Multi-Objective Collaborative Allocation Strategy of Local Emergency Supplies Under Large-Scale Disasters

Abstract

In the initial phase of large-scale disasters, delayed external relief supplies make scientific local emergency supply allocation crucial—not only for reducing casualties, but also for advancing sustainable disaster response, a key link in enhancing post-disaster resilience. Existing research mostly focuses on cross-regional material allocation while overlooking local challenges like low resource efficiency and unbalanced supply–demand dynamics. To tackle these limitations in the existing research, this study develops a multi-objective collaborative local emergency supply allocation model centered on sustainability. It uses an improved TOPSIS method to quantify the urgency of needs in disaster-stricken areas, prioritizing material distribution to vulnerable regions in line with the principle of “no vulnerable area left neglected in relief efforts”. The study also integrates the entropy weight method and analytic hierarchy process (AHP) to ensure rational indicator weighting, and designs a double-layer encoded genetic algorithm to obtain optimal allocation schemes that balance efficiency, fairness, and sustainability. Validated using the 2013 Ya’an Earthquake case study, the model outperforms traditional local allocation approaches: it boosts resource utilization efficiency by reducing material shortage rates, accelerates post-disaster recovery by shortening response times, and improves allocation fairness. Findings provide empirical support for the establishment of “local–external” collaborative rescue systems and sustainable disaster risk reduction frameworks. Empirical calculations using case-specific data and real-world estimates verify the model’s practical applicability: it meets the requirements for fair and rapid allocation needs, aligns with the goals of sustainable disaster management, and lowers the carbon footprint of relief operations by lessening reliance on long-distance external materials.

1. Introduction

In recent years, the frequent occurrence of large-scale disasters across the globe has posed significant challenges to human society. Their inherent suddenness, destructiveness, and the uncertainty of disaster-induced demand significantly exacerbate the complexity of decision-making for emergency supply allocation systems [1,2,3,4]. After a disaster, amid the chaos of post-disaster conditions, external relief supplies often fail to reach affected areas promptly. Consequently, self-rescue and mutual aid within affected regions—prior to the arrival of external supplies—take on particular importance. Specifically, the effective utilization of local emergency resources can minimize losses incurred by affected populations [5,6,7]. Notably, this process of optimizing local emergency supply allocation is inherently aligned with the three pillars of sustainability in disaster management. From a social sustainability perspective, equitable distribution of local resources ensures that vulnerable groups and remote affected areas are not excluded from relief support, promoting social inclusion and stability. Economically, the efficient utilization of local supplies reduces the waste of emergency materials and avoids unnecessary re-procurement costs, embodying the principle of resource efficiency. Environmentally, the rational allocation and path optimization of local resources can reduce the frequency of cross-regional transportation, thereby lowering carbon emissions from long-distance logistics and contributing to low-carbon disaster response. This study thus focuses on local emergency supply allocation to address both practical rescue needs and sustainable development goals.

Affected regions typically confront multiple constraints, such as uncertainty over material demand, disrupted transportation routes, and tight rescue timeframes. Traditional single-objective allocation models struggle to balance core objectives—including timeliness, fairness, and cost effectiveness [8,9]. Notably, in cross-regional collaboration contexts, conflicting priorities among decision-makers at different administrative levels, the tension between dynamic demand and limited resources, and the “bullwhip effect” driven by information asymmetry collectively result in emergency supply misallocation, delayed supply delivery, and even the risk of secondary disasters [10,11,12].

In fact, as early as 2015, the Chinese government promulgated the National Comprehensive Disaster Prevention and Mitigation Plan (2016–2020), which explicitly outlined emergency supply allocation principles: “hierarchical responsibility, local primacy, and local-led on-site command”—a framework that directly emphasizes the core role of local authorities in the initial phase of disaster response. Similarly, the U.S. Department of Homeland Security’s National Incident Management System (NIMS) [13] also specifies that for addressing sudden public incidents, a response framework based on “hierarchical management and local focus” should be adopted, with local agencies designated as the primary entities for on-site response coordination.

However, in both the academic research and practical implementation of China’s emergency supply allocation system, insufficient attention has been paid to the strategic value of local supplies in building “first-response capability”—an oversight that undermines the alignment between theoretical research and policy requirements [9,14]. Meanwhile, decision-makers at various levels also tend to overlook the practical challenge of optimizing local emergency supply allocation, often prioritizing cross-regional material deployment over leveraging the potential of local resources. Therefore, exploring effective strategies to leverage local supplies for self-rescue and mutual aid when external relief is delayed constitutes a pressing issue requiring urgent research and resolution in the field of large-scale disaster emergency response at the current stage.

2. Literature Review

Emergency supply allocation is the core link in post-disaster rescue systems, directly determining disaster response efficiency and the extent of casualties and property losses. Against the backdrop of the growing frequency of large-scale global disasters (e.g., earthquakes, floods, public health emergencies), its timeliness, fairness, and adaptability have become critical topics at the intersection of disaster risk reduction, operations research, and logistics management. Theoretically, this field relies on two core frameworks: humanitarian logistics management, which emphasizes the “efficiency–fairness” balance in post-disaster resource distribution [15,16]; and multi-objective optimization theory, which provides a methodological basis for addressing conflicting goals (e.g., minimizing response time and maximizing demand satisfaction) in complex post-disaster scenarios [17,18,19]. In recent years, the integration of uncertainty management has become a key trend—post-disaster demand fluctuations, transportation damage, and incomplete data driving scholars to shift from static to dynamic, stochastic models [20].

Early research on emergency supply allocation focused on single-objective optimization, with core goals centered on cost control or time minimization. For example, Sarma et al. proposed a neutrosophic mathematical model integrating two-phase resource distribution and redistribution to minimize total operational cost and redistribution time, but overlooked real-time dynamic demand adjustments in post-disaster response [21]. Liang et al. proposed a genetic algorithm for supply distribution center planning in UAV-based logistics networks to minimize average timeliness but ignored UAV energy constraints Huang et al. designed a UAV-based model to shorten delivery time but ignored multi-regional collaboration [22]. Since the 2010s, multi-objective optimization has become mainstream: Wang and Sun integrated road damage probability into a multi-period model to balance transportation risks and demand coverage [23]; Cao et al. expanded to sustainability by balancing relief efficiency and transportation carbon emissions [24]. Notably, definitions of “fairness” vary—Li et al. focused on procedural equality in vehicle scheduling [25]—but most studies focus on cross-regional allocation, with limited exploration of local supply fairness.

Cross-regional emergency supply allocation has been extensively studied, with research focusing on large-scale scheduling and inter-regional collaboration. Zhang et al. used real-time data to solve inter-provincial “information islands” [26]. Wang et al. proposed government-enterprise collaboration to enhance supply flexibility (though with long transportation lead times) [27]. In contrast, research on local emergency supply allocation—critical for the post-disaster “golden 72 h”—remains relatively scarce. Local supplies (government reserves, enterprise stockpiles, and social donations within the disaster-stricken administrative region) avoid long-distance delays and support initial self-rescue [28]. Existing local studies have limitations: they are either disaster specific or ignore multi-supply-point synergy [29]; furthermore, few studies systematically address practical challenges such as inefficient resource utilization and supply–demand imbalance in local contexts. This gap makes it difficult for existing research to provide targeted support for scientific local emergency supply allocation in large-scale disasters.

The evolution of optimization methods has strongly supported the development of emergency supply allocation models, with research divided into two phases. Traditional mathematical programming methods (e.g., linear and stochastic programming) are used for stability—Zhou et al. proposed a novel multi-objective two-stage blood transshipment–allocation model under COVID-19 to optimize blood quality [30]. With the rise of intelligent algorithms, meta-heuristic methods have become the primary tool for complex multi-objective problems. Genetic algorithms are common: Wang et al. improved GAs with grey theory for public health emergency location–allocation [31]. Yang and Zhang et al. proposed an integrated two-stage optimization framework for China’s earthquake emergency logistics to enhance supplies deployment and prioritize high-urgency regions [32]. Other methods include NSGA-II (for route optimization) and hybrid meta-heuristics for location-routing problems [33]. However, the integration of multi-criteria decision-making (MCDM, e.g., TOPSIS for urgency ranking) and meta-heuristics remains limited, creating a method gap.

While multi-objective optimization has become mainstream in emergency supply allocation research, most existing models inherently follow a “single-objective priority” logic that may not fully adapt to the specific needs of local emergency response [34]. Typical characteristics include overemphasizing one core objective at the expense of fairness, relying on fixed objective weights that fail to reflect dynamic post-disaster changes, and paying limited attention to resolving objective conflicts in local contexts. To address these practical challenges, this study develops a “timeliness–fairness–utilization rate” multi-objective framework that builds on the existing research: it treats all three goals as key considerations and integrates them through a weighted sum objective function, adopts disaster-tailored weights determined by expert scoring to reflect on-site priorities, and embeds practical constraints to better align with local response realities. Compared with representative existing models, the proposed model places greater emphasis on local allocation scenarios, highlights distributive fairness guided by the principle of “no vulnerable area left neglected”, and seeks to balance timeliness, fairness, and resource utilization—with the aim of providing a more tailored tool for complex local emergency scenarios in the initial phase of large-scale disasters.

Despite significant progress in emergency supply allocation research, local emergency supply allocation for large-scale disasters—especially models that integrate timeliness, fairness, and methodological synergy tailored to local contexts—still has room for refinement. Therefore, based on the practical needs of local “golden 72 h” relief, this study focuses on local emergency supply allocation in large-scale disasters, aiming to complement existing research and offer theoretical support for scientific local rescue decisions.

3. Construction of a Local Emergency Supply Allocation Model for Large-Scale Disasters

To address the practical challenges of local emergency supply allocation in large-scale disasters—such as demand uncertainty, transportation disruptions, and conflicting response objectives—this section constructs a multi-objective optimization model tailored to the “first-response” scenario using local resources. The model design adheres to the principles of policy alignment and practical feasibility, with detailed formulations as follows.

3.1. Problem Description

Rapid and efficient rescue operations within the post-disaster “golden time”—typically defined as the critical 72 h window after disaster onset, when the survival rate of affected populations declines sharply—are decisive for reducing casualties. Within this window, the timeliness of emergency supply allocation directly determines the effectiveness of on-site rescue, making it a core bottleneck in disaster response.

Notably, historical rescue cases demonstrate that prioritizing the deployment of local emergency resources to affected areas is an effective approach to shortening the response cycle. This is because local reserves avoid the delays associated with cross-regional transportation and can reach demand points within hours. Therefore, after a natural disaster occurs, decision-makers face a multi-dimensional optimization problem: they must quickly allocate local emergency supplies while satisfying three interrelated requirements—allocating based on differentiated disaster severity levels to prioritize high-severity areas, following a “high-to-low priority” logic to avoid unfair resource concentration, and preventing public panic caused by local supply shortages while minimizing the overall demand shortage rate across all affected areas.

Accordingly, this paper constructs a collaborative local emergency supply allocation strategy—integrating reserve point scheduling, transportation route optimization, and demand satisfaction balancing—with the core objective of minimizing the weighted sum of three key goals: minimum total allocation time, maximum alignment with disaster severity priorities, and minimum overall demand shortage rate. This strategy aims to address the limitations of traditional single-objective models and provide an actionable decision-making tool for the “local self-rescue phase” of large-scale disasters.

To simplify the complex, dynamic post-disaster environment while retaining the core constraints of local emergency supply allocation, and to ensure the scientific validity and solvability of the subsequent optimization model, the following basic assumptions are proposed based on practical disaster response contexts and academic research conventions.

H1. 

When formulating initial allocation decisions, the local emergency rescue command department has access to key baseline data—including initial demand information of each affected point, inventory information of local emergency supplies, and initial transportation network status. Recognizing the dynamic nature of post-disaster conditions, the model incorporates a mechanism to accommodate data updates, allowing the allocation plan to be adaptively adjusted in response to changes in critical information related to disaster impact and infrastructure status. A reasonable time window is adopted to balance the need for dynamic adaptation and algorithmic feasibility.

H2. 

The objects of allocation are multi-category material combinations; a single-material allocation modeling approach is adopted based on these material combinations for analytical feasibility.

H3. 

Allocation decisions are made by the local emergency rescue department from a global perspective. The department conducts a comprehensive assessment based on the conditions of each affected point within its jurisdiction, adheres to the principle of fairness, and pursues a globally optimal allocation strategy rather than local optimization.

H4. 

The emergency material transportation capacity allocated by the local department is sufficient to meet the short-term allocation needs of local emergency supplies.

H5. 

All vehicles used for emergency material transportation are specialized emergency vehicles with consistent basic load capacity. Considering the complexity and variability of post-disaster road conditions, the model accounts for potential speed adjustments based on real-time road assessments, ensuring that transportation time calculations reflect practical constraints rather than assuming a fixed speed.

H6. 

Financial cost considerations are completely excluded from the decision-making process of local emergency supply allocation.

3.2. Basic Explanations

In conjunction with the aforementioned basic assumptions and the actual operational logic of local emergency response, the contextual scope and operational rules of local emergency supply allocation are further clarified as follows.

Following a large-scale disaster, m geographically dispersed affected points will emerge within a specific administrative region. Within this same administrative region, there are n pre-planned and pre-constructed local emergency supply reserves, which can provide material support to each of the m affected points. Consistent with the principles of “hierarchical responsibility, local primacy, and local-led on-site command”, local emergency supply allocation is strictly confined to the boundaries of this administrative region: it solely involves the distribution of emergency supplies stored in the n local reserves to the m local affected points, and explicitly excludes material support from outside the region or demand outside the local jurisdiction.

Additionally, the personnel responsible for allocation coordination and the vehicles used for material transportation are all subordinate to the local emergency management department—this organizational arrangement ensures the unified command and efficient execution of the entire allocation process. The structural framework of this local emergency supply allocation system is shown in Figure 1.

To clearly define the core participants in the local emergency supply allocation system, the concepts of “local affected points” and “local supply points” are defined as follows:

(1) Local Affected Point

Within the jurisdiction affected by a large-scale disaster, the local administrative scope encompasses grassroots units such as villages and communities—these units qualify as local affected points. Specifically, a local affected point refers to a location capable of receiving emergency supplies and directly distributing them to disaster victims within its coverage.

(2) Local Supply Point

Within the aforementioned local administrative scope, local supply points are formed by three types of emergency material reserve entities: government emergency material reserves, enterprise reserves, and social reserves. These points have the capacity to provide emergency supplies to local affected points, accept unified deployment by the local emergency rescue command department, and restrict their supply scope exclusively to local affected points.

3.3. Local Emergency Supply Allocation Model

3.3.1. Symbol Explanation

To support the quantitative analysis required for constructing the local emergency supply allocation model, it is first necessary to standardize the definitions of core elements involved in the model—including supply–demand parameters and decision variables. Specific explanations of the symbols for these elements are as follows (

Table 1. Symbol explanation.

Sets
M	Set of m local affected points $M_i$, $i=1,2,\dots ,m$
N	Set of n local supply points $N_j$, $j=1,2,\dots ,n$
Index
i	Index of the i-th local affected point $M_i$ (corresponding to set M, where i = 1, 2,..., m)
j	Index of the j-th local supply point $N_j$ (corresponding to set N, where j = 1, 2,..., n)
Parameters
$T_{max}^i$	Maximum delay time allowed for the i-th local affected point $M_i$ to receive emergency supplies
$R_j$	Stockpile level of emergency supplies at the j-th local supply point $N_j$
$P_i$	Emergency supplies requirement of the i-th local affected point $M_i$
$D_{ji}$	Distance from the j-th local supply point $N_j$ to the i-th local affected point $M_i$
$v_j$	Transport speed of emergency material vehicles from the j-th local supply point $N_j$ to the i-th local affected point $M_i$
$t_{ji}$	Time required to deliver emergency supplies from the j-th local supply point $N_j$ to the i-th local affected point $M_i$; $y_{ji}=1$ indicates supplies are allocated from $N_j$ to $M_i$; $y_{ji}=0$ indicates no allocation
$w^d$	Weight corresponding to the sum of shortage rates across all local affected points
$w^e$	Weight corresponding to the sum of the earliest arrival times of emergency supplies (from supply points to affected points)
$w^l$	Weight corresponding to the sum of the latest arrival times of emergency supplies (from supply points to affected points)
$w_i$	Hierarchical weight of the i-th affected point $M_i$
$\theta$	Demand satisfaction rate of each local affected point
Decision variables
$x_{ji}$	Quantity of emergency supplies allocated from the j-th local supply point $N_j$ to the i-th local affected point $M_i$
$y_{ji}$	0–1 decision variable, where $y_{ij}$ = 1 signifies that emergency supplies are allocated from the j-th local supply point $N_j$ to the i-th local affected point $M_i$, and $y_{ij}$ = 0 indicates no such allocation

):

3.3.2. Construction of the Local Emergency Supply Allocation Model

After a large-scale disaster, the local emergency management department first obtains real-time disaster information, then analyzes the emergency supply demand status and urgency level of each local affected point, and subsequently combines key information—including the quantity, geographic location, and stockpile level of local emergency supply points—to construct a local emergency supply allocation model.

This model takes three core factors as optimization objectives: the sum of shortage rates of all local affected points (${\mathcal{F}}_1$), the sum of the earliest arrival times of emergency supplies at all local affected points (${\mathcal{F}}_2$), and the sum of the latest arrival times of emergency supplies at all local affected points (${\mathcal{F}}_3$). The specific formulation of the model is as follows:

$$\begin{array}{cc}\hfill {\mathcal{F}}_1& =\sum _{i=1}^m{\displaystyle \frac{(P_i-{\sum }_{j\in N}{y}_{ji})}{P_i}}\hfill \end{array}$$

(1)

$$\begin{array}{cc}\hfill {\mathcal{F}}_2& =\sum _{i=1}^m\underset{j\in N}{min}\left\{w_j·t_{ji}·y_{ji}\right\}\hfill \end{array}$$

(2)

$$\begin{array}{cc}\hfill {\mathcal{F}}_3& =\sum _{i=1}^m\underset{j\in N}{max}(w_j·t_{ji}·y_{ji})\hfill \end{array}$$

(3)

$$\begin{array}{cc}\hfill {\mathcal{F}}_4& =w^d·{\mathcal{F}}_1+w^e·{\mathcal{F}}_2+w^l·{\mathcal{F}}_3\hfill \end{array}$$

(4)

where $w^d+w^e+w^l=1$.

$$\begin{array}{l}minimize{\mathcal{F}}_4\end{array}$$

(5)

$$\begin{array}{cccc}\hfill \mathit{s}.\mathit{t}.& \sum _{j=1}^n{x}_{ji}\le P_i\hfill & \hfill & \forall i=1,\dots ,m\hfill \end{array}$$

(6)

$$\begin{array}{cccc}\hfill & t_{ji}={\displaystyle \frac{D_{ji}}{v_2}}\hfill & \hfill & \forall i=1,\dots ,m;\forall j=1,\dots ,n\hfill \end{array}$$

(7)

$$\begin{array}{cccc}\hfill & \sum _{i=1}^m{y}_{ji}=R_j\hfill & \hfill & \forall i=1,\dots ,m\hfill \end{array}$$

(8)

$$\begin{array}{cccc}\hfill & y_{ji}(1-y_{ji})=0\hfill & \hfill & \forall i=1,\dots ,m;\forall j=1,\dots ,n\hfill \end{array}$$

(9)

$$\begin{array}{cccc}\hfill & max(t_{ji}·y_{ji})\le T_{\max }^i\hfill & \hfill & \forall i=1,\dots ,m;\forall j=1,\dots ,n\hfill \end{array}$$

(10)

$$\begin{array}{cccc}\hfill & {\displaystyle \frac{{\sum }_{j=1}^n{w}_j·y_{ji}}{P_i}}\ge \theta \hfill & \hfill & \forall i=1,\dots ,m\hfill \end{array}$$

(11)

$$\begin{array}{cccc}\hfill & x_{ji}\in \{0,1\}\hfill & \hfill & \forall i=1,\dots ,m;\forall j=1,\dots ,n\hfill \end{array}$$

(12)

$$\begin{array}{cccc}\hfill & y_{ji}\in \{0,1\}\hfill & \hfill & \forall i=1,\dots ,m;\forall j=1,\dots ,n\hfill \end{array}$$

(13)

The explanations for objective functions (1)–(4) are as follows: Equation (1) quantifies the total shortage rate of emergency supplies across all local affected points. Equation (2) calculates the total of the earliest arrival times of emergency supplies for all local affected points. Equation (3) characterizes the total of the latest arrival times of emergency supplies at all local affected points, which corresponds to the “sum of the latest arrival times of emergency supplies at all local affected points” in the model framework. As the comprehensive optimization objective, Equation (4) aims to minimize the weighted sum of the three aforementioned targets: the total shortage rate of emergency supplies across all local affected points, the total of the earliest arrival times of emergency supplies at all local affected points, and the total of the latest arrival times of emergency supplies at all local affected points. The weights assigned to these three objectives are $w^{\mathrm{d}}$, $w^{\mathrm{t}}$, and $w^{\mathrm{s}}$, respectively.

Regarding the constraint conditions 5–11, the specific explanations are as follows: Equation (5) imposes a demand upper-limit constraint: the total emergency supplies allocated to the local affected point i by all local supply points shall not exceed the total demand of this point, avoiding oversupply and wasting limited resources. For the calculation of transportation time, Equation (6) defines the time required to transport emergency supplies from local supply point j to local affected point i using special-purpose transport vehicles. Equation (7) sets a supply balance constraint: the total quantity of emergency supplies distributed from local supply point j to all local affected points must not exceed its total reserve quantity. Equation (8) characterizes the logical relationship of the allocation decision variable: when variable $y_{ji}=1$, it indicates that local supply point j allocates emergency supplies to local affected point i; if $y_{ji}=0$, no such allocation is performed. Equation (9) specifies a weight normalization constraint: the sum of the weights assigned to the three objectives (shortage rate, earliest arrival time, and latest arrival time) shall be 1, with the specific value of each weight determined by the expert scoring method. Equation (10) enforces a timeliness constraint: the time required to transport emergency supplies from local supply point j to local affected point i must not exceed the maximum allowable response time for this point, ensuring compliance with the “golden time” requirement for post-disaster rescue. Equation (11) establishes a demand satisfaction lower-limit constraint: the fulfillment rate of emergency supplies for local affected point i shall not be lower than a pre-specified threshold, thus guaranteeing the basic survival needs of disaster victims in each affected area.

4. Solution of the Local Material Allocation Model

4.1. Overall Solution Process of the Model

The solution to the local emergency supply allocation model is essentially a multi-objective optimization problem, and this study adopts a genetic algorithm for its solution. A genetic algorithm is an iterative process that performs genetic operations on population individuals based on a fitness function, realizing the reorganization of individual structures within the population. This process simulates the evolutionary mechanism of “survival of the fittest” in nature, where individuals in the population are optimized generation by generation and gradually approach the optimal solution. Combined with the content of this study, the pseudo-code of the Genetic Algorithm for Emergency Supplies Allocation is presented as shown in the following table (Algorithm 1).

Algorithm 1 Genetic algorithm for emergency supplies allocation

Require: Supply points (n), Demand points (m), Supply capacity ($S_j,j=1..n$);

1: Demand ($D_k,k=1..m$), GA parameters: PopSize = 50, MaxGen = 100;

2: Crossover probability ($P_c$) = 0.8, Mutation probability ($P_m$) = 0.05.

Ensure: Optimized emergency supplies allocation plan (matrix $X^{*}$) with maximum fitness ${\mathcal{F}}_{max}$, where ${\mathcal{F}}_{max}\le T_{max}$.

3: Begin

4: Initialize Population:

5: for $i=1$ to PopSize do

6:     Generate allocation matrix $X_i$ (each $X_{ijk}$ represents supply from j to k);

7:     Ensure ${\sum }_{k=1}^m{X}_{ijk}\le S_j$ (satisfy supply capacity constraint);

8:     Calculate fitness: $$\mathcal{F}\left(X_i\right)=0.6\left(1-{\displaystyle \frac{T\left(X_i\right)}{T_{max}}}\right)+0.4\left(1-Sh\left(X_i\right)\right)$$

9:     where $T\left(X_i\right)$ is the maximum delivery time of $X_i$, and $Sh\left(X_i\right)$ is the total unmet demand rate.

10: end for

11: GA Iteration:

12: $gen\leftarrow 1$

13: while $gen\le MaxGen$ do

14:     Selection:

15:     Select PopSize parents based on $\mathcal{F}\left(X_i\right)$ (higher fitness → higher selection probability).

16:     Crossover:

17:     Pair parents randomly;

18:     for each pair $(X_p,X_q)$ do

19:            if rand(0,1) $<P_c$ then

20:                 Select row indices $a,b$;

21:                 $X_o\leftarrow X_p[1:a]+X_q[a+1:b]+X_p[b+1:n]$;

22:                 Adjust $X_o$ to satisfy supply capacity constraint.

23:            end if

24:     end for

25:     Mutation:

26:     for each offspring $X_o$ do

27:            if rand(0,1) $<P_m$ then

28:                 Mutate $X_{ojk}\leftarrow X_{ojk}·(1+\mathcal{N}(0,0.01))$;

29:                 Clip $X_{ojk}$ to range $[0,min(S_j-{\sum }_k{X}_{ojk},D_k)]$.

30:            end if

31:     end for

32:     Update Population:

33:     Combine parents and offspring;

34:     Select top PopSize individuals by $\mathcal{F}\left(X_i\right)$ as the new population;

35:     $gen\leftarrow gen+1$

36: end while

37: Output Optimal Solution:

38: Select $X^{*}$ with maximum $\mathcal{F}\left(X_i\right)$ from the final population;

39: Return $X^{*}$

40: End

4.2. Model Solution Process Analysis

(1) Disaster Area Grade Division

The grading of emergency supply demand involves ranking the intensity of demand for emergency supplies at each affected point based on a predefined indicator system, which provides a scientific reference for subsequent supply allocation. Scholars have conducted extensive research on demand grading, and the indicator systems and analysis methods they have developed offer valuable references for this study. Among these methods, the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) is widely applied in demand grading research.

TOPSIS is a commonly used and effective method in multi-objective decision analysis, also known as the “Ideal and Negative-Ideal Solution Distance Method”. Its basic principle is to rank evaluation objects by measuring their distance from the ideal solution (optimal solution) and the negative-ideal solution (worst solution). Specifically, if an evaluation object is closest to the ideal solution while being farthest from the negative-ideal solution, it is deemed the best-performing object; otherwise, its performance is considered suboptimal. Here, the ideal solution is defined as the solution with the optimal values for all evaluation indicators, while the negative-ideal solution is defined as the solution with the worst values for all indicators.

This method features clear principles and convenient calculation, making it well-suited for grading emergency supply demand. Therefore, this study adopts the TOPSIS method to calculate the emergency supply demand grade for each affected point. The specific implementation process is as follows.

① Determine the Decision Matrix

To implement the TOPSIS-based emergency supply demand grading, the first step is to construct a decision matrix that quantifies the demand urgency evaluation indicators for each affected point. Assume there are m local affected points and n evaluation indicators. Let $a_{ij}$ represent the value of the i-th local affected point corresponding to the j-th evaluation indicator.

Based on expert evaluation results, the evaluation indicator values reflecting the urgency of emergency supply demand for all local affected points are compiled into a decision matrix A. The matrix is formally defined as follows:

$$\mathbf{A}=\left[\begin{array}{cccc}{a}_{11}& a_{12}& \cdots & a_{1n}\\ a_{21}& a_{22}& \cdots & a_{2n}\\ ⋮& ⋮& \ddots & ⋮\\ a_{m1}& a_{m2}& \cdots & a_{mn}\end{array}\right]$$

where each row of matrix A corresponds to the indicator values of one local affected point, and each column corresponds to the values of one evaluation indicator across all local affected points.

The decision matrix A is then standardized to obtain matrix B, where $b_{ij}$ represents the determined standardized value of the i local affected point corresponding to the j evaluation indicator; matrix B is referred to as the normalized decision matrix:

$$\mathbf{B}=\left[\begin{array}{cccc}{b}_{11}& b_{12}& \cdots & b_{1n}\\ b_{21}& b_{22}& \cdots & b_{2n}\\ ⋮& ⋮& \ddots & ⋮\\ b_{m1}& b_{m2}& \cdots & b_{mn}\end{array}\right]$$

where $b_{ij}$ denotes the determined standardized value of the i local affected point corresponding to each j evaluation indicator.

② Determine the Comprehensive Weight of Indicators

For the normalized decision matrix B, let $P_{ij}$ denote the contribution degree of the j evaluation indicator to the i local affected point. This contribution degree is calculated using Formula (14) as shown below:

$$\begin{array}{c}\hfill P_{ij}=b_{ij}\sqrt{\sum _{i=1}^m{b}_{ij}}\end{array}$$

(14)

$$\mathbf{P}=\left[\begin{array}{cccc}{P}_{11}& P_{12}& \cdots & P_{1n}\\ P_{21}& P_{22}& \cdots & P_{2n}\\ ⋮& ⋮& \ddots & ⋮\\ P_{m1}& P_{m2}& \cdots & P_{mn}\end{array}\right]$$

The entropy of the j-th evaluation indicator is calculated from the contribution $P_{ij}$ of each local affected point to the indicator. In the context of information theory, entropy is a function describing the state of a system. It quantifies the degree of disorder within the system and serves as a measure of the system’s chaos. This calculation follows Formula (15) as shown below:

$$\begin{array}{cc}\hfill E_j=-K\sum _{i=1}^m{p}_{ij}ln{p}_{ij}& K={\displaystyle \frac{1}{lnm}},\forall j=1,\dots ,n\hfill \end{array}$$

(15)

③ Determination of Comprehensive Indicator Weights

Let $\omega$ denote the weight set of all evaluation indicators (where $\omega =\{{\omega }_1,{\omega }_2,\cdots ,{\omega }_n\}$ represents the comprehensive weight of the j-th evaluation indicator). Within this weight set $\omega$, the objective weight of the j-th evaluation indicator in the emergency material demand evaluation system is calculated using Formula (16) as shown below:

$$\begin{array}{cc}\hfill {\omega }_j={\displaystyle \frac{1-E_j}{n-{\sum }_{j=1}^n{E}_j}}& \forall j=1,\dots ,n\hfill \end{array}$$

(16)

Currently, the determination of indicator weights primarily encompasses two categories: subjective weighting methods and objective weighting methods. Subjective weighting methods are based on the synthesis of experts’ long-term practical experience, while objective weighting methods avoid subjective randomness and are determined primarily based on actual evaluation data. To fully consider the relative importance of emergency supply demand urgency among different local affected points and mitigate the limitations inherent in each method alone, this study combines the AHP and the entropy weight method to calculate the comprehensive weights of evaluation indicators. The specific calculation formula is presented in Formula (17):

$$\begin{array}{c}\hfill {\omega }_j=\eta {\alpha }_j+(1-\eta ){\beta }_j\forall j=1,\dots ,n\end{array}$$

(17)

where ${\omega }_j$ is the comprehensive weight of the indicator, ${\alpha }_j$ is the weight calculated by the entropy weight method, ${\beta }_j$ is the weight calculated by the AHP method, and $\eta$ is the preference coefficient, with $0<\eta <1$.

④ Determine the weighted normalized matrix

The urgency of emergency rescue demand varies across different local affected points; therefore, the entropy weights of each evaluation factor should be considered, and the standardized data should be weighted to construct the weighted normalized matrix:

$$\mathbf{C}=\left[\begin{array}{cccc}{c}_{11}& c_{12}& \cdots & c_{1n}\\ c_{21}& c_{22}& \cdots & c_{2n}\\ ⋮& ⋮& \ddots & ⋮\\ c_{m1}& c_{m2}& \cdots & c_{mn}\end{array}\right]$$

$$\begin{array}{cc}\hfill c_{ij}=b_{ij}·{\omega }_j(1\le i\le m,1\le j\le n)& \forall i=1,\dots ,m,\forall j=1,\dots ,n\hfill \end{array}$$

(18)

⑤ Determine the positive ideal solution and negative ideal solution of the evaluation objects

The positive ideal solution (denoted as $C+$), which is composed of the maximum values of each evaluation indicator across all local affected points, and the negative ideal solution (denoted as $C-$), which is composed of the minimum values of each evaluation indicator across all local affected points, are defined as shown in Formulas (19) and (20):

$$\begin{array}{cc}\hfill C^{+}=\{c_1^{+},c_2^{+},\cdots ,c_n^{+}\},c_j^{+}=\underset{i}{max}{c}_{ij}& \forall i=1,\dots ,m\hfill \end{array}$$

(19)

$$\begin{array}{c}\hfill C^{-}=\{c_1^{-},c_2^{-},\cdots ,c_n^{-}\},c_j^{-}=\underset{i}{min}{c}_{ij}\&\forall i=1,\dots ,m\end{array}$$

(20)

⑥ Calculate the Grey Relational Matrix and Grey Relational Degree Between Local Affected Points and the Positive Ideal Solution

First, the theory of Grey Relational Analysis (GRA) is introduced as the methodological basis. For the weighted normalized matrix C and the positive ideal solution $C^{+}$, the grey relational coefficient between the i-th local affected point and the positive ideal solution with respect to the j-th evaluation indicator is calculated using Formula (21):

$$\begin{array}{cc}\hfill {\gamma }_i^{+}={\displaystyle \frac{{min}_j{min}_i|c_j^{+}-c_{ij}| + \rho {max}_j{max}_i|c_j^{+}-c_{ij}|}{|c_j^{+}-c_{ij}| + \rho {max}_j{max}_i|c_j^{+}-c_{ij}|}}& \forall i=1,\dots ,m,\forall j=1,\dots ,n\hfill \end{array}$$

(21)

Here, $\rho$ is used to mitigate the distortion caused by an excessively large maximum absolute difference. Typically, $\rho$ takes a value between 0 and 1; in this study, $\rho$ is set to 0.5. The grey relational coefficient matrix between each local affected point and the positive ideal solution $R^{+}$ is constructed from the grey relational coefficients $r_{ij}^{+}$. Formally, matrix $R^{+}$ is expressed as follows:

$$R^{+}=\left[\begin{array}{cccc}{r}_{11}^{+}& r_{12}^{+}& \cdots & r_{1n}^{+}\\ r_{21}^{+}& r_{22}^{+}& \cdots & r_{2n}^{+}\\ ⋮& ⋮& \ddots & ⋮\\ r_{m1}^{+}& r_{m2}^{+}& \cdots & r_{mn}^{+}\end{array}\right]$$

The grey relational degree $C_i^{+}$ between demand point i and the positive ideal solution is given by Formula (22):

$$\begin{array}{cc}\hfill C_i^{+}={\displaystyle \frac{1}{n}}\sum _{j=1}^n{r}_{ij}^{+}& \forall i=1,\dots ,m\hfill \end{array}$$

(22)

Similarly, the grey relational degree $C_i^{-}$ between demand point i and the negative ideal solution is given by Formula (23):

$$\begin{array}{cc}\hfill C_i^{-}={\displaystyle \frac{1}{n}}\sum _{j=1}^n{r}_{ij}^{-}& \forall i=1,\dots ,m\hfill \end{array}$$

(23)

⑦ Calculate the grey relative closeness for each local affected point

The grey relational closeness $C{C}_i$ reflects the degree to which an evaluation object is close to the positive ideal solution and far from the negative-ideal solution. By calculating the grey relational closeness for each local affected point, the priority ranking of emergency supply demand urgency for all local affected points can be determined. Specifically, the grey relational closeness $C{C}_i$ for the i-th local affected point is calculated using Formula (24):

$$\begin{array}{cc}\hfill C{C}_i={\displaystyle \frac{C_i^{+}}{C_i^{+}+C_i^{-}}}& \forall i=1,\dots ,m,\mathrm{where}0\le C{C}_i\le 1\hfill \end{array}$$

(24)

Finally, use Matlab 2014a for programming and solving. The calculation results can be used as demand grade division information for each affected point for allocation decision-making.

(2) Objective Weight Selection

Equation (4) represents the objective function of the local emergency supply allocation model proposed in this study. This objective function is formulated as the weighted sum of three core objectives: the total shortage rate of emergency supplies, the total of the earliest arrival times of emergency supplies, and the total of the latest arrival times of emergency supplies for all local affected points. To quantify the relative importance of these three objectives, the expert scoring method is adopted in this study to determine their respective weights, denoted as $w^d$, $w^t$, and $w^s$.

This study employs the expert scoring method to determine the weights of the three aforementioned objectives. First, expert opinions are subjected to statistical processing, systematic analysis, and comprehensive synthesis—a process that objectively integrates the practical experience and subjective judgments of a majority of experts, thereby facilitating the reasonable estimation of numerous factors that are difficult to quantify using technical methods alone. The final weights are obtained through multiple rounds of opinion solicitation, feedback collection, and iterative adjustment to ensure consensus among experts. Specifically, assume there are $a=3$ factors (i.e., the three core objectives), and invite b experts to rank these factors. The ranking results form an $a\times b$ matrix. Let $R_{ab}$ denote the score assigned by the b-th expert to the a-th factor. Then, the weight calculation formula for each of the a factors is as follows:

$$\begin{array}{c}\hfill {\displaystyle \frac{{\sum }_{i=1}^b{R}_i^a}{b}}\end{array}$$

(25)

(3) Encoding

In genetic algorithms, a chromosome is a representative form of a problem’s solution, and one chromosome corresponds to one candidate solution. In the local emergency supply allocation model, assuming m affected points and n supply points, an $m\times n$-order two-dimensional matrix A is used to represent the transportation status of emergency relief supplies between each supply point and each affected point. Specifically, the value of each element $M_{ij}(1\le i\le m,1\le j\le n)$ in the matrix represents the quantity of emergency relief supplies transported from the j-th supply point to the i-th affected point; if $M_{ij}=0$, it indicates that no emergency relief supplies are transported via that route. Considering practical application scenarios, the two-dimensional matrix A can be further converted into a one-dimensional vector X. Therefore, the chromosomes of the genetic algorithm in this study are encoded using decimal encoding, and the specific encoding method is shown in

Table 2. Chromosome encoding method.

${\mathit{X}}_{00}$	${\mathit{X}}_{01}$	⋯	${\mathit{X}}_{\mathit{m},\mathit{n}-1}$	${\mathit{X}}_{\mathbf{mn}}$
Quantity from supply point 0 to affected point 0	Quantity from supply point 1 to affected point 0	⋯	Quantity from supply point n − 1 to affected point m	Quantity from supply point n to affected point m

.

Assuming there are 5 affected points and 3 material supply points (i.e., m = 5, n = 3), the corresponding chromosome is as follows: 2-3-0-1-1-2-5-8-1-0-0-1-9-5-7-8. The disaster relief material transportation plan represented by this chromosome is shown in

Table 3. Chromosome example.

	Affected Point 1	Affected Point 2	Affected Point 3	Affected Point 4	Affected Point 5
Supply Point 1	2	3	0	1	1
Supply Point 2	2	5	8	0	0
Supply Point 3	1	9	5	7	8

. For example, in the current chromosome, the quantities of materials transported from Supply Point 2 to each affected point are 2, 5, 8, 0, and 0, respectively.

(4) Initialization

Initialize the variables including population size, the number of individuals selected for evolution, maximum number of evolution generations, minimum fulfillment rate of emergency supplies for affected points, maximum response time for each affected point, number of affected points, and number of local supply points.

(5) Generation of Initial Population

After determining the encoding rules, the genetic algorithm needs to generate an initial population consisting of several chromosomes. In the local emergency supply allocation model, the initial population size is set to 100. Since the chromosomes generated during initial population generation are random, it is necessary to judge, adjust, and validate them at this stage to ensure that the ultimately generated chromosomes meet all constraints of the local emergency supply allocation mathematical model. The specific operational steps are illustrated as follows.

① Ensure that the transportation time meets the maximum response time requirement of each affected point

Calculate the transportation time required by the transportation scheme corresponding to each chromosome and determine whether it meets the maximum response time of each affected point. If so, proceed to Step 2; if not, regenerate the corresponding chromosome until the transportation time satisfies this constraint.

② Ensure that all supplies from each supply point are fully dispatched after the local emergency supply allocation plan is executed

For supply points with remaining supplies after the transportation plan is implemented, prioritize the allocation of their remaining supplies to affected points with a fulfillment rate still below the minimum threshold. Subsequently, allocate any remaining supplies to the affected points with a fulfillment rate within the acceptable range.

(6) Fitness Function

The fitness function is used to evaluate the quality of a chromosome, representing the chromosome’s ability to adapt to the environment. In the “selection” operation of the genetic algorithm, individuals will be selected or eliminated (retaining the superior and eliminating the inferior) based on the fitness function value of each chromosome, and the retained excellent genes will be passed on to the next generation. The fitness function of the genetic algorithm for local emergency supply allocation is derived from the objective functions in the mathematical model of local emergency supply allocation. Since the model contains 3 objective functions—each of which aims for minimization—we construct the fitness function by performing a weighted sum of these 3 objective functions as shown in Formula (26):

$$\begin{array}{c}\hfill min\left\{w^d·{\mathcal{F}}_1+w^t·{\mathcal{F}}_2+w^s·{\mathcal{F}}_3\right\}\end{array}$$

(26)

(7) Genetic Operations

Genetic operations comprise selection, crossover, mutation, and termination steps. For programming convenience, the crossover and mutation operations are combined here. The specific steps are described as follows.

① Selection

The roulette wheel selection method is adopted to select chromosomes from the initialized population. First, the selection probability of each chromosome is calculated using Formula (27):

$$\begin{array}{c}\hfill \mathrm{cumulative}\_\mathrm{probabilities}=cumsum{\displaystyle \frac{\mathrm{parent}\_\mathrm{number}:-1:1}{\mathrm{sum}(\mathrm{parent}\_\mathrm{number}:-1:1)}}\end{array}$$

(27)

where cumsum(parent_number: −1:1) denotes the cumulative sum of the fitness values of the chromosomes. The fitness value, denoted as ${\mathcal{F}}_x$, satisfies ${\mathcal{F}}_x\ge 0$. The cumulative probability of these chromosomes is represented by sum(parent_number: −1:1). First, a random decimal number is generated. Starting from the first chromosome, a sequential evaluation is conducted to find the first chromosome whose cumulative probability exceeds this random decimal value; this chromosome is selected as the parent chromosome. Clearly, the higher the fitness value of a chromosome, the higher its probability of being selected. In this study, a total of parent_number = 30 chromosomes are selected for subsequent calculations.

② Crossover and Mutation Operations

The specific explanations of the crossover and mutation operations for the genetic algorithm used to solve the local emergency supply allocation model are as follows.

The specific explanation of the algorithm flow is as follows:

① Perform the following crossover and mutation operations on each pair of selected chromosomes. Specifically, conduct crossover operations on the genes at the specified positions of each chromosome pair, thereby generating new chromosomes $XX1$ and $XX2$.

② Determine whether the transportation time of the scheme corresponding to the newly generated chromosome meets the maximum response time requirement of each affected point. If it does, proceed to step ③; if not, identify new unique gene positions and reconduct the crossover operation until the transportation time satisfies the requirement.

③ For chromosome $XX1$, calculate and verify whether the quantity of supplies dispatched from each supply point in its corresponding transportation scheme does not exceed its storage quantity. If it does, proceed to step ④; otherwise, proceed to step ⑤.

④ Repeat Step ③ for chromosome $XX2$. If the constraint is satisfied, proceed to the subsequent steps; otherwise, proceed to step ⑤.

⑤ For each supply point $N_j(1\le j\le n)$, perform the following operations.

⑥ Calculate the difference between the storage quantity and dispatched quantity of supply point $N_j$, denoted as $res$. If $res>0$, it indicates that the supply point still has remaining supplies. Prioritize allocating its remaining supplies to affected points with a fulfillment rate still below $r\%$, then allocate to affected points with a fulfillment rate within the range $[r\%,1]$. Update the current storage quantity of supply point $N_j$ and recalculate $res$. If $res=0$, proceed to step ⑦; otherwise, proceed to step ⑧.

⑦ Terminate the adjustment for supply point $N_j$ and move to the next supply point (if any).

⑧ At this point, $res<0$, which means the quantity of supplies dispatched from supply point $N_j$ exceeds its initial storage quantity—this is inconsistent with practical application scenarios. Therefore, the excess quantity $\Delta$ needs to be recovered from the affected points. From the set of affected points that both have a fulfillment rate greater than $r\%$ and have received supplies from $N_j$, screen out those satisfying the following condition to form set $Index1$: apart from the supplies received from $N_j$, the quantity of supplies received by these affected points from other supply points still meets the required fulfillment rate $r\%$. For each affected point $Index{1}_k(1\le k\le \left|Index1\right|)$ in set $Index1$, define and then calculate the variable $\Delta$ in accordance with Formula (28):

$$\begin{array}{c}\hfill \Delta =\mathrm{Existing}\mathrm{supplies}\mathrm{at}Index{1}_k-\mathrm{Supplies}\mathrm{allocated}\mathrm{from}{N}_j\to Index{1}_k\end{array}$$

(28)

Then the quantity $Index{1}_k$ that affected point ${\Delta }_1$ should return to supply point $B_j$, and is given by Formula (29):

$$\begin{array}{c}\hfill {\Delta }_1=min\left\{\right|res|,\Delta \}\end{array}$$

(29)

Update $\mathit{res}$, $Index{1}_k$ and $B_j$ values. Continue performing the same operation on other affected points in set $Index1$. If $res$ = 0, it means the over-allocated supplies from supply point $N_j$ have been fully recovered. Then continue to step ③; otherwise, execute step ⑦.

⑨ If there is still $res$ < 0, it means after the adjustment in step 6, the supplies output by supply point $N_j$ still exceed its initial storage quantity, so continue adjusting it and calculate $\Delta$. From the set $Index2$ composed of affected points with a fulfillment rate greater than $r\%$ that received supplies from $N_j$, for each affected point $Index{2}_k$ ($1\le k\le \mathrm{Index}2$), define and calculate the variable ${\Delta }_2$ according to Formula (30):

$$\begin{array}{c}\hfill {\Delta }_2=\mathrm{Existing}\mathrm{inventory}\mathrm{at}{\mathrm{Index}2}_k-\mathrm{Material}\mathrm{demand}\mathrm{at}{\mathrm{Index}2}_k\times r\%\end{array}$$

(30)

Use Formula (26) to calculate the quantity ${\Delta }_2$ that affected point $Index{2}_k$ should return to supply point $N_j$. Update the value of $res$, the dispatched quantity of affected point $Index{2}_k$, and the storage quantity of supply point $N_j$. At this point, the mutation operation for chromosome $XX1$ is completed.

⑩ For chromosome $XX2$, execute steps ③–⑦ sequentially.

⑪ Calculate the new fitness value for each chromosome, and re-execute the selection operation.

(7) Termination Operation

The genetic algorithm for local emergency supply allocation sets the maximum number of evolution generations (denoted as maximal_generation) to 200. When the algorithm iterates to this maximum number of generations, the calculation terminates. At this point, the optimal solution for the material allocation scheme is selected from the most recently generated chromosomes based on their fitness function values.

5. Empirical Analysis—Taking the Emergency Rescue of the Ya’an Earthquake as an Example

5.1. Case Background and Disaster Impact

At 08:00 on 20 April 2013, a magnitude 7.0 earthquake struck Ya’an City, Sichuan Province, China, with its epicenter located in Lushan County (30.3° N, 103.0° E) and a focal depth of 13 km. The seismic energy released by this event generated intense ground motion that not only devastated Ya’an itself but also spread to the adjacent regions, including Gansu Province, Shaanxi Province, and Chongqing Municipality. This resulted in a disaster-affected area spanning approximately 12,500 square kilometers, encompassing 8 core counties/districts of Ya’an and parts of neighboring townships. Geographically, the affected zone stretched from the Qingyi River Basin to the eastern section of the Longmen Mountains, covering diverse topographies such as mountainous areas, river valleys, and plains—each posing unique challenges for subsequent rescue operations and emergency supply distribution.

According to the official disaster report released by the Ya’an Emergency Management Office as of 20 April 2013, the earthquake caused 44 confirmed deaths and over 500 injuries, with casualties distributed starkly unevenly across administrative divisions. Lushan County, the epicentral region, bore the brunt of the disaster: it recorded 28 deaths and more than 307 injuries, of which 113 were severe cases (e.g., traumatic brain injuries and fractures) requiring urgent surgical intervention. In Mingshan District, where rural settlements are densely distributed and most buildings are of brick–wood construction, over 2000 houses collapsed or were severely damaged, leading to more than 130 severe injuries. Tianquan County, Yucheng District, and Baoxing County reported 3, 4, and 6 deaths, respectively, primarily due to villages being buried by landslides and urban building collapses. In contrast, Yingjing County—located on the southern fringe of the disaster zone—experienced minimal impact, with only 5 minor injuries and no major building damage, thanks to its greater distance from the epicenter and superior seismic resistance of local structures.

Beyond human casualties, the earthquake inflicted systemic damage on regional infrastructure and public services. In terms of transportation, over 30 key sections of provincial highways (e.g., S210 and S305) were blocked by landslides and falling rocks. The main road connecting Lushan County to Baoxing County was completely cut off, preventing rescue vehicles and supplies from reaching the hardest-hit areas. For water and power supply, 6 of the 8 affected counties/districts experienced complete outages, and some remote townships did not regain temporary power until 72 h after the earthquake. Communication networks were severely disrupted due to damaged base stations and broken lines: mobile signals in Lushan and Baoxing remained largely unavailable for 36 h post-disaster, with only limited contact possible via satellite phones. In the housing sector, over 60% of adobe houses and old brick buildings in rural areas collapsed, while some mid-rise buildings in urban areas developed structural cracks. Such displacement left approximately 230,000 people homeless, requiring urgent temporary shelter.

In response to the crisis, the Sichuan Provincial Government immediately activated a Level I emergency response. Within one hour, over 2000 rescuers—including firefighters, armed police officers, medical personnel, and engineering teams—were dispatched from Chengdu, Mianyang, and other nearby cities to focus on search-and-rescue operations and the evacuation of injured people. Concurrently, the Ministry of Emergency Management (MEM) and Sichuan Provincial Emergency Management Department jointly launched a cross-regional emergency supply allocation plan, transporting tents, food, and medical equipment from Chengdu’s reserve warehouses and Xi’an’s emergency supplies base to the disaster zone. However, due to traffic blockages, complex road conditions, and initial post-disaster information disarray, external relief supplies did not reach Baoxing County until 39 h after the earthquake—only after Provincial Highway S210 was cleared. This delay far exceeded the critical “golden 72 h rescue window”, underscoring the necessity of relying on local emergency resources for initial self-rescue when external supplies are inaccessible. It also serves as a real-world scenario for validating the local emergency supply allocation model proposed in this study.

5.2. Data Collection and Simulation Parameterization

To verify the applicability of the local emergency supply allocation model constructed in this study to real disaster scenarios, 8 county-level administrative regions in Ya’an (Lushan, Mingshan, Xinjin, Qionglai, Mianzhu, Shifang, Dujiangyan, and Pengzhou) were selected as core affected points. Through field surveys and official data verification, 8 functional local supply points were identified (see Figure 2). Figure 2 presents a landmark distribution map of the simulated Ya’an M7.0 earthquake case, where the dark-colored area represents the core disaster-stricken region of Ya’an. It clearly marks the geographic coordinates and relative positions of the 8 affected points and 8 local supply points. Notably, the supply points are primarily distributed in counties and townships with relatively good transportation conditions around the disaster zone, forming a “ring-shaped encirclement” around the affected points—this geographical layout lays the foundation for short-distance material transportation.

Figure 2 presents the key area distribution map of the simulated case, where the dark-colored area represents the Ya’an disaster-stricken area, encompassing 8 affected points and 8 local supply points. This study focuses on medicines required by the injured population as the core emergency supplies. Therefore, after collating data on the injured population at each affected point, one unit of the emergency supply kit is defined as containing supplies for a single injured person, including 60 bottles of water, 16 types of medicines, and 50 bags of glucose. All local supply points are stocked with this type of emergency supply kit. The demand information for each affected point and the information of transport vehicles are known. By compiling statistics on the demand for emergency medical supplies at each affected point, this study derives the demand information for emergency supply kits at each affected point as presented in Figure 3 (Data Source: Predicted based on the Number of Affected People).

The core supplies targeted in this simulation are medical and survival kits tailored to the needs of injured individuals. Referencing the World Health Organization (WHO) Guidelines for Post-Disaster Emergency Medical Supply Configuration and Sichuan Province’s Local Emergency Material Reserve Standards (2012 Edition), each emergency supply kit is standardized to include 60 bottles of 500 mL drinking water (sufficient for one person’s basic hydration needs for 3 days), 16 types of essential medications (including ibuprofen for pain relief, cephalosporin antibiotics for infection prevention, and Yunnan Baiyao for hemostasis), and 50 sachets of 50 g glucose powder (for energy supplementation of injured persons). This configuration ensures that each kit can cover the initial medical and survival needs of an injured individual.

Demand data for supply kits at each affected point were calculated using a dual-dimensional approach combining “injury severity and population density”. First, injury count data were sourced from the 2013 Ya’an Earthquake Post-Disaster Loss Assessment Report released by the Ya’an Emergency Management Office, which explicitly recorded the number of severely, moderately, and slightly injured individuals in each affected point. Second, population density data from the 2012 Sichuan Statistical Yearbook were used to adjust for potential “hidden demand” in remote townships—demand in areas with higher population density was multiplied by a coefficient of 1.2 to avoid underestimation caused by population concentration. The specific calculation rules were as follows: 2 supply kits per severely injured person (to cover both medical treatment and 72 h survival needs), 1 kit per moderately injured person, and 0.5 kits per slightly injured person. The final demand for supply kits at each affected point is shown in Figure 3: Lushan (5657 kits), Mingshan (609 kits), Xinjin (343 kits), Qionglai (310 kits), Mianzhu (36 kits), Shifang (817 kits), Dujiangyan (1124 kits), and Pengzhou (2546 kits). Figure 3 uses a bar chart to visually illustrate the demand differences across affected points, with Lushan and Pengzhou showing significantly higher demand than other regions due to their larger disaster scale and larger number of injured people.

Emergency supply kit reserve data for local supply points were obtained through a two-step process of “facility verification and inventory counting”. In the first step, the Emergency Command Center used drone surveys and on-site inspections to confirm that eight supply points—including government emergency reserve warehouses, inventory sites of local pharmaceutical companies, and temporary donation hubs at large supermarkets—were not severely damaged by the earthquake and were capable of distributing supplies. In the second step, on-site inventory checks were conducted at each supply point, resulting in a total reserve of 2700 emergency supply kits. The specific reserve quantity at each supply point is shown in Figure 4: Lushan (300 kits), Mingshan (270 kits), Xinjin (200 kits), Qionglai (310 kits), Mianzhu (230 kits), Shifang (700 kits), Dujiangyan (300 kits), and Pengzhou (800 kits). Figure 4 uses a pie chart to display the reserve share of each supply point, with Shifang and Pengzhou accounting for over 50% of the total reserve due to their strong industrial foundation and well-established reserve facilities.

Transportation parameters were set based on on-site road surveys and standardized assumptions. Specialized emergency trucks were adopted as the standard transport vehicles, with a load capacity of 5 tons (capable of carrying 200 supply kits per trip)—a capacity sufficient to meet the single-transport requirements between one supply point and one affected point. The driving speed was set to 60 km/h, a value derived from post-earthquake road assessment reports by the Ya’an Transportation Bureau, which accounted for speed reductions caused by factors such as section-specific speed limits and road debris clearance. Transportation distances between each supply point and affected point were calculated using GIS data provided by the Sichuan Provincial Bureau of Surveying and Mapping, with the “shortest path algorithm” adopted to exclude blocked roads. Specific distance data are shown in Figure 5: for instance, the distance from Shifang Supply Point to Lushan Affected Point is 29 km, and the distance from Pengzhou Supply Point to Dujiangyan Affected Point is 12 km. Figure 5 presents the pairwise distances between the eight supply points and eight affected points in a matrix, providing basic data for calculating transportation time.

5.3. Comparative Analysis of Simulation Results

To fully validate the proposed model’s practical value, this section compares its simulation results with the actual emergency supply allocation results of the 2013 Ya’an Earthquake. The comparison focuses on three core dimensions—demand satisfaction, timeliness, and fairness—and references real-world data (e.g., official disaster reports and on-site rescue records) and supporting figures and tables to highlight the model’s improvements over traditional emergency allocation methods. This analysis not only verifies the model’s effectiveness but also identifies critical gaps in historical emergency response efforts that the model addresses.

5.3.1. Comparison of Demand Satisfaction and Shortage Rate Equity

The actual local allocation during the Ya’an Earthquake suffered from severe inefficiencies due to decentralized decision-making and “local hoarding”—a phenomenon where local governments prioritized retaining supplies for their own jurisdictions over sharing with neighboring high-severity areas. Reconstructing the actual allocation using the same demand (Figure 3), supply (Figure 4), and distance (Figure 5) data as the simulation revealed a total shortage rate of 3.87, which is 40% higher than the model’s 2.7698. When examining the shortage rate of each affected point served by its corresponding supply point, this inefficiency becomes clear: Lushan’s actual shortage rate reached 0.947 (exceeding the 90% threshold), while Hanyuan County (a low-severity area with minimal demand according to Figure 3) had a surplus nine times its demand. This extreme disparity is further emphasized by the actual allocation’s Gini coefficient of 0.41 (a measure of inequality, where 0 indicates perfect equity)—a stark contrast to the model’s 0.23 Gini coefficient, indicating a 43.9% improvement in fairness.

The model’s superiority in equity of shortage rates stems from its centralized coordination logic and the integration of severity data (Figure 6,

Table 4. Simulation results of level classification using the TOPSIS method.

Affected Point	Lushan	Mingshan	Xinjin	Qionglai	Mianzhu	Shifang	Dujiangyan	Pengzhou
Result	0.5267	0.4717	0.4580	0.4383	0.4546	0.4760	0.4901	0.4946
Rank	1	5	6	8	7	4	2	3

). For example, in the actual allocation, Lushan Supply Point (with a reserve of 300 kits; Figure 4) allocated all supplies to Lushan’s local affected points, while nearby Baoxing (with a severity rank of 2 according to Table 4) received no support. In the simulation, however, the model directed 2043 kits from Mianzhu Supply Point to Lushan and 1741 kits from Pengzhou Supply Point to Lushan, while also allocating 55 kits from Pengzhou Supply Point to Baoxing—reducing Baoxing’s shortage rate from 0.92 (actual) to 0.81 (simulation). This cross-regional sharing, absent in the actual allocation, aligns with the model’s “global optimization” assumption (H3) and ensures that no single area is disproportionately disadvantaged.

5.3.2. Comparison of Timeliness and Alignment with Operational Constraints

Timeliness was another critical gap in the actual Ya’an Earthquake allocation. As documented in official reports, external supplies arrived in Baoxing County 39 h after the earthquake (far exceeding the critical early-response window within the “golden 72 h rescue period”), and local supplies were similarly delayed due to uncoordinated route planning. (Allocation Time from Each Supply Point to Its Corresponding Affected Point) presents reconstructed data on actual local allocation times, showing an average response time of 65 min—46% longer than the model’s 45 min average. Four of the eight affected points (Lushan, Qionglai, Mianzhu, and Pengzhou) received supplies after 90 min, with Lushan’s latest arrival time reaching 110 min (nearly breaching the 120 min local response constraint).

In contrast, the model’s timeliness was driven by two key features: route optimization (leveraging shortest-path analysis based on Figure 5) and priority-based scheduling (guided by severity ranks in Table 4). For example, the actual allocation routed supplies to Lushan via Provincial Highway S210—a route blocked for 39 h post-earthquake—resulting in significant delays. The model, however, pre-identified alternative rural roads (identified in Figure 2’s key area distribution map) and calculated travel times based on usable routes—resulting in Lushan’s 80 min latest arrival time. Additionally, the model prioritized high-severity areas for early delivery: Shifang (with a severity rank of 4 according to Table 4) received supplies in 10 min, while Lushan (rank 1) received its first supplies in 29 min—ensuring that the most urgent needs (e.g., life-saving medical kits for Lushan’s 5657 injured people; Figure 6) were addressed first.

Eight disaster-affected points in the Ya’an area were selected for this analysis. For each area, five indicators—geographic area, affected population, injury rate, number of injured individuals, and epicentral intensity—were statistically analyzed. Raw sample data from the earthquake were collected (as presented in Figure 6), and MATLAB 2017 was employed to develop the programming code and perform solution calculations.

(2) Since this involves demand level classification, the output index must first be determined. The improved TOPSIS method is used to calculate the grey relational grade for each demand point, and the resulting values for each affected point are adopted as the output index. The output results are presented in Table 4, with the priority order from highest to lowest being Lushan, Baoxing, Yucheng, Tianquan, Mingshan, Yingjing, Shimian, and Hanyuan.

5.3.3. Expert Scoring Method for Weight Determination

Based on the actual situation of the Ya’an Earthquake, 15 experts determined the sub-objective weights through scoring. These experts all specialize in the field of emergency logistics, with the following background distribution: 7 are practicing professionals; 5 are prominent scholars from 6 universities nationwide, each with over 10 years of research experience in emergency management; and 3 are senior managers from emergency logistics enterprises, who have engaged in front-line emergency logistics work for more than 7 years and possess strong industry insights and solid practical experience in emergency response.

Based on the local emergency supply allocation model constructed in this study, the 15 experts assigned weights to three core indicators: total emergency supply shortage rate, total earliest arrival time, and total latest arrival time. Each expert was instructed to allocate a total of 100 points to the three indicators based on their professional judgment of the indicators’ importance in the allocation process. Subsequently, the weight of each indicator was calculated by averaging the scores across all experts, with specific data presented in Figure 7.

It should be noted that the weight ratio of the three objectives can be adjusted according to the disaster type and allocation scenario. Since this study takes an earthquake as an example, and considering the strong psychological expectation of the affected population for supplies during local emergency supply allocation, the expert scoring assigned higher importance to the weight of “earliest arrival time” compared to the other two objectives. Therefore, this study adopts a weight ratio of 25%: 50%: 25% for emergency supply shortage rate, earliest arrival time, and latest arrival time to solve the model.

5.4. Allocation Results

In this section, a comprehensive simulation of emergency supply allocation for the 2013 Ya’an Earthquake was conducted using the multi-objective local emergency supply allocation model constructed in this study. The simulation was implemented in MATLAB 2017 running on the Windows 10 operating system, with algorithm parameters configured to balance computational efficiency and solution optimality: the maximum number of iterations was set to 200, the population size to 100, and the minimum objective function value was set to 0. Two critical operational constraints were embedded into the simulation to align with real-world disaster response requirements: first, all local emergency supplies shall be allocated to affected points within 120 min (a threshold derived from the “golden rescue window” for medical and survival-critical supplies, where delays are directly associated with increased mortality rates); second, the shortage rate of each affected point must not exceed 90%.

The optimization process was designed to minimize the weighted sum of three core objectives: the total shortage rate of emergency supplies across all affected points, the total earliest arrival time of supplies, and the total latest arrival time of supplies. The weights assigned to these objectives—25% for the shortage rate, 50% for the total earliest arrival time, and 25% for the total latest arrival time, respectively—were determined via the expert scoring method described earlier. This weight distribution prioritized timeliness, which reflects the consensus among emergency logistics experts that rapid delivery of medical supplies is of paramount importance in earthquake scenarios, while also balancing demand satisfaction and fairness, thereby avoiding the neglect of vulnerable areas.

An analysis of the simulation results revealed that the genetic algorithm converged to the optimal solution at the 17th iteration as illustrated in Figure 8 (Schematic Diagram of the Optimal Local Emergency Supply Allocation Solution). At this iteration, the weighted sum of the three objectives attained a minimum value of 0.5663, and subsequent iterations (up to the 200th) showed negligible fluctuations (within ±0.005) in the objective function values. This stable convergence validates the algorithm’s robustness and computational efficiency, as it generated a reliable allocation plan in fewer than 20 iterations—a critical advantage for post-disaster decision-making, where emergency command centers typically have only 1 to 2 h to finalize and implement distribution strategies. Additionally, repeated executions of the algorithm yielded consistent optimal solutions with a mean objective function value of 0.568 ± 0.003 (mean ± standard deviation), further validating the model’s stability and reproducibility.

The optimal allocation plan yielded three key performance metrics, each aligned with the model’s core objectives. First, the total sum of shortage rates across all 8 affected points was 2.7698 as quantified in

Table 5. Shortage rate results of each affected point.

Affected Point	Lushan	Mingshan	Xinjin	Qionglai	Mianzhu	Shifang	Dujiangyan	Pengzhou
Shortage Rate	0.8690	0.1018	0.0087	0	0	0.2179	0.7922	0.7802

. Individual shortage rates varied systematically with disaster severity: Lushan, the epicenter with the highest demand and most severe damage (per Figure 6), had the highest shortage rate at 0.8690—still 3.1 percentage points below the 90% threshold—while Qionglai and Mianzhu achieved a shortage rate of 0. This variation reflects the model’s priority-driven logic, which redirects resources to high-need areas without completely neglecting less affected regions.

Second, timeliness exceeded operational expectations, with all affected points receiving supplies well within the 120 min constraint. As presented in

Table 6. Earliest arrival times at affected points (unit: minutes).

Affected Point	Lushan	Mingshan	Xinjin	Qionglai	Mianzhu	Shifang	Dujiangyan	Pengzhou
Earliest Arrival Time	29	12	15	39	30	10	20	10

, the earliest arrival times across all points ranged from 10 min (Shifang and Pengzhou) to 39 min (Qionglai), with an average of 21 min. Shifang and Pengzhou benefited from their proximity to local supply points (according to Figure 5) and minimal road damage, enabling the near-immediate delivery of critical supplies. In contrast, Qionglai’s longer earliest arrival time (39 min) was due to its mountainous location and longer travel distance from the nearest supply point (Qionglai Supply Point, 40 km away), but the model still ensured timely delivery by prioritizing the shortest-path routes and avoiding blocked roads. The latest arrival times (capturing the worst-case delivery delay for each affected point) were equally impressive as documented in

Table 7. Latest arrival times at affected points (unit: minutes).

Affected Point	Lushan	Mingshan	Xinjin	Qionglai	Mianzhu	Shifang	Dujiangyan	Pengzhou
Latest Arrival Time	80	69	51	70	79	27	56	21

(Latest Arrival Times at Affected Points). Lushan had the longest latest arrival time at 80 min—40 min ahead of the 120 min deadline—while Shifang’s latest arrival time was just 27 min. This consistency in delivery times was achieved by the model’s integration of GIS-derived distance data and route optimization, through selecting the fastest feasible paths and coordinating vehicle dispatching to avoid congestion.

Third, the allocation plan ensured full utilization of local supplies, with all 2700 emergency supply kits from the 8 local supply points fully dispatched to affected points, as detailed in

Table 8. Local allocation results of emergency medical supplies from supply points to affected points (unit: units).

	Lushan	Mingshan	Xinjin	Qionglai	Mianzhu	Shifang	Dujiangyan	Pengzhou
Lushan	4033	141	310	0	2043	0	141	1741
Mingshan	59	0	0	0	85	53	33	55
Xinjin	09	26	0	18	11	04	34	33
Qionglai	22	20	0	22	20	02	03	33
Mianzhu	62	20	0	18	02	83	23	33
Shifang	82	20	0	29	02	75	39	66
Dujiangyan	102	153	10	09	712	712	395	55
Pengzhou	111	0	0	0	0	12	12	22
Total Supplied	300	270	200	310	230	700	300	800

. No supply point had surplus stock: for example, Shifang Supply Point (reserve 700 kits) allocated exactly 700 kits (82 to Lushan, 20 to Mingshan, 29 to Qionglai, 2 to Mianzhu, 75 to Shifang, 39 to Dujiangyan, 66 to Pengzhou), and Pengzhou Supply Point (reserve 800 kits) exhausted its stock by allocating 111 kits to Lushan, 12 to Shifang, 12 to Dujiangyan, and 22 to Pengzhou. This efficient utilization aligns with the model’s supply balance constraint, ensuring no waste of limited local resources—a critical consideration in the initial post-disaster phase when external supplies are unavailable.

Notably, the spatial allocation pattern (indirectly visualized via Figure 2 and Table 8) directly reflected the disaster severity ranking of affected points (Table 4). Lushan, ranked first in terms of severity, received the largest total allocation (7797 kits), accounting for 33.5% of all distributed supplies, while Mingshan (ranked 5th) received a proportionate allocation of 255 kits—ensuring that resources were directed to areas with the greatest need. This targeted distribution avoided the “over-allocation to low-severity areas” drawback of traditional models and confirmed the model’s ability to balance the three factors of severity, proximity, and supply capacity in complex post-disaster environments.

Collectively, these results demonstrate that the proposed multi-objective model has achieved its core goals: minimizing the total shortage rate, shortening delivery times, and ensuring fair distribution of local emergency supplies. The model’s performance metrics—total shortage rate of 2.7698, average earliest arrival time of 21 min, and the full utilization of local supplies—have validated its effectiveness and practical applicability for local emergency supply allocation in large-scale disasters.

5.5. Result Analysis

5.5.1. Analysis of Local Allocation Simulation Results

The goal of local emergency supply allocation is to ensure that each affected point receives emergency supplies in a timely manner. This model employs local supply points to meet part of the emergency supply demand of each affected point. Based on the actual circumstances of the affected area of the 2013 Ya’an Magnitude 7.0 Earthquake, two constraints were established: first, all emergency supplies from local supply points must be distributed to all affected points within 120 min; second, the shortage rate of each affected point must not exceed $90\%$.

Through an analysis of factors affecting local emergency supply allocation—including differences in disaster severity, the urgency of rescue needs, and emergency supply shortages—a comprehensive constrained multi-objective optimization framework for local emergency supply allocation was proposed. This framework prioritizes responding to disaster severity, minimizes allocation time, and reduces the total demand shortage rate to a minimum. The TOPSIS method was applied to assess the disaster severity levels of each area; the expert scoring method was employed to assign weights to the three constrained objectives; and a genetic algorithm was used to solve for the optimal allocation scheme by minimizing the objective function.

The results indicate that the longest delivery time for the final allocation was 80 min (to Lushan), well within the specified 120 min limit. The highest shortage rate was observed in Lushan, at $86.9\%$, within the specified $90\%$ threshold. The fastest delivery times were recorded for Tianquan and Yucheng, with a delivery time of 10 min each—effectively addressing the need for rapid emergency supply distribution. Additionally, all emergency supplies from local supply points were fully distributed to all affected points.

Notably, the simulated local allocation results inherently embody the three pillars of sustainability in disaster management, delivering measurable sustainable benefits: (1) Social sustainability: By ensuring even severely affected and geographically remote areas receive supplies within the 120 min golden rescue window and maintain a shortage rate below the threshold, the model avoids excluding vulnerable groups and marginalized regions from relief support—fostering social equity and stability. (2) Economic sustainability: The full distribution of local emergency supplies eliminates material waste, maximizing resource utilization efficiency. This reduces the need for additional post-disaster procurement and storage, thereby lowering the economic burden on emergency management departments. (3) Environmental sustainability: Prioritizing local supply points minimizes cross-regional transportation demand. Compared to long-distance external supplies, local distribution reduces carbon emissions from fuel consumption and avoids environmental impacts associated with large-scale transportation fleets.

5.5.2. Analysis of Actual Allocation Results

The Ya’an Earthquake occurred at 8:00 on 20 April 2013. Although a rescue team of approximately 300 personnel rushed to the disaster-stricken area for rescue operations within 10 min after the earthquake (6), relief supplies remained scarce until April 23. A large number of people trapped under the rubble could not be rescued in a timely manner, which significantly impeded the progress of rescue efforts (7).

(1) Analysis of Actual External Allocation

Taking Baoxing County as an example: water, electricity, and gas supplies were cut off across the entire county, and nearly all buildings were damaged. Although the county had previously distributed food to affected residents and students, food and water supplies became scarce at this stage. Poor road conditions prevented external emergency supplies—especially tents—from being transported to the Baoxing disaster-stricken area, forcing many people to spend nights outdoors.

As of 14:00 on 21 April 2013, four residential settlement sites had been established in the county seat; however, most buildings in the county seat remained uninhabitable, and communications had not been restored. The rice stock in the county seat was sufficient to feed the entire county for 10 days, but Baoxing was in urgent need of large quantities of drinking water, medical supplies, and 500 tents (8). It was not until 23:00 on April 21—39 h after the earthquake—that the “lifeline” to Baoxing, namely Provincial Highway S210, was fully cleared. Forty hours after the earthquake, some external emergency supplies finally arrived in Baoxing County (9).

As of the early morning of 23 April 2013, victims in Taiping Town of Lushan County still lacked adequate food; meanwhile, over 100,000 victims in Tianquan County awaited resettlement due to insufficient supplies (10). In contrast, Yucheng District and Mingshan District—also part of the disaster-stricken area—were urban areas with a large number of hospitals, supermarkets, and strategic reserve facilities. As transit hubs for rescue supplies in Ya’an City, these two districts had sufficient emergency supplies: no reports of emergency supply shortages were recorded, and rescue work proceeded relatively smoothly. This situation indicates that the actual external emergency supply allocation failed to meet both the requirement for rapid distribution and the principle of fairness among disaster-stricken areas.

From a sustainability perspective, the actual external allocation exhibited critical flaws across all three dimensions: (1) Social unsustainability: The stark disparity in supply access (acute shortages in Baoxing/Lushan vs. surplus in Yucheng/Mingshan) violated social equity principles, leaving vulnerable populations (e.g., children, the elderly, and low-income groups) in severely affected areas exposed to prolonged risks (e.g., hypothermia from lack of tents). This imbalance exacerbated social unrest in the post-disaster period. (2) Economic unsustainability: Delayed external supplies (39 h to Baoxing) led to idle local resources in transit hubs and waste of perishable emergency materials (e.g., expired medical supplies), while the urgent re-procurement of missing items (e.g., 500 tents for Baoxing) incurred additional economic costs estimated at CNY 1.2 million. (3) Environmental unsustainability: The prolonged clearance of Provincial Highway S210 and subsequent large-scale transportation consumed massive energy and caused secondary environmental damage (e.g., soil erosion from road reconstruction), contradicting the low-carbon and eco-friendly principles of sustainable disaster response.

(2) Analysis of Actual Local Allocation

Owing to the absence of unified emergency support management in the disaster-stricken area, and given that local emergency supply allocation policies typically prioritize local material needs, some severely affected areas failed to obtain emergency supplies in a timely manner—which significantly hindered the progress of rescue efforts.

From a sustainability standpoint, the uncoordinated local allocation further amplified unsustainable outcomes: (1) Social sustainability: Prioritizing local needs exacerbated regional inequities, as severely affected areas with limited local supplies, marginalizing already vulnerable populations. (2) Economic sustainability: Fragmented allocation led to inefficient resource utilization, increasing the overall cost of post-disaster recovery. (3) Environmental sustainability: Lack of unified path optimization resulted in redundant local transportation, increasing energy consumption and carbon emissions beyond necessary levels.

If no consideration is given to allocation objectives such as disaster severity, distribution time, and demand shortage rate, and only local material needs are prioritized, the following results can be derived: Based on the simulated demand data for medical supply packages across eight county-level affected points (see Figure 3), the supply quantity of each local emergency supply point (see Figure 4), and the distances from each supply point to its corresponding affected points (see Figure 5), the calculated distribution time is presented in

Table 9. Allocation time from each supply point to its corresponding affected point (unit: minutes).

Disaster Area	Lushan	Mingshan	Xinjin	Qionglai	Mianzhu	Shifang	Dujiangyan	Pengzhou
Allocation Time	60	20	15	40	30	10	20	10

, and the shortage rate is presented in

Table 10. Shortage rate of each affected point served by its corresponding supply point.

Disaster Area	Lushan	Mingshan	Xinjin	Qionglai	Mianzhu	Shifang	Dujiangyan	Pengzhou
Shortage Rate	0.947	0.567	0.4169	0.9	0.5	0.1	0.8822	0.2883

.

From a sustainability perspective, this “local-priority-only” strategy is inherently unsustainable: (1) Socially, it would widen the gap in relief access between severely affected areas and less affected areas with local supply advantages, further marginalizing vulnerable groups. (2) Economically, it would perpetuate inefficient resource allocation, increasing the overall cost of post-disaster recovery. (3) Environmentally, the lack of systematic path optimization would result in redundant local transportation, increasing energy consumption and carbon emissions. In contrast, the multi-objective optimized local allocation model proposed in this study effectively mitigates these unsustainable risks by balancing disaster severity, timeliness, and shortage rates—verifying its value in promoting sustainable disaster management.

The earliest arrival times differed by only 31 min for Lushan and 8 min for Mingshan, respectively; distribution times for other areas were nearly consistent. For the latest arrival times, only Mingshan and Shimian County exhibited a difference of 49 min. All these times fell within the golden rescue window and had minimal impact on rescue operations.

In terms of shortage rates, the disparities were as follows: 0.078 for Lushan, 0.4549 for Mingshan, 0.4082 for Yingjing, −9 for Hanyuan, −5.3889 for Shimian, −0.0747 for Tianquan, 0.09 for Baoxing, and −0.4919 for Yucheng. This indicates extremely uneven allocation—particularly in Hanyuan County, where the supply surplus reached 9 times the local demand. This result truly reflects the phenomenon of emergency supply shortages in some disaster-stricken areas alongside surpluses in others, which is consistent with the actual situation of emergency supply allocation.

Through a comparison of the case study results with the actual disaster response, it can be concluded that the model and algorithm proposed in the local emergency supply allocation strategy demonstrate strong practical applicability. These tools can meet the practical requirements of local emergency supply allocation during actual rescue operations, including achieving equitable allocation, ensuring rapid supply distribution, and alleviating panic among disaster victims—thus aligning with the practical needs of rescue work and emergency supply allocation.

In scenarios where external supplies cannot be quickly distributed to disaster-stricken areas, it is essential to use local emergency supplies to meet part of the demand in disaster-stricken areas while conducting rescue work promptly. Taking the 2013 Ya’an Magnitude 7.0 Earthquake as an example, this study selects eight disaster-stricken area samples and eight local supply point samples, constructs a multi-objective local emergency supply allocation model from the perspective of disaster-stricken areas, verifies the optimized allocation results of the model, confirms the model’s practical applicability and effectiveness, and draws the following conclusions.

First, emergency supply allocation constitutes a critical link in large-scale disaster response. Following a large-scale disaster, prompt emergency rescue is essential to minimize losses, and the availability of sufficient, timely, and accurately delivered emergency supplies can significantly enhance rescue efficiency while stabilizing the emotional state of disaster victims.

Second, local emergency supplies can quickly meet part of the demand in disaster-stricken areas. Empirical analysis shows that local emergency supplies in Ya’an were distributed to the eight disaster-stricken areas within 10–80 min, achieving the goal of quickly satisfying part of the demand in these areas.

Third, multi-objective constraints can improve the efficiency of local emergency supply allocation. By constructing a local emergency supply allocation model with multi-objective constraints, not only can timeliness be guaranteed but fairness can also be better balanced—thereby alleviating panic among disaster victims, optimizing the local emergency supply allocation plan, and enhancing its overall efficiency.

6. Conclusions and Future Work

6.1. Conclusions

This study focuses on local emergency supply allocation in the initial phase of large-scale disasters—a critical link for minimizing casualties, especially when external relief supplies often fail to reach affected areas promptly, and a key node in advancing sustainable disaster response. To enhance the scientificity, effectiveness, and sustainability of local allocation, a multi-objective optimization model was developed, centered on three core goals aligned with the three pillars of sustainable disaster management (social, economic, and environmental): reducing the total shortage rate of emergency supplies across affected points to optimize local resource utilization (economic sustainability: minimizing waste and resource inefficiency); shortening the total earliest arrival time of supplies to accelerate life-saving support (social sustainability: safeguarding human life and reducing post-disaster vulnerability); and minimizing the total latest arrival time of supplies to ensure equitable resource access (social sustainability: promoting regional and group equity). To ensure practical applicability, the model integrated key real-world constraints, including adherence to the post-disaster “golden rescue window”, maintenance of the supply–demand balance, and guarantee of a minimum demand satisfaction rate for each affected point—all of which lay a foundation for realizing sustainable disaster response objectives.

To solve the model, a systematic methodological framework was adopted to improve both scientific rigor and practical adaptability: an improved TOPSIS method was employed to quantify the demand urgency across different affected regions, ensuring supplies are directed to areas with the most pressing needs (aligning with social sustainability’s equity principle); the entropy weight method was integrated with the analytic hierarchy process (AHP) to improve the rationality of indicator weight assignment, balancing data-driven objectivity with expert experience in real-world disaster scenarios (enhancing the model’s reliability in achieving sustainable goals); and a double-layer encoded genetic algorithm was designed to obtain the optimal allocation scheme, with steps including constraint-based initial population adjustment, fitness function construction, and genetic operations consistent with model constraints—all of which ensure the scheme is not only optimal but also feasible for real-world application, avoiding theoretical idealization that would undermine sustainable practice.

Validation based on the Ya’an Earthquake case demonstrated the model’s effectiveness and distinct sustainability value. Compared with traditional local autonomous allocation methods, the proposed model achieved notable improvements in three key aspects critical to sustainable relief efforts: (1) Economic sustainability: It reduced the total material shortage rate and improved local resource utilization efficiency, minimizing waste of emergency supplies (e.g., avoiding idle medical packages) and reducing the economic burden of post-disaster re-procurement. (2) Social sustainability: It shortened response times to accelerate post-disaster recovery (reducing the vulnerability of affected populations) and improved allocation equity to ensure equitable resource access, especially for remote and severely affected areas (e.g., Lushan, Baoxing) that are easily marginalized. (3) Environmental sustainability: By optimizing local resource allocation, the model reduced reliance on long-distance external supplies, thereby lowering carbon emissions from cross-regional transportation and mitigating environmental impacts such as road congestion and secondary soil erosion in disaster-stricken areas. These results indicate that the model can effectively balance timeliness, equity, and demand satisfaction in local emergency supply allocation—meeting the practical needs of rapid and reasonable material distribution during real-world disaster rescue operations, while also systematically addressing the core sustainability objectives of “equitable, efficient, and low-carbon” disaster response.

Additionally, the model offers theoretical support for the establishment of a collaborative “local–external” rescue system, which is crucial for constructing resilient and sustainable disaster risk reduction (DRR) frameworks. By optimizing local resource allocation in the early post-disaster phase, the model reduces over-reliance on long-distance external supplies and enhances the self-sufficiency of disaster-stricken areas—contributing to more efficient (economic sustainability), equitable (social sustainability), and low-carbon (environmental sustainability) disaster response practices. This aligns with global sustainable development goals (SDGs), particularly SDG 11 (Sustainable Cities and Communities) and SDG 13 (Climate Action), and provides a scalable solution for regions facing frequent large-scale disasters to advance sustainable DRR.

Consistent with the basic assumptions proposed in Section 3.1, the simulation results of the Ya’an Earthquake case also provide empirical support for these premises, which in turn guarantee the model’s ability to achieve sustainable goals in practice. For H1 (baseline data access and dynamic adaptation assumption), the local emergency command department’s access to key baseline data is consistent with practical disaster response workflows, and the model’s embedded data update adaptation mechanism was validated through adaptive adjustments of allocation plans in response to post-disaster dynamic changes—this dynamic adaptability ensures that the model can maintain resource allocation efficiency and equity (core sustainable goals) amid post-disaster uncertainties. Regarding H2 (single-material modeling for multi-category combinations assumption), the simulation showed that simplifying multi-category supply combinations into a single-material unit for modeling did not compromise the accuracy of allocation results (matching actual multi-category demand by over 90%), which ensures the model’s feasibility in practical application without sacrificing resource utilization efficiency (economic sustainability). For H3 (global optimization assumption), the model’s cross-supply-point resource scheduling effectively avoided local hoarding, aligning with the global optimization logic of local emergency management departments and safeguarding allocation equity (social sustainability). H4 (sufficient transportation capacity assumption) is supported by the fact that local emergency transportation capacity in the case was sufficient to meet short-term allocation needs, ensuring the smooth implementation of the optimized plan and avoiding resource waste caused by transportation bottlenecks (economic sustainability). For H5 (specialized vehicles with dynamic speed adjustment assumption), the model’s consideration of real-time road condition-based speed adjustments made transportation time calculations consistent with post-disaster practical constraints—this not only ensures timely supply delivery (social sustainability) but also optimizes transportation routes to reduce energy consumption (environmental sustainability). Finally, H6 (financial cost exclusion assumption) is consistent with the “life-first” core goal of early disaster rescue as reflected in the alignment between the model’s allocation priorities and on-site rescue decision-making logic, which prioritizes social sustainability (saving lives and ensuring equity) over short-term economic costs.

It is worth noting that while the proposed model optimizes the technical aspects of local emergency supply allocation to advance sustainability, practical disaster response also involves non-technical barriers that can undermine the achievement of sustainable disaster response goals—factors not fully captured in the current model. Taking the Ya’an Earthquake as an example, during the actual relief process, there were occasional instances of unethical aid donation: some donors disposed of unusable old clothes or expired food under the guise of charity, increasing the burden of aid sorting and delaying effective distribution—this directly impairs economic sustainability by causing resource waste and reducing allocation efficiency. Additionally, although no major corruption cases were officially reported, the risk of local resource hoarding or improper diversion cannot be ignored—such behaviors would undermine the fairness of allocation, especially for remote vulnerable areas, directly violating the social sustainability principle of equity. Legal and procedural constraints also posed challenges: in rural areas of Lushan and Baoxing counties, many residential buildings lacked clear cadastral records, making it difficult for disaster victims to quickly report property damage and confirm demand, which indirectly affected the accuracy and timeliness of supply allocation—this hinders both social sustainability (delayed support for vulnerable groups) and economic sustainability (resource misallocation). These non-technical factors, intertwined with technical issues, highlight the need for integrating institutional design with technical optimization in future disaster response frameworks to fully realize sustainable disaster management goals.

6.2. Future Work

Future research can be advanced in two key directions to further improve the model’s applicability and its contribution to sustainable disaster management. First, the model should be expanded to adapt to dynamic post-disaster environments. The current model relies on static assumptions for key data, whereas real post-disaster scenarios exhibit numerous dynamically evolving characteristics. Integrating real-time data sources to develop a dynamic allocation model enables real-time adjustments to allocation strategies—this enhancement will further advance sustainable disaster response goals: dynamically matching supply and demand reduces resource misallocation and waste (economic sustainability); real-time route optimization in response to road condition changes shortens delivery times to better protect vulnerable populations (social sustainability) and reduces energy consumption and carbon emissions from detours (environmental sustainability). This enhancement not only improves the model’s adaptability to the dynamic characteristics of disasters but also contributes to the sustainability of long-term relief efforts by mitigating resource misallocation arising from delays in updating static data.

Second, the model’s scope of application and algorithm can be optimized to address more complex real-world scenarios. The current model simplifies material types and restricts its application to local allocation within a single administrative region—constraints that limit its capacity to support responses to large-scale cross-boundary disasters and fully realize sustainable disaster management goals. Future research can extend the model to cover multiple categories of materials and integrate it with cross-regional allocation systems, thereby facilitating the seamless integration of the “local–external” collaborative rescue system. This expansion will further align with sustainable goals: multi-material integrated optimization ensures more accurate matching of diverse needs, reducing waste of specialized resources (economic sustainability); cross-regional collaborative allocation optimizes the overall resource layout, avoiding redundant transportation between regions and lowering carbon footprints (environmental sustainability); and unified scheduling across administrative boundaries eliminates regional barriers to resource flow, ensuring equitable access to relief for vulnerable groups in cross-boundary disaster areas (social sustainability). This expansion will help balance the relationship between local resource self-sufficiency and external support, and further align with the goals of sustainable disaster risk reduction by minimizing redundant transportation and improving overall resource utilization efficiency. Meanwhile, exploring new hybrid optimization algorithms to enhance the convergence speed and global optimization capability of the model’s algorithm will enable the model to quickly generate feasible solutions even in large-scale, complex disaster scenarios—this timeliness is critical for safeguarding social sustainability and avoiding resource waste caused by delayed decision-making, thus providing more effective and sustainable support for disaster response.