of each emergency material are obtained as follows: communication equipment stands at 22.45, drinking water at 28.34, cotton-padded clothes at 20.91, food at 25.53, lifting hooks at 23.39, rescue tools at 28.50, tents at 18.29, power fuel at 22.05, medical supplies at 28.56, ambulance equipment at 28.48 and hygiene and protective articles at 28.20.

Table 13. Single factor evaluation matrix of 11 kinds of emergency materials.

	Urgency	Seriousness	General
Communication equipment
Degree of life hazard due to insufficient supply	0.5405	0.3793	0.0802
Degree of shortage of emergency supplies	0.5350	0.3694	0.0955
Irreplaceable degree of materials	0.5434	0.3815	0.0751
Drinking water
Degree of life hazard due to insufficient supply	0.9600	0.0300	0.0100
Degree of shortage of emergency supplies	0.6712	0.2671	0.0616
Irreplaceable degree of materials	0.9604	0.0297	0.0099
Cotton-padded clothes
Degree of life hazard due to insufficient supply	0.1739	0.7101	0.1159
Degree of shortage of emergency supplies	0.2174	0.6000	0.1826
Irreplaceable degree of materials	0.1837	0.6122	0.2041
Food
Degree of life hazard due to insufficient supply	0.8165	0.0917	0.0917
Degree of shortage of emergency supplies	0.3077	0.6154	0.0769
Irreplaceable degree of materials	0.0952	0.7524	0.1524
Lifting hook
Degree of life hazard due to insufficient supply	0.4087	0.5130	0.0783
Degree of shortage of emergency supplies	0.4186	0.4884	0.0930
Irreplaceable degree of materials	0.6104	0.2273	0.1623
Rescue tool
Degree of life hazard due to insufficient supply	0.9417	0.0291	0.0291
Degree of shortage of emergency supplies	0.6735	0.2653	0.0612
Irreplaceable degree of materials	0.9494	0.0253	0.0253
Tent
Degree of life hazard due to insufficient supply	0.0407	0.6911	0.2683
Degree of shortage of emergency supplies	0.4274	0.3162	0.2564
Irreplaceable degree of materials	0.0604	0.3154	0.6242
Power fuel
Degree of life hazard due to insufficient supply	0.5363	0.4022	0.0615
Degree of shortage of emergency supplies	0.5105	0.4158	0.0737
Irreplaceable degree of materials	0.4637	0.4581	0.0782
Medical Medicine
Degree of life hazard due to insufficient supply	0.9920	0.0050	0.0030
Degree of shortage of emergency supplies	0.9900	0.0060	0.0040
Irreplaceable degree of materials	0.9880	0.0080	0.0040
Ambulance equipment
Degree of life hazard due to insufficient supply	0.9180	0.0732	0.0088
Degree of shortage of emergency supplies	0.9032	0.0599	0.0369
Irreplaceable degree of materials	0.9280	0.0672	0.0047
Health Protection equipment
Degree of life hazard due to insufficient supply	0.8646	0.1311	0.0043
Degree of shortage of emergency supplies	0.9474	0.0440	0.0086
Irreplaceable degree of materials	0.9558	0.0413	0.0029

shows the single factor evaluation matrix, and

Table 14. Evaluation vector of emergency supplies.

Material	Urgency	Seriousness	General
Communication equipment	0.5393	0.3768	0.0839
Drinking water	0.8776	0.0977	0.0247
Cotton-padded clothes	0.1877	0.6647	0.1476
Food	0.5681	0.3357	0.0962
Lifting hook	0.4403	0.4652	0.0945
Rescue tool	0.8662	0.0961	0.0378
Tent	0.1540	0.5303	0.3157
Power fuel	0.5186	0.4141	0.0673
Medicine	0.9909	0.0057	0.0034
Ambulance equipment	0.9152	0.0686	0.0162
Health protection equipment	0.9013	0.0934	0.0054

shows the evaluation vector.

The fuzzy comprehensive evaluation approach enables the efficient categorization of emergency products based on their urgency of need. It assigns a value to the severity of each kind of emergency material. Therefore, when the transportation capacity is limited, it is crucial to assess the urgency of need for emergency supplies and the general level of demand for these commodities. By effectively using the limited resources available, it is possible to carefully allocate and distribute various types of emergency supplies. This will enhance the efficiency and effectiveness of rescue operations, ultimately achieving optimum outcomes with little resource investment.

4.4. Suggestions

The establishment of a comprehensive and effective emergency supply storage and procurement system is crucial to optimizing inventory management, improving procurement efficiency and strengthening social participation. The following are the relevant suggestions proposed in this paper. (1) Optimize the material reserve strategy: according to the main categories and attributes of natural disasters, combined with the material needs of people’s daily lives, according to the urgency of the demand for urgent materials, rationally purchase the reserve of emergency materials, improve the reserve structure of emergency materials, and implement the collaborative inventory management strategy to completely solve the needs of various disaster relief materials storage locations in the whole region. (2) Improve emergency procurement efficiency: decision-makers select the best quality suppliers according to the supplier evaluation network model utilizing DEMATEL-ANP to improve supplier selection efficiency. At the same time, according to the specific emergency situation and the urgency of materials, emergency materials are selectively dispatched successively to improve the efficiency and effect of emergency rescue and maximize the time utility of emergency materials. Especially under the dual constraints of scarce resources and limited emergency transportation capacity, the accurate identification and hierarchical management of emergency material demand urgency has become the key to optimizing resource allocation and improving the efficiency of emergency responses. (3) Standard synergy: the collaborative adaptation mechanism for “peacetime and emergency integration”, constructed in this paper, significantly promoted the transparency and standardization process of the emergency material management system and made the material distribution process more open and transparent, reducing the possibility of human intervention and misunderstanding through the clear classification and quantitative assessment of the urgency of needs. At the same time, the standardized assessment process and results promote information sharing and collaborative work among different departments and regions, enhance the coherence and consistency of the emergency response and effectively break departmental barriers and regional restrictions.

4.5. Impact and Recommendation

By implementing a digital management system based on the “emergency integration” collaborative adaptation mechanism, governments and managers can achieve the flexible transformation and effective management of emergency resources in peacetime and crisis. To ensure adequate storage and the effective management of peacetime emergency supplies and to respond quickly in emergency situations, resources will be sent from various reserve locations to meet unexpected needs. The mechanism of this study emphasizes the rapid response and efficient deployment capabilities of emergency supply providers through efficient supplier selection, evaluates the urgency of emergency supply needs and allocates emergency values for each demand. This approach enables the systematic distribution of various emergency supplies to develop centralized and stratified deployment plans that maximize the use of scarce resources and thus improve the efficiency and effectiveness of rescue operations. In peacetime, the government should use the established supplier evaluation framework to identify the appropriate suppliers, correctly evaluate the reserve amount according to the urgency of materials, implement block reserve and dynamic monitoring, use an intelligent storage system, integrate intelligent storage resources and realize the coordinated reserve and intelligent management of emergency supplies. In the emergency transformation, the government must continuously evaluate the existing storage conditions in real time according to the disaster scenario so that emergency materials can be quickly responded to and effectively distributed, optimize logistics routes, improve transportation efficiency and ensure that emergency materials reach the disaster area in time to meet the rescue needs. Ensuring that resources are intelligently accessed and allocated according to the severity of the crisis and establishing a division of labor in emergency logistics and the distribution of supplies is critical to ensuring the rapid delivery of resources and the effectiveness of relief operations.

5. Conclusions

With the continuous development of society and the frequent occurrence of global natural disasters and public security events, the reserve and management of emergency materials become more important. The frequent occurrence of major natural disasters necessitates that governments improve their disaster prevention, mitigation and relief capacities, as the conventional emergency material support system cannot satisfy current needs. As a result, all governments are obligated to increase the building of emergency material support systems and establish an effective emergency material management model.

This paper investigates and analyzes the current management and reserve mode of emergency materials in China, compiles and reads the relevant literature on emergency material management and recognizes that emergency materials are the foundation of emergency rescue and that selecting the right supplier has become a social, economic, environmental and other decision-making concern. After developing an evaluation system for impact emergency material suppliers, the DEMATEL approach was utilized to analyze and calculate the comprehensive impact matrix, revealing the causal relationship between numerous variables. On this premise, this study conducts an in-depth analysis and calculations to better understand the interaction and influence of each variable, thereby providing a solid foundation for the selection of emergency supply suppliers. At the same time, to compensate for the drawbacks of the DEMATEL technique, this study incorporates the ANP method, stresses the interdependence of elements, and constructs a supplier-comprehensive evaluation network structure. By creating a matrix, the weight of each element is computed, the importance of the criterion is evaluated and the best supplier is chosen based on the supplier selection environment.

This study also reviews and examines the current condition and function of emergency materials in China, as well as the Chinese emergency material support system. On this premise, the fuzzy comprehensive evaluation approach is utilized to create a fuzzy evaluation matrix and the model’s viability is validated using case analysis. It offers recommendations for the urgent and hierarchical deployment of emergency materials, maximizing the utility of emergency material resources and improving China’s emergency material management system.

This study focuses on the selection of emergency materials providers, as well as the allocation and reserve mode of emergency supplies under supply risk, providing realistic recommendations to the government for improving the emergency material management system. Although this study has significant weaknesses in data analysis, future studies can strengthen data gathering and analysis to improve and optimize the research results. Furthermore, future relevant research can help to improve the classification of emergency supplies, as well as offer more accurate storage and deployment techniques for responding to diverse catastrophes.