An Evaluation of the Humanitarian Supply Chains in the Event of Flash Flooding

Abstract

Humanitarian supply chains play a major role in enabling disaster-affected areas to recover in a timely manner and enable economic and social activities to be restored. However, the sudden onset and increasing frequency of natural disasters such as flash floods require humanitarian supply chains to be resilient during the relief process. In this study, the evaluation indicators were identified from the literature and the Delphi method, and the weights of the evaluation indicators were calculated using the ANP method; the ANP method was combined with the Pythagorean fuzzy VIKOR (PFs-VIKOR) to propose the ANP-PFs-VIKOR method model. The model was used to examine the example of the 2021 megaflood event in Zhengzhou City to evaluate the performance of the humanitarian supply chain in four cities. The findings suggest that the indicator with the strongest impact on the effectiveness of humanitarian supply chains is coordination among participating organizations. Dengfeng City was found to have the best performing humanitarian supply chain. The findings of this research provide some helpful indication of the importance of the various emergency measures which can help to inform policy recommendations for the Zhengzhou municipal government.

1. Introduction

Flash flooding events can have a devastating impact on a country’s productivity and the lives of its citizens. For example, on 22 November 2013, torrential rains in the southern part of Rhode Island killed four people, damaged much infrastructure and caused economic damage amounting to EUR 4 million. Moreover, Diakakis et al. suggest that human casualties due to flooding often occur on paved river crossings that are highly susceptible to damage during sudden floods [1]. Over the past 50 years, more than 11,000 weather, climate, and water-related disasters have been reported, causing more than 2 million deaths and USD 3.64 trillion in economic losses [2]. A review of flooding events in the latest report of the Centre for Research on the Epidemiology of Disasters (CREDS) shows that the number of global floods in 2022 totaled 387, the total number of deaths was 7954, and the economic losses were as high as USD 44.9 billion [3]. Statistics from the Chinese Ministry of Water Resources and the National Disaster Reduction Center of the Ministry of Emergency Management show that between 1991 and 2020, more than 60,000 people died or went missing as a result of floods in China, resulting in a cumulative total of about RMB 4.81 trillion in direct economic losses [2].

The devastating impact of flash flooding on a country underscores the importance of the humanitarian supply chain in providing emergency relief to affected areas. Humanitarian supply chains involve the planning, execution, and control of goods, medical supplies, and information needed from their production to the affected areas based on humanitarianism in the context of disaster relief as well as post-disaster reconstruction [4]. In recent years, an increasing number of scholars have begun to study the humanitarian supply chains. Zhou Lei proposed that differentiating and studying the different stakeholders in the humanitarian supply chain can ensure that the humanitarian supply chain is more efficient [5]. Yang Jinglei et al. compared the differences between humanitarian logistics and general commercial logistics and proposed that humanitarian supply chains have higher requirements for behavioral standards [6]. Ali Anjomshoae et al. (2022) suggested that in order to overcome future supply chain disruptions due to pandemics and large-scale disasters, an assessment of the performance of humanitarian supply chains is important [7].

The multi-criteria decision-making method (MCDM) is the method most commonly used to study humanitarian supply chains. Peng et al. (2014) used a system dynamics model to simulate and predict post-disaster traffic road damage and information system delays [8]; Sharma et al. (2022) undertook a vulnerability and resilience assessment of humanitarian supply chains using fuzzy DEMATEL method [9]; Dubey et al. (2020) discussed humanitarian supply chain performance indicators from the perspective of agility and improving the evaluation index system [10].

In conclusion, the existing literature considers the evaluation indicators in terms of their governance and performance, but there is a lack of insight into those receiving these rescue services. While the existing literature has used many qualitative and quantitative MCDM methods to assess the resilience of humanitarian supply chains, few studies have integrated fuzzy logic theory to evaluate the performance of humanitarian supply chains. In order to fill these research gaps, this research adds to the evaluation of performance by adding service quality to make the evaluation more comprehensive; furthermore, it adds the fuzzy theory to evaluate the performance of the supply chain to make the results more applicable to the actual situation. Therefore, the purpose of this research is as follows:

• To add the perspective of service quality to construct an evaluation index system that is more complete and comprehensive;
• To integrate the fuzzy theory into the evaluation method to make the evaluation results closer to the real-life situation;
• To evaluate the performance of humanitarian supply chains using an ensemble ANP-PFs-VIKOR method.

This paper poses the following questions: (1) What are the most significant factors affecting humanitarian supply chain performance? (2) How is humanitarian supply chain performance in an area best studied?

The results of this research will provide an important reference and data to support decision making for the key emergency management stakeholders, relevant participants, and governments.

2. Literature Review

This review is based on the following two aspects: firstly, we systematically review the literature related to humanitarian supply chain resilience, summarize the relevant concepts of supply chain resilience, and propose and introduce the key indicators; secondly, through this literature review, we identify which MCDM methods have been applied in existing humanitarian supply chain resilience evaluation articles.

2.1. Definition of Indicators

The humanitarian supply chain is a process of moving materials from the supply side to the demand side that involves multiple relevant participants and relief providers in a complex internal and external environment. In this research, after conducting an extensive literature review and consulting with humanitarian supply chain experts, and considering various factors, an index system for the assessment of resilience was constructed as shown in

Table 1. Summarizes the findings of the literature review.

Standard	Indicator	Main Contents
Organizational involvement A	Active government involvement (F1)	Government plays a major role in the humanitarian supply chain [11,12,13]
	Active participation of NGOs (F2)	NGOs are gaining ground in the humanitarian supply chain [14]
	Coordination among participating organizations (F3)	Coordination among supply chain members is important for humanitarian supply chain resilience [15,16]
Reliability B	Logistics provider reliability (F4)	Logistics providers can accelerate the relief process and improve the resilience of the humanitarian supply chain [17,18,19]
Agility C	Material supplier reliability (F5)	Timely supply of materials helps to speed up the rescue process and enhance rescue efficiency [20,21,22]
	Responsiveness (F6)	Rapid supply chain response enhances supply chain agility [23,24,25]
	Resource scheduling capability (F7)	Having the ability to quickly dispatch resources makes the humanitarian supply chain more resilient [26,27]
Cost factor D	Timeliness of transportation (F8)	Timely transportation allows for smooth relief efforts and further improves supply chain resilience performance [28,29]
	Transportation costs (F9)	Lower transportation costs can lead to increased supply chain revenue and increased supply chain operability [30,31]
	Inventory costs (F10)	Reducing inventory costs contributes to a sustainable supply chain, thereby increasing its resilience [32,33]
	Material mobilization and procurement costs (F11)	Lower material raising and procurement costs allow for more material to be raised on the same budget, and increased material availability helps improve supply chain performance [34,35]
Quality of service E	Supply of necessities of life (F12)	The main function of the humanitarian supply chain is to provide the necessities of life to the relief workers [36,37,38]
	Distribution of relief supplies (F13)	Distribution of relief supplies can protect the lives and livelihoods of those waiting for help [39,40,41]

.

Organizational involvement (A). Humanitarian relief may be led by governmental organizations, NGOs, or UN relief organizations, and involves many other participants including the affected community members. The selection of suppliers in humanitarian supply chains requires the joint participation of the government and the market [15,42]. At the same time, stakeholders in the humanitarian supply chain are unique, but some have the same wants and needs [43,44,45] and are important for coordination across organizations.

Reliability (B). Humanitarian supply chain reliability is about ensuring that supplies are delivered accurately to the people being rescued [18]. Uncertainty in the relief process has the potential to cause disruptions throughout the supply chain, and reliability is one way to ensure that the supply chain is functioning properly [22].

Agility (C). In emergency relief, an agile and flexible supply chain ensures that the supply chain can react quickly and adjust to the appropriate state in the event of an emergency [27]. Agility has a positive impact on the operational performance of the supply chain [23]. Agility is now gaining attention as an important influencing factor in assessing supply chain resilience in a constantly fluctuating and unpredictable environment [27].

Cost factor (D). Costs in the supply chain are mainly derived from order delivery costs, warehousing and inventory costs, supply chain management costs, procurement costs, transportation costs, and marketing costs [46,47,48]. Compared to traditional commercial supply chains, the emergency management costs in humanitarian supply chain management costs can be significantly higher [42]. Low-cost supply chains are more resilient and sustainable.

Quality of service (E). Most of the previous studies on humanitarian supply chains have focused on the supplier and humanitarian relief party perspectives. While the rescued parties are also key nodal members of the overall supply chain, Ali Anjomshoae et al. (2022) suggested that the existing humanitarian supply chain literature has little consideration of the perceptions of the served parties [7,49]. Meanwhile, as the willingness of the demand side is increasingly valued, many studies on the evaluation of supply chain resilience have included the demand side perspective [50,51,52,53].

2.2. Review of Humanitarian Supply Chain Assessment Methods

In previous studies, many methods have been used to assess humanitarian supply chain resilience (refer to

Table 2. Research methods and descriptions.

References	Description	Method
[54]	A combination of pre-positioning relief items in the mainland and anticipating them onboard ships and at terminals is proposed to help improve the efficiency of disaster relief operations as well as the resilience of the supply chain	Goal planning
[55]	The impact of supply chain agility (SCAG) and supply chain resilience (SCRES) on performance, mediated by organizational culture, was investigated	DCV
[56]	Fuzzy MICMAC methodology was used to identify and analyze the factors that develop resilience in humanitarian supply chains	Fuzzy-MICMAC
[59]	Interpretive structural modeling (ISM) was used to assess the barriers in the humanitarian supply chain in coastal Bangladesh under the influence of cyclones	ISM
[60]	A dynamic systems model approach was used to compare centralized and decentralized supply chain configurations and apply them to humanitarian supply chains	Dynamic systems model
[61]	Weighting of humanitarian supply chain barriers in a big-data-driven context assessed by fuzzy full explanatory structural model (F-T-ISM)	F-T-ISM
Proposed method	Thirteen representative indicators were selected to evaluate humanitarian supply chain resilience factors, and the VIKOR evaluation method was used to rank the resilience of humanitarian supply chains in five typical disaster areas	PFs-ANP-VIKOR

). Sharifyazdi et al. (2018) used a target planning approach and proposed that a combination of pre-positioning relief items in the interior and anticipating relief items on board ships and at the docks could help improve the efficiency of relief operations as well as improve supply chain resilience [54]. Altay et al. (2018) used the dynamic capability view (DCV) to conceptualize a theoretical model of the humanitarian supply chain (HSC) in different phases before and after a disaster to investigate the impact of supply chain agility (SCAG) and supply chain resilience (SCRES) on performance, mediated by organizational culture [55]. Singh et al. (2018) identified and analyzed factors for developing resilience in humanitarian supply chains using the fuzzy MICMAC approach [56,57,58]. Rahman Md Mostafizur et al. (2022) used Interpretive Structural Modeling (ISM) to assess the barriers in the humanitarian supply chain in coastal Bangladesh under the influence of cyclones [59]. Giedelmann-L Nicolas et al. (2022) used a dynamic systems model approach to compare centralized and decentralized supply chain configurations and applied it to humanitarian supply chains to provide applicable inventory management strategies for food relief in relief operations [60]. There are several entropy factors in the system dynamics model, and different entropy factors have different roles for the system as a whole, which are considered as MCDM in this paper. Bag et al. assessed the weights of humanitarian supply chain barriers in a big-data-driven context by means of a fuzzy full explanatory structural model (F-T-ISM) [61,62].

Based on the systematic literature review, we found that the current research in humanitarian supply chain resilience mainly focuses on the following three aspects: 1. studying the relationship between various elements in the humanitarian supply chain; 2. analyzing each element in the humanitarian supply chain and evaluating the most critical influencing factors through evaluation methods; 3. using fuzzy theory to make improvements to the evaluation methods to achieve evaluation results closer to the actual. We also found that the previous studies on the humanitarian supply chain have been very useful. In addition, we found that the previous studies on the resilience of humanitarian supply chains were mostly from the perspective of “providers” and rarely from the perspective of “recipients”. This suggests that there is some room for improvement in the study of humanitarian supply chain resilience. Therefore, based on the above findings, this research considers the “recipient” perspective and the relationship between the factors to make a comprehensive assessment of humanitarian supply chain resilience using the ANP-PFs-VIKOR approach.

3. Methods

As shown in Figure 1, this research is divided into the following three steps to assess humanitarian supply chain resilience: in the first stage, the key indicators of humanitarian supply chain resilience are identified based on the views of experts and the findings from a review of the literature; in the second stage, the interrelationships between the indicators are determined using the combined results from a Delphi study, questionnaire survey and an extensive literature review, while the weights of the indicators are derived using the ANP method; in the third stage, the results of the indicator weights obtained in stage 2 are brought into the calculation of VIKOR, and the Pythagorean fuzzy theory (PFs) is used to fuzzify the VIKOR method. Furthermore, in order to make the values of VIKOR parameters more reasonable, this research uses the idea of minimization of deviation to solve the parameters and make some improvements to the VIKOR method. Meanwhile, four typical areas threatened by flood disasters in Zhengzhou are selected to evaluate and rank the resilience of their humanitarian supply chains.

3.1. ANP Method

The ANP method focuses on the feedback relationship of interdependence and mutual influence among indicators [63], establishes the judgment matrix by expert scoring, and calculates the unweighted matrix, weighted supermatrix, and limit supermatrix in turn to obtain the weights of each indicator [64].

Step 1:

• Construct the judgment matrix [64]

Using the findings from a review of the literature review, expert scoring method, and questionnaire survey, the relative importance between factors was derived in a two-by-two comparison. Then, a judgment matrix, $A={\left(C_{ij}\right)}_{n\times n}$ was constructed to determine the relative importance between the lower level and the upper level indicators and assigned.

2.

Calculate the weight vector [64]

The steps are as follows:

(1)

Element normalization process. $\overline{{\mathit{C}}_{\mathit{i}\mathit{j}}}$=$\frac{{\mathit{C}}_{\mathit{i}\mathit{j}}}{\sum _{k=1}^n{\mathit{C}}_{\mathit{k}\mathit{j}}}$, (i,j = 1, 2, …, n)

(2)

Summing the normalized matrices by rows: $\overline{{\mathit{\omega }}_{\mathit{i}}}$ = ${\sum }_{j=1}^n{\mathit{C}}_{\mathit{i}\mathit{j}}$

(3)

For $\overline{{\mathit{\omega }}_{\mathit{i}}}$=${(\overline{{\mathit{\omega }}_1},\overline{{\mathit{\omega }}_2},\dots ,\overline{{\mathit{\omega }}_{\mathit{n}}})}^{\mathit{T}}$, normalized, ${\mathit{\omega }}_{\mathit{i}}=\frac{\overline{{\mathit{\omega }}_{\mathit{i}}}}{{\sum }_{\mathit{j}=1}^{\mathit{n}}\overline{{\mathit{\omega }}_{\mathit{j}}}}$,(i,j = 1, 2, …, n)

Step 2: Consistency check [64]

The consistency test can be a good way to avoid the problem of reliability reduction due to unreasonable setting of the number weight.

• Calculate the maximum eigenvalue

${\mathit{\lambda }}_{\mathit{m}\mathit{a}\mathit{x}}=\frac{1}{n}\sum _{i=1}^n\frac{(\mathit{A}{\mathit{\omega })}_{\mathit{i}}}{{\mathit{\omega }}_{\mathit{i}}}$, $(\mathit{A}{\mathit{\omega })}_{\mathit{i}}$ denotes the ith component of vector $\mathit{\omega }$;

2.

Calculate the consistency index CI

$$\mathit{C}\mathit{I}=\frac{{\mathit{\lambda }}_{\mathit{m}\mathit{a}\mathit{x}}-\mathit{n}}{\mathit{n}-{\displaystyle 1}}$$

3.

Calculate consistency ratio

$$\mathit{C}\mathit{R}=\frac{\mathit{C}\mathit{I}}{\mathit{R}\mathit{I}}$$

(1)

When CR ≤ 0.1, the judgment matrix can be obtained with good consistency. If CR > 0.1, it means that the judgment matrix fails the consistency test, and it is necessary to return to step 1 and reconstruct the judgment matrix again.

Step 3: Build Super Matrix [64]

Let there be elements $P_1$, $P_2$, $P_3$, …, $P_n$, in the control layer of ANP, and under the control layer, there are element groups $C_1$, $C_2$, $C_3$, …, $C_N$ in the network layer, where $C_i$ has elements $e_{i1}$, …, $e_{i{n}_j}$, (i = 1, …, N). Taking the control layer element $P_s$ (s = 1, …, m) as the criterion and the element $e_{jl}$(l = 1, …, $n_j$) in $C_j$ as the sub-criterion, the elements in the element group $C_i$ are compared in terms of their influence on $e_{j1}$ for indirect dominance, i.e., the judgment matrix is constructed and the sorting vector ${{\omega }_{i1}}^{\left(jl\right)}$, …, ${{\omega }_{i{n}_j}}^{\left(jl\right)}$) is obtained by the characteristic root method, and ${\omega }_{ij}$ is

$${\omega }_{ij}=\left[\begin{array}{ccc}{{\omega }_{i1}}^{\left(j1\right)}& \cdots & {{\omega }_{i1}}^{\left(jl\right)}\\ ⋮& \ddots & ⋮\\ {{\omega }_{i{n}_j}}^{\left(j1\right)}& \cdots & {{\omega }_{i{n}_j}}^{\left(jl\right)}\end{array}\right]$$

(2)

Here, the column vector of ${\omega }_{ij}$ is the ranked vector of the degree of influence of the elements $e_{i1}$, …, $e_{i{n}_j}$ in $C_i$ on the elements $e_{j1}$, …, $e_{j{n}_j}$ in $C_j$. If the elements in $C_j$ are not affected by the elements in $C_i$, then ${\omega }_{ij}$ = 0, so that the final supermatrix W under $P_s$ can be obtained:

$$W=\left[\begin{array}{ccc}{W}_{11}& \cdots & W_{1N}\\ ⋮& \ddots & ⋮\\ W_{N1}& \cdots & W_{NN}\end{array}\right]$$

(3)

Step 4: Construct the weighted supermatrix [64]

Using $P_s$ as a criterion, the judgment matrix is constructed for each group of elements $C_j$ (j = 1, …, N) under $P_s$ and the importance comparison is performed to obtain the normalized feature vector $a_{Nj}$, (j = 1, …, N). The set of vectors unrelated to $C_j$ is assigned a ranking vector component of 0, which gives the weighting matrix that

$$A=\left[\begin{array}{ccc}{a}_{11}& \cdots & a_{1N}\\ ⋮& \ddots & ⋮\\ a_{N1}& \cdots & a_{NN}\end{array}\right]$$

(4)

Weight the elements of the supermatrix W, $\overline{W}=(\overline{W_{ij}}$), where $(\overline{W_{ij}}$) = $a_{ij}{W}_{ij}$, (i = 1, …, N; j = 1, …, N).

Step 5: Construct the limit supermatrix [64]

Let the elements of the (weighted) supermatrix W be $W_{ij}$, then $W_{ij}$ reflects the one-step dominance of i over j. The dominance of i over j can also be obtained by $\sum _{K=1}^N{W}_{ik}{W}_{kj}$, which is called the two-step dominance. When $W^{\infty }$ = $\underset{l\to \infty }{\lim }{W}^l$ exists, the jth column of $W^{\infty }$ is the limit relative ranking vector of each element to element j in the network layer under $P_s$.

3.2. Pythagoras (PFs) Fuzzy Theory

Pythagorean fuzzy sets (PFs) are built on top of intuitionistic fuzzy sets (IFs). Both PFs and IFs quantify the decision maker’s linguistic description of the decision criterion using affiliation, non-affiliation, and hesitancy values. PFs describe fuzzy phenomena where the sum of affiliation and non-affiliation exceeds 1 and the sum of squares does not exceed 1, and can accommodate more uncertainty than IFs. It also describes the hesitation of the expressed decision maker in terms of affiliation and non-affiliation, which is much closer to the actual decision-making situation than IFs, and thus, it is a powerful tool for explaining the uncertainty phenomenon and better modeling the real decision-making situation.

3.2.1. Pythagorean Fuzzy Set Definition [65]

Assuming that $X$ is a nonempty set, there exists a fuzzy set $\Lambda$ that

$$\Lambda =⟨x,{\mu }_P\left(x\right),{\upsilon }_P\left(x\right)\left|x\in X\right.⟩$$

(5)

${\mu }_p\left(x\right),v_p\left(x\right)$ are the subordination and non-subordination values in the fuzzy set, respectively, and for any $x$, there is $x\in X$, ${\mu }_p\left(x\right),v_p\left(x\right)⟶\left[\mathrm{0,1}\right],0\le {\mu }_p{\left(x\right)}^2+v_p{\left(x\right)}^2\le 1$. For any $\Lambda$, there is a hesitant function ${\pi }_p\left(x\right)$, ${\pi }_p\left(x\right)=\sqrt{1-\left({\mu }_p{\left(x\right)}^2+v_p{\left(x\right)}^2\right)}$.

3.2.2. Pythagorean Fuzzy Set Arithmetic Rule [65]

Assuming that $P_1$ and $P_2$ are two Pythagorean fuzzy numbers, denoted as, $P_1=P_1\left({\mu }_{p1},v_{p1}\right)$, ${P_2=P}_2\left({\mu }_{p2},v_{p2}\right)$, respectively, then there are

$$P_1\oplus P_2=P(\sqrt{{\left({\mu }_{P1}\right)}^2+{\left({\upsilon }_{P2}\right)}^2-{\left({\mu }_{P1}\right)}^2{\left({\upsilon }_{P2}\right)}^2},{\upsilon }_{P1}{\upsilon }_{P2})$$

(6)

$$P_1\otimes P_2=P\left({\mu }_{P1}{\mu }_{P2}\sqrt{{\left({\mu }_{P1}\right)}^2+{\left({\upsilon }_{P2}\right)}^2-{\left({\mu }_{P1}\right)}^2{\left({\upsilon }_{P2}\right)}^2}\right)$$

(7)

$$P_1-P_2=P\left(\sqrt{\frac{{\left({\mu }_{P1}\right)}^2+{\left({\mu }_{P2}\right)}^2}{1-{\left({\mu }_{P2}\right)}^2}},\frac{{\upsilon }_{P1}}{{\upsilon }_{P2}}\right),\left({\mu }_{P1}\ge {\mu }_{P2},{\upsilon }_{P1}\le \mathit{min}\left\{{\upsilon }_{P2},\left.\frac{{\upsilon }_{P2}{\pi }_{P1}}{{\pi }_{P2}}\right\}\right.\right)$$

(8)

$$P_1÷P_2=P\left(\frac{{\mu }_{P1}}{{\mu }_{P2}},\sqrt{\frac{{\left({\upsilon }_{P1}\right)}^2+{\left({\upsilon }_{P2}\right)}^2}{1-{\left({\upsilon }_{P2}\right)}^2}}\right),\left({\mu }_{P1}\le \mathit{min}\left\{{\mu }_{P2},\left.\frac{{\mu }_{P2}{\pi }_{P1}}{{\pi }_{P2}}\right\},{\upsilon }_{P1}\ge {\upsilon }_{P2}\right.\right)$$

(9)

$$\lambda P_1=P\left(\sqrt{1-\left(1-{{\mu }_{p1}}^2\right)},{{\upsilon }_{p1}}^{\lambda }\right)$$

(10)

$${P_1}^{\lambda }=P\left({{\mu }_{p1}}^{\lambda },\sqrt{1-\left(1-{{\upsilon }_{p1}}^2\right)}\right),\lambda >0$$

(11)

3.2.3. Comparison of Fuzzy Numbers and the Hemming Distance [65]

Let P be a Pythagorean fuzzy number, then the score function of P is as follows:

$$S_P={\left({\mu }_P\right)}^2+{\left({\upsilon }_P\right)}^2$$

(12)

A larger value of $S\left(P\right)$ means a larger $P$. According to this rule, one can have the following judgment:

• If $S\left(P_1\right)<S\left(P_2\right)$, then $P_1{\prec P}_2$
• If $S\left(P_1\right)>S\left(P_2\right)$, then $P_1{\succ P}_2$
• If $S\left(P_1\right)=S\left(P_2\right)$, then $P_1{\sim P}_2$

To better illustrate the gap between two fuzzy numbers, the Hemming distance is measured here using the following formula:

$$D_h=\frac{1}{2}\times \left(\left|({{\mu }_{p1}}^2\right.-\left.{{\mu }_{p2}}^2)+({{\upsilon }_{p1}}^2-{{\upsilon }_{p2}}^2)+({{\pi }_{p1}}^2-{{\pi }_{p2}}^2)\right|\right)$$

(13)

3.2.4. Pythagorean Fuzzy Weighted Averaging [65]

In Pythagorean fuzzy theory, Yager proposed Pythagorean fuzzy weighted averaging (PWFA).

$$\Psi =PFWA\left(\sqrt{1-{\prod }_{k=1}^e{\left(1-({\mu }_{ij}^k{)}^2\right)}^{w_k}},{\prod }_{k=1}^e{\left(({\upsilon }_{ij}^k{)}^2\right)}^{w_k}\right)$$

(14)

${\mu }_{ij}^k$ and $v_{ij}^k$ are the judgments given by the decision maker, and $W_k$ is the fixed weight of the decision maker’s decision, ${\sum }_{k=1}^e{W}_k=1$.

3.2.5. Fuzzy Semantic Transformation [65]

In this research, the fuzzy language involved in the fuzzy set is transformed into binary fuzzy numbers to facilitate the numerical clarity process by referring to the results in the study by Shafiee et al. [65].

Table 3. Pythagorean fuzzy semantic transformation scale.

Fuzzy Natural Semantics	The Pythagorean Fuzzy Set $({\mathit{\mu }}_{\mathit{P}}{,\mathit{\upsilon }}_{\mathit{P}}$)
Very low (VL)	(0.15, 0.85)
Low (L)	(0.25, 0.75)
Moderately low (ML)	(0.35, 0.65)
Medium (M)	(0.55, 0.45)
Moderately high (MH)	(0.65, 0.35)
High (H)	(0.75, 0.25)
Very high (VH)	(0.85, 0.15)

gives the reference scale for fuzzy semantic transformations, which is divided into a total of seven levels, very low (VL), low (L), moderately low (ML), medium (M), moderately high (MH), high (H), and very high (VH).

3.3. PFs-VIKOR Steps

Before we introduce the specific steps of the VIKOR method, let us define the meaning of the specific symbols in the formula as follows:

${\rho }_j$—Attribute weights for the jth evaluation indicator;

$J^{+}$—The total set of attribute values for the benefit type;

$J^{-}$—Aggregate set with attribute values of cost type;

$P_j^{+}$—Positive ideal solutions for each alternative under criterion j;

$P_j^{-}$—Negative ideal solutions for each alternative under criterion j;

${Ed}_i$—Group benefit value for the ith alternative;

${EH}_i$—Individual regret value for the ith alternative;

$Q_i$—VIKOR value for the ith alternative.

Step 1: Obtain the initial fuzzy evaluation matrix.

Suppose the problem has n decision criteria, $j=\mathrm{1,2},3\dots ,n$ $m$ evaluation schemes $(i=\mathrm{1,2},3\dots ,m)$, and the fuzzy semantic evaluation result of each scheme is given by e experts, $k=\mathrm{1,2},3\dots ,e$. The final fuzzy evaluation results constitute the initial fuzzy evaluation matrix R (all elements in R are PFs).

$$R=R\left(r_{ij}^k\right)=PFWA\left(\sqrt{1-{\prod }_{k=1}^e{\left(1-({\mu }_{ij}^k{)}^2\right)}^{w_k}},{\prod }_{k=1}^e{\left(({\upsilon }_{ij}^k{)}^2\right)}^{w_k}\right)$$

(15)

$$R=R(r_{ij}^k)=p_{ij}=\left(\begin{array}{cccc}{r}_{11}^k& r_{12}^k& \cdots & r_{1n}^k\\ r_{21}^k& r_{22}^k& \cdots & r_{21}^k\\ ⋮& ⋮& \ddots & ⋮\\ r_{m1}^k& r_{m2}^k& \cdots & r_{mn}^k\end{array}\right)$$

(16)

$w_k$ is the expert weight, and in this paper, we use the length of work experience to determine the expert weights.

$$W_k=\frac{T^k}{{\sum }_{k=1}^e{T}^k}$$

(17)

$T^k$ is the working time of the expert.

Step 2: Calculate the Pythagorean fuzzy number positive ideal solution PFPIS$\left(P_j^{+}\right)$ and the Pythagorean fuzzy number negative ideal solution PFNIS$\left(P_j^{-}\right)$, where $r_{ij}^k=p_{ij}$ is a Pythagorean fuzzy number that can be expressed as $r_{ij}^k=\left({\mu }_{ij},{\nu }_{ij}\right)$.

$$p_j^{+}=R(r_{ij}^k)=R({\mu }_j^{+},{\upsilon }_j^{+})=\left\{\begin{array}{c}R\left(\mathit{max}{\mu }_{ij},\mathit{min}{\upsilon }_{ij}\right),j\in J^{+}\\ R\left(\mathit{min}{\mu }_{ij},\mathit{max}{\upsilon }_{ij}\right),j\in J^{-}\end{array}\right.$$

(18)

$$p_j^{-}=R(r_{ij}^k)=R({\mu }_j^{-},{\upsilon }_j^{-})=\left\{\begin{array}{c}R\left(\mathit{min}{\mu }_{ij},\mathit{max}{\upsilon }_{ij}\right),j\in J^{+}\\ R\left(\mathit{max}{\mu }_{ij},\mathit{min}{\upsilon }_{ij}\right),j\in J^{-}\end{array}\right.$$

(19)

Step 3: Calculate the group benefit value ${Ed}_i$ and individual regret value ${EH}_i$ of each program.

$${Ed}_i={\sum }_{j=1}^n{\rho }_j\frac{D_h(p_j^{+},p_{ij})}{D_h(p_j^{+},p_j^{-})},i=\mathrm{1,2},3,...,m$$

(20)

$${EH}_i=\mathit{max}\left({\rho }_j\frac{D_h(p_j^{+},p_{ij})}{D_h(p_j^{+},p_j^{-})}\right),i=\mathrm{1,2},3,...,m$$

(21)

where ${\rho }_j$ is the weight calculated by ANP, 0 ≤ ${\rho }_j$ ≤ 1, and $\sum _{j=1}^n{\rho }_j$ = 1.

Step 4: Calculate the final VIKOR value $Q_i$ for each scenario.

$$Q_i=x_1\frac{{Ed}_i-{Ed}^{+}}{{Ed}^{-}-{Ed}^{+}}+x_2\frac{{EH}_i-{EH}^{+}}{{EH}^{-}-{EH}^{+}},i=\mathrm{1,2},\dots ,m$$

(22)

where, ${Ed}^{+}=\underset{i}{\mathrm{m}\mathrm{i}\mathrm{n}}\left\{{Ed}_i\right\}$, ${Ed}^{-}=max\left\{{Ed}_i\right\}$, ${EH}^{+}=\underset{i}{\mathrm{m}\mathrm{i}\mathrm{n}}\left\{{EH}_i\right\}$, ${Ed}^{-}=\underset{i}{\mathrm{m}\mathrm{a}\mathrm{x}}\left\{{EH}_i\right\}$.

$x_1, x_2$ ∈ [0, 1] denote the decision coefficients. When $x_1>x_2$, it indicates that the decision maker prefers the group view; $x_1<x_2$, indicating that the decision maker is more biased toward personal view; $x_1=x_2=0.5$, indicating that there is no clear preference of the decision maker. In this paper, we use the $x_1=x_2=0.5$ parameter coefficient approach.

Step 5: Rank the alternatives according to the calculated ${Ed}_i,{EH}_i$ and $Q_i$, ${Ed}_i,{EH}_i$, and $Q_i$ are cost variables; the smaller the value, the better the alternative.

4. Case Study

4.1. Study Areas

The Zhengzhou City municipal area is located in the north-central part of Henan Province, where the middle and lower reaches of the Yellow River divide, with a total area of 7567 square kilometers. Four of the cities in this region, Xinmi, Xingyang, Dengfeng, and Gongyi, are located in the mountainous area to the west of Zhengzhou City and are known as the “Mountainous 4” (as shown in Figure 2). Gongyi District has a total area of 1043 square kilometers, and in 2022, the city’s resident population was 803,100, with a GDP of RMB 96.26 billion. Xingyang District has a total area of 943 square kilometers. The city has a resident population of 732,500 and a gross domestic product (GDP) of RMB 55.42 billion. Dengfeng District has a total area of 1217 square kilometers, a resident population of 733,100, and a GDP of RMB 47.840 billion. Xinmi District has a total area of 1001 square kilometers, the city’s total resident population is 827,100 people, and its gross domestic product is RMB 71.3252 billion. In the period of 17–21 July 2021, precipitation in the four cities exceeded the historical value of extremely heavy rainfall. Because of the large number of houses, bridges and roads have been built across the river, blocking the release of water from the river during flood peaks and exacerbating the rise in river levels. The flooding and landslides led to more than 40,000 houses being destroyed, resulting in 251 people being killed in the four cities. The disaster caused RMB 40.9 billion of economic losses in Zhengzhou City.

4.2. Data Collection

In this research, the expert survey method and literature review methods were first used to establish an evaluation index system containing 5 levels and 13 key indicators. In the questionnaire survey, experts were invited anonymously to participate, preserving their heterogeneity [66,67]. A questionnaire was then used to gather expert opinions on the humanitarian supply chain. Two types of questionnaires were used, and the expert judgment gathered from these two rounds of questionnaires was converted to data and used to support the evaluation of humanitarian supply chain resilience in the study area. The first questionnaire was used in the ANP calculation, in which the experts compared the 13 indicator factors based on the 1–9 scale methodology two by two. Using the results, a comparison matrix was derived to be used in the calculation of the weights of the indicators of the evaluation of the resilience of the humanitarian supply chain(results are shown in

Table 4. ANP weights and rankings.

Standard	Weight	Indicator	Weight	Rank
Organizational involvement A	0.2813	Active government involvement (F1)	0.0987	5
		Active participation of NGOs (F2)	0.0573	8
		Coordination among participating organizations (F3)	0.1474	1
Reliability B	0.1663	Logistics provider reliability (F4)	0.0832	6
		Material supplier reliability (F5)	0.0831	7
		Responsiveness (F6)	0.1174	3
Agility C	0.3777	Resource scheduling capability (F7)	0.1253	2
		Timeliness of transportation (F8)	0.1129	4
Cost factor D	0.1223	Transportation costs (F9)	0.0559	9
		Inventory costs (F10)	0.0238	12
		Material mobilization and procurement costs (F11)	0.0426	10
Quality of service E	0.0524	Supply of necessities of life (F12)	0.0337	11
		Distribution of relief supplies (F13)	0.0187	13

). This questionnaire was distributed in March–April 2023. The second questionnaire was used in the calculation of VIKOR ordering, and required the experts to carry out a semantic evaluation of the four disaster areas in Zhengzhou according to the established index system (details of the semantic evaluation are shown in

Table 5. Initial evaluation matrix.

	Xingyang		Gongyi		Dengfeng		Xinmi
	${\mathit{\mu }}_{\mathit{j}}$	${\mathit{\nu }}_{\mathit{j}}$	${\mathit{\mu }}_{\mathit{j}}$	${\mathit{\nu }}_{\mathit{j}}$	${\mathit{\mu }}_{\mathit{j}}$	${\mathit{\nu }}_{\mathit{j}}$	${\mathit{\mu }}_{\mathit{j}}$	${\mathit{\nu }}_{\mathit{j}}$
F1	0.6113	0.1521	0.5500	0.2025	0.7500	0.0625	0.6113	0.1521
F2	0.5110	0.2406	0.5500	0.2025	0.6982	0.0917	0.5974	0.1631
F3	0.3973	0.3660	0.4971	0.2546	0.6500	0.1225	0.5500	0.2025
F4	0.4500	0.3025	0.5110	0.2406	0.7500	0.0625	0.6113	0.1521
F5	0.4500	0.3025	0.4971	0.2546	0.7500	0.0625	0.6113	0.1521
F6	0.3973	0.3660	0.4500	0.3025	0.6500	0.1225	0.5110	0.2406
F7	0.3973	0.3660	0.4111	0.3492	0.7500	0.0625	0.6113	0.1521
F8	0.5500	0.2025	0.6500	0.1225	0.5500	0.2025	0.6500	0.1225
F9	0.5974	0.1631	0.5500	0.2025	0.7500	0.0625	0.5500	0.2025
F10	0.4500	0.3025	0.5500	0.2025	0.6500	0.1225	0.5110	0.2406
F11	0.6500	0.1225	0.6500	0.1225	0.4500	0.3025	0.6500	0.1225
F12	0.4500	0.3025	0.4500	0.3025	0.6982	0.0917	0.5500	0.2025
F13	0.5500	0.2025	0.4500	0.3025	0.7500	0.0625	0.6113	0.1521

). The evaluation results are used in the calculation of the group benefit value ${Ed}_i$ and the individual regret value ${EH}_i$. This questionnaire was distributed in May–June 2023. Scholars generally believed that the number and experience of experts have a decisive impact on the accuracy of the evaluation results, and some scholars suggest that selecting a group of 5–12 experts with more than 5 years of work experience to conduct the evaluation can make the evaluation results more accurate [50,51,52,53]. Therefore, this research distributed questionnaires to 18 experts in the field of humanitarian supply chain and finally collected 14 valid responses. In order to ensure the accuracy and reliability of the findings, the experts selected included scholars in the field of humanitarian supply chain, managers of governmental relief organizations, and staff members of the International Red Cross relief organizations. The details of the expert group are shown in Figure 3:

4.3. Modeling Based on the ANP-PFs-VIKOR Approach

Step 1: Calculate indicator weights.

Based on the questionnaire, an initial judgment matrix was derived and the results are shown in the Appendix A, Appendix B and Appendix C. The weights were solved according to the steps of the ANP method presented in Section 3.1 above. At the same time, we use Figure 4 to represent the weights of each indicator so that we can show the importance of each indicator more clearly. The weighting results are shown in Table 4 below.

Step 2: Obtain the PFs-VIKOR initial evaluation matrix.

The experts conducted semantic evaluations of each evaluation object, and the semantic evaluations were converted into the initial evaluation matrix (Table 5).

Step 3: Calculate positive and negative ideal solutions $p_j^{+}$ and $p_j^{-}$, respectively. The results of the calculations are shown in

Table A5. Positive ideal solution $p_j^{+}$ and negative ideal solution $p_j^{-}.$ Calculation results.

	${\mathit{P}}_{\mathit{j}}^{+}$		${\mathit{P}}_{\mathit{j}}^{-}$
	${\mathit{\mu }}_{\mathit{j}}$	${\mathit{\nu }}_{\mathit{j}}$	${\mathit{\mu }}_{\mathit{j}}$	${\mathit{\nu }}_{\mathit{j}}$
F1	0.7500	0.0625	0.5500	0.2025
F2	0.6982	0.0917	0.5110	0.2406
F3	0.6500	0.1225	0.3973	0.3660
F4	0.7500	0.0625	0.4500	0.3025
F5	0.7500	0.0625	0.4500	0.3025
F6	0.6500	0.1225	0.3973	0.3660
F7	0.7500	0.0625	0.3973	0.3660
F8	0.6500	0.1225	0.5500	0.2025
F9	0.5500	0.2025	0.7500	0.0625
F10	0.4500	0.3025	0.6500	0.1225
F11	0.4500	0.3025	0.6500	0.1225
F12	0.6982	0.0917	0.4500	0.3025
F13	0.7500	0.0625	0.4500	0.3025

in Appendix C.

Step 4: Calculate the Heming distance $D_h$ between $P_{ij}$ and $P_j^{-}$, $P_j^{+}$ and $P_j^{-}$.

Based on Equation (13), the sea-mining distances $D_h$ between $P_{ij}$ and $P_j^{-}$, $P_j^{+}$ and $P_j^{-}$ were calculated (as shown in Appendix C,

Table A6. Hemming distance $D_h$.

${\mathit{D}}_{\mathit{h}}({\mathit{p}}_{\mathit{j}}^{+},{\mathit{p}}_{\mathit{i}\mathit{j}})$	Xingyang	Gongyi	Dengfeng	Xinmi	${\mathit{D}}_{\mathit{h}}({\mathit{p}}_{\mathit{j}}^{+},{\mathit{p}}_{\mathit{j}}^{-})$
F1	0.0848	0.1115	0.0000	0.0848	0.1115
F2	0.0884	0.0762	0.0000	0.0562	0.0884
F3	0.0729	0.0628	0.0000	0.0470	0.0729
F4	0.1362	0.1237	0.0000	0.0848	0.1362
F5	0.1362	0.1272	0.0000	0.0848	0.1362
F6	0.0729	0.0718	0.0000	0.0592	0.0729
F7	0.1373	0.1377	0.0000	0.0848	0.1373
F8	0.0470	0.0000	0.0470	0.0000	0.0470
F9	0.0200	0.0000	0.1115	0.0000	0.1115
F10	0.0000	0.0248	0.0718	0.0125	0.0718
F11	0.0718	0.0718	0.0000	0.0718	0.0718
F12	0.1009	0.1009	0.0000	0.0762	0.1009
F13	0.1115	0.1362	0.0000	0.0848	0.1362

), and the ratio of the two sea-mining distances was calculated (as shown in Appendix C,

Table A7. Distance ratio of Heming.

$\frac{{\mathit{D}}_{\mathit{h}}({\mathit{p}}_{\mathit{j}}^{+}, {\mathit{p}}_{\mathit{i}\mathit{j}})}{{\mathit{D}}_{\mathit{h}}({\mathit{p}}_{\mathit{j}}^{+}, {\mathit{p}}_{\mathit{j}}^{-})}$	Xingyang	Gongyi	Dengfeng	Xinmi
F1	0.7610	1.0000	0.0000	0.7610
F2	0.9998	0.8615	0.0000	0.6354
F3	1.0003	0.8618	0.0000	0.6451
F4	1.0000	0.9081	0.0000	0.6227
F5	1.0000	0.9342	0.0000	0.6227
F6	1.0003	0.9849	0.0000	0.8130
F7	1.0001	1.0029	0.0000	0.6177
F8	1.0000	0.0000	1.0000	0.0000
F9	0.1794	0.0000	1.0000	0.0000
F10	0.0000	0.3449	1.0000	0.1745
F11	1.0000	1.0000	0.0000	1.0000
F12	1.0000	1.0000	0.0000	0.7548
F13	0.8183	1.0000	0.0000	0.6227

).

Step 5: Calculate the group benefit value ${Ed}_i$ and individual regret value ${EH}_i$ for each scenario.

According to Equations (20) and (21) and combined with the weight ${\rho }_j$ calculated by ANP method, the group benefit value ${Ed}_i$, individual regret value ${EH}_i,$ and VIKOR value $Q_i$ are calculated, and the results are shown in

Table 6. Group benefit value ${Ed}_i$, individual regret value ${EH}_i$, and VIKOR value $Q_i$ and rank.

		Rank		Rank		Rank
Xingyang	0.4986	4	0.1018	4	0.5221	4
Gongyi	0.3739	3	0.0930	3	0.4365	3
Xinmi	0.2859	2	0.0811	2	0.4279	2
Dengfeng	0.2701	1	0.0605	1	0.4008	1

.

5. Discussion

Flash floods are, by their nature, extremely sudden and unpredictable. The resilience of humanitarian supply chains is important in flood-prone areas. Effective humanitarian supply chains can respond quickly to natural disasters such as floods, mitigating in a timely manner the damage they cause to areas and the inconvenience and harm they cause to residents. In this research, ANP-PFs-VIKOR was used to evaluate the resilience of humanitarian supply chains in four county-level cities under Zhengzhou City, which were severely affected by floods. The weighting of the indicators is shown in Table 4, and the results of the evaluation of the resilience of humanitarian supply chains in the four regions are shown in Table 6.

5.1. ANP Discussion

Coordination between participating organizations (F3) is the most important indicator, as can be seen in Table 4. Agarwal et al. (2020) identified the lack of interagency coordination and collaboration as the most important difficulty to overcome in reducing HSC risk [11]. The findings of Agarwal et al. are consistent with the findings of this paper. Among the members of the humanitarian supply chain, the government is the main initiator and various humanitarian relief-related nongovernmental organizations are the main participants. The ability to work closely and coordinate between initiators and participants affects the efficiency of the humanitarian response, which in turn affects the level of resilience of the humanitarian supply chain as a whole. John et al. have also suggested that lack of coordination between organizations can lead to the fatalities of those waiting for rescue [49]. Therefore, humanitarian supply chain managers should pay particular attention to the relationships among organizations in order to achieve the goal of a clear division of labor and close cooperation at all levels of the organization. Close coordination between the various organizations involved in the humanitarian supply chain can be effective in enhancing the operational efficiency of the supply chain and can further increase the resilience of the entire supply chain.

Resource scheduling capability (F7) is the second key indicator. It refers to the integrated capacity of members of the humanitarian supply chain to procure, plan, transport, and distribute emergency supplies, such as medical supplies and food, from the place of supply to the affected area in a rational manner. Rapid and efficient resource scheduling can reduce casualties in disaster-affected areas, accelerate reconstruction, and improve the resilience of the humanitarian supply chain. Therefore, members of the humanitarian supply chain should pay close attention to this indicator and use a number of methods to improve it. Samiksha Mathur et al. (2023) suggested that the application of emerging technological achievements such as machine learning, AI, and big data in the supply chain can significantly improve resource scheduling capabilities. Therefore, the resilience level of humanitarian supply chains can be improved by applying emerging technological achievements in supply chains.

Response capacity (F6) is the third most important indicator. Ding et al. also suggested that emergency response capacity has a significant role in humanitarian supply chain and emergency relief [67]. The findings of this study are consistent with those in this research. The responsiveness of the supply chain affects the agility of the supply chain, and the agility of the humanitarian supply chain is important as it determines the efficiency and level of the humanitarian supply chain. The overall efficiency of a humanitarian supply chain will enable it to respond quickly to emergencies, thereby increasing its overall level of resilience. Improved responsiveness can improve the speed of relief for the humanitarian supply chain, which also can enhance the level of resilience of the entire supply chain. Ding et al. suggested that establishing an emergency supply system is an important way to improve emergency response capabilities [67]; humanitarian supply chain managers should improve the resilience performance of humanitarian supply chains by establishing timely and efficient emergency supply systems.

5.2. PFs-VIKOR Discussion

From the ranking of ${Ed}_i,{EH}_i$, and $Q_i$ in Table 6, it can be seen that the resilience level of humanitarian supply chains in the four regions is ranked: Dengfeng > Xinmi > Gongyi > Xingyang.

Dengfeng City had the best performance in humanitarian supply chain resilience during the flooding, mainly because of the local government’s rapid integration and planning at the time of the event. Regarding the “Zhengzhou” 7.20 “extraordinarily heavy rainfall disaster”, the investigation report shows that at 20:00 in the 19th Dengfeng City, a sudden rainstorm triggered by flooding prompted a level Ⅳ emergency response, and at 23:30, based on analysis, it was found that this flood could cause more serious disasters and was quickly upgraded to a level I emergency response. The Dengfeng City Flood Control and Drought Relief Command, in conjunction with local nongovernmental humanitarian relief organizations, quickly carried out resource dispatch as well as emergency response, gaining the initiative in disaster response and disposal [68]. In contrast, the Xingyang municipal government only activated its level I emergency response at 4:00 on the 21st, failing to cooperate with local nongovernmental humanitarian organizations such as the Red Cross in a timely and effective manner, and failing to provide an effective emergency response at the same time. These make Xingyang’s humanitarian supply chain weak in terms of agility and reliability. Furthermore, according to the State Council Disaster Investigation Group, on July 20, Xingyang City, Cuimiao Township, Wang Zongdian village flood flow rose to 768 cubic meters/second, the flood rose 7.15 m, resulting in the death of 23 people. Analysis of the reasons found that the Xingyang municipal government failed to rationalize the flood control command system, the responsibilities of the subordinate units were unclear, and failed to achieve close coordination and mutual cooperation of the flood control units. This resulted in a failure to achieve a rapid response to the floods and the timely deployment of emergency resources to the most affected areas.

We found that the root cause of the failure to respond to the floods in a timely manner was a lack of awareness of the extreme flood hazard risks in the region and poor command of flood control efforts by both governmental and nongovernmental organizations. Xinmi, Gongyi, and Xingyang all failed to activate their emergency response in a timely manner, and most government staff in all three areas were complacent and negligent. Therefore, a series of emergency rescue training under sudden-onset disasters should be carried out to enhance the risk awareness of governmental organizations; at the same time, emergency evacuation drills should be carried out for local residents to improve their self-protection ability in the event of a disaster. Through the joint efforts of both relief organizations and those being rescued, the number of casualties and economic losses could be minimized while contributing to a higher level of resilience in the humanitarian supply chain.

In summary, the study concluded that coordination among participating organizations (F3), resource scheduling capacity (F7), and responsiveness (F6) are the three most critical indicators affecting humanitarian supply chain resilience. Based on this research finding, this research further assessed and ranked the humanitarian supply chain resilience of the four cities. Dengfeng City government cooperated closely with the local relief organizations, carried out rapid distribution of resources, and activated the level I emergency response to the flood. This has helped the city to perform better than the other three cities in the aspects of coordination among participating organizations (F3), resource scheduling capacity (F7), and responsiveness (F6). Xinmi, Gongyi, and Xingyang cities should pay more attention to these three indicators to optimize their emergency response plans and make timely and accurate emergency decisions. This study is based on the rescue activities in the four cities in the Zhengzhou region during the occurrence of a megaflood. The results highlight useful policy insights into the emergency management of Zhengzhou and also suggest improvements in the emergency management practices to the municipal government of Zhengzhou City.

6. Conclusions and Recommendations

This research has assessed the resilience of humanitarian supply chains in four cities in the mountainous region of Zhengzhou using the ANP-PFs-VIKOR approach. The weights of the indicators were derived through ANP analysis. The four cities were analyzed and ranked using the VIKOR analysis, demonstrating that the ANP-PFs-VIKOR method has strong operability in such practical applications. With respect to the research question mentioned in Section 1, we found that coordination among participating organizations (F3) is the most important factor affecting the resilience of humanitarian supply chains, a result that is in line with the findings of Cao Keyan [13] et al. Meanwhile, the results of the study demonstrated that the best performing humanitarian supply chain was in Dengfeng City. In response to the findings, this research makes the following recommendations:

(1)

Improving the coordination of participating organizations in humanitarian relief. The analysis of the ANP results shows that the coordination of participating organizations is the most important factor affecting the resilience of the humanitarian supply chain. John et al. argue that the introduction of coordination mechanisms in humanitarian supply chains significantly increases the efficiency of the entire supply chain and contributes to its resilience level [49]. Therefore, in the process of emergency and humanitarian relief, a coordination mechanism should be introduced to enable close cooperation between the participating organizations.

(2)

Improving resource mobilization capacity and response of humanitarian supply chains. It is concluded that resource scheduling capacity (F7) and responsiveness (F6) are important influences on the resilience of humanitarian supply chains. Therefore, all parties in the humanitarian supply chain should pay close attention to this indicator, improve response capacity and response speed, and improve resource scheduling capacity, so as to make the humanitarian supply chain more resilient.

(3)

Improving service quality in humanitarian supply chains. In recent years, Ali Anjomshoae et al. (2022) proposed that the service quality of the rescued should be considered in the humanitarian supply chain [7]. Hence, service quality should be included in the evaluation of resilience of humanitarian supply chains, and this can help improve the performance of the system while also making the results more accurate and valid.

Notwithstanding these important findings, there are some shortcomings in this research which need to be acknowledged. The impacts of flooding events on countries and local populations are of a continuous nature, and how to quickly restore the local economy and the living standards of the population to pre-disaster conditions after a sudden flood should also be an issue for the humanitarian supply chain to consider. This research has only considered the emergency relief phase of the humanitarian supply chain in the event of a flash flood, and future research could look deeper from the perspective of how to quickly restore the affected area to the state it was in before the event. This should also include looking at how learning from the experience of the events could lead to improved resilience.