https://orcid.org/0009-0009-7999-8451
Figures
Abstract
Emergency dispatching and rescue during emergencies have become a hot research topic in the field of transportation planning. Therefore, to address the low efficiency of cross-regional police emergency dispatch, the study carries out relevant exploration on the basis of emergency event level analysis and transportation planning. The emergency rescue demand evaluation system is constructed using the superior and inferior solution distance method to carry out the emergency hierarchy analysis. The police emergency dispatch model is constructed and solved using the improved particle swarm algorithm. The validation revealed that the improved solution algorithm improved the iteration efficiency by 54.33% on average and reduced the iteration time overhead by 56.10% on average over the particle swarm algorithm and the beetle antennae search algorithm. In the scheduling of emergency 1, the material demand satisfaction rate of all demand points was above 80%, among which the vegetable material demand satisfaction rate was 100%. In the scheduling of emergency 2, the demand for supplies at all demand points was above 91.3%, with the demand satisfaction rate for tent supplies as high as 100%. The above results indicate that the police emergency dispatch method can leverage the full advantages of transportation networks. By integrating intelligent optimization algorithms with artificial intelligence technology, the method achieves material dispatch for cross-regional emergency rescue incidents. This method is both feasible and practical.
Citation: Qiao S, Xu P (2026) Police emergency dispatch model based on emergency level analysis and traffic planning. PLoS One 21(7): e0348072. https://doi.org/10.1371/journal.pone.0348072
Editor: Nik Hisamuddin Nik Ab. Rahman, Universiti Sains Malaysia, MALAYSIA
Received: October 24, 2025; Accepted: April 11, 2026; Published: July 27, 2026
Copyright: © 2026 Qiao, Xu. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Data Availability: All relevant data are within the manuscript and its Supporting information files.
Funding: The author(s) received no specific funding for this work.
Competing interests: The authors have declared that no competing interests exist.
1. Introduction
In recent years, the increasing integration of urban transportation and the intensification of cross-regional socioeconomic activities have made emergency incidents one of the primary threats to public safety and social stability. Emergencies are typically characterized by suddenness, urgency, randomness, destructiveness, and unpredictability. Moreover, once they occur, they often affect multiple administrative regions, requiring rapid and coordinated responses across departments and regions [1]. However, in practice, cross-regional Police Emergency Dispatch (PED) still faces operational bottlenecks and challenges. First, border handoff procedures often constrain the dispatch of vehicles and personnel across administrative boundaries. Convoys must wait or undergo re-coordination at regional checkpoints, which leads to significant delays in response time [2]. Second, the limited number of frontline escort personnel and transport vehicles makes it difficult to achieve rapid and flexible resource allocation when multiple high-priority missions occur simultaneously. In addition, the absence of unified information portals and standardized interfaces between regions hinders real-time data sharing and diminishes the effectiveness of cross-regional coordination. More critically, differences in priority classification and resource allocation rules among jurisdictions result in inconsistent and fragmented emergency resource distribution, which may lead to unmet demands and the loss of optimal rescue opportunities. These issues directly undermine the timeliness and efficiency of emergency response. Moreover, existing dispatch strategies are usually reactive and lack a unified framework for evaluating priorities and a coordinated, multimodal scheduling mechanism.
The objective of this study is to develop and validate a cross-regional PED model that utilizes Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS)-based priorities for routing and allocation via Improved Particle Swarm Optimization (IPSO) to minimize weighted response time and unmet demand. This approach is intended to address the identified problems. The proposed model has clear practical applications, with intended users including Emergency Operation Centers (EOCs), police logistics divisions, and transportation authorities. The PED model enhances the coordination and dispatch efficiency of cross-regional escort convoys by dynamically ranking and scheduling emergency priorities. It also reduces border handoff delays, improves Emergency Supply (ES) satisfaction rates, and optimizes the integrated use of air, rail, and road transportation modes, thereby improving overall response efficiency. These improvements are expected to be reflected in Key Performance Indicators (KPIs) such as average response time, demand satisfaction rate, and total rescue transportation cost.
The remaining parts of the research are organized as follows. The Literature Review Section reviews related studies and highlights the contributions of this work. The Methods and Materials Section presents the Emergency Level Analysis (ELA) method, the PED model framework, and the improved IPSO algorithm. The Results Section reports the results of scenario-based validation. The Discussion and Conclusion Section concludes the research and outlines future research directions.
2 Literature review
2.1 Concepts and variables
Emergency dispatch research typically involves several core components. Supply Points (SP) represent the origin of emergency materials, Collector-Distributor Points (CDP) act as transfer hubs, and Demand Points (DPs) represent affected areas. ES refers to materials distributed during emergencies. Decision variables typically describe allocation quantities and transportation flows. KPIs, on the other hand, include response time, supply satisfaction rate, and transportation cost.
2.2 Theoretical linkages
Most studies follow a similar theoretical framework in which disaster severity indicators (e.g., casualty levels, infrastructure damage, and material shortages) are assessed first to determine urgency levels. These levels are mapped into priority rankings for dispatch planning. These priority levels guide optimization models that balance efficiency (timeliness and cost) with equity (minimum service guarantees for each DP).
2.3 Typical calculation pipelines and algorithm development
Previous studies have developed various approaches to improve emergency Dispatch Models (DMs). In the field of urgent evaluation and DM, Liu and Qian [3] proposed a multi-objective Emergency Services (ESs) distribution model. They did so by specifying objective functions and vehicle constraints. Kergosien et al. [4] applied discrete event simulation to optimize ambulance fleet scheduling. Ding et al. [5] addressed multi-point ES scheduling using interval grey numbers and Genetic Algorithms (GAs). Zhang et al. [6] introduced entropy weight (EW) and dynamic PSO to optimize emergency medical supply distribution. For algorithmic optimization, Wang et al. [7] presented an adaptive weighted differential evolutionary algorithm to improve dispatch global optimality. Yuan and Wang [8] applied super network theory and projection algorithms for chemical park emergencies. Chen et al. [9] used spatiotemporal transformer networks for dynamic prediction regarding advanced artificial intelligence and learning-based methods. Shaik et al. [10] adopted multi-agent reinforcement learning for real-time monitoring. Li et al. [11] proposed ReinforceRouting to handle real-time route changes during disasters.
These studies commonly use Analytic Hierarchy Process-TOPSIS (AHP-TOPSIS), CRiteria Importance Through Intercriteria Correlation-TOPSIS (CRITIC-TOPSIS), or VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) for urgency assessment [12,13]. They usually use normalization and closeness coefficients to quantify severity levels, as well as metaheuristics or deep learning methods to improve optimization and real-time decision-making. In general, existing research mainly focuses on prioritizing emergncy needs through multi-indicator decision-making methods and improving resource scheduling efficiency using optimization algorithms. However, most of this research concentrates on emergency resource scheduling problems in single-region or localized disaster scenarios, typically assuming that supply nodes, transit nodes, and demand nodes are located within the same administrative region and coordinated by a unified scheduling entity. Research on emergency scheduling problems involving coordination across multiple administrative regions, complex transportation networks, and cross-regional resource allocation remains relatively limited.
2.4 Research gap and contributions
Although existing research offers valuable insights into emergency dispatching, most studies are confined to a single region. Cross-regional scheduling is still in the conceptual stage. Quantitative modeling and algorithmic optimization for large-scale, multi-node, multi-modal networks are still scarce. Moreover, priority mapping mechanisms between urgency evaluation and dispatch are often absent or simplistic. This study closes these gaps by combining TOPSIS-based ELA and an enhanced IPSO algorithm to develop a cross-regional PED model. The study focuses on enhancing scheduling efficiency and rescue effectiveness within multi-regional, multi-modal transportation networks.
3 Methods and materials
The study first conducts an ELA and uses TOPSIS to build an analytical model to estimate the urgency of the rescue demand, to address the low PED efficiency for cross-regional transportation in emergency situations. On this basis, PED model construction for cross-regional TP is carried out, and the PSO algorithm is improved to solve the model using IPSO algorithm.
The data used in this study are obtained from publicly available sources or authorized emergency drill materials. They do not contain personal privacy or sensitive information and have been anonymized and desensitized. The data complies with scientific research ethics and relevant management requirements. No human subjects or animal experiments are involved, and no additional ethical approval is required.
3.1 Modeling and operational assumptions
To ensure the model’s solubility and computational efficiency, as well as its alignment with the operational mechanisms of cross-regional emergency dispatch, several basic assumptions are made during the construction and simulation processes, as illustrated in Fig 1.
The model assumes that: (1) the transportation network structure remains static; (2) travel time between nodes is deterministic; (3) emergency supplies at each supply point satisfy the minimum demand; (4) scheduling is completed within a single planning period; (5) emergency levels remain unchanged after analysis; and (6) multiple transportation modes are available with fixed capacities and costs. SP denotes supply point.
In Fig 1, the assumption of a static transport network structure provides a stable optimization foundation for the overall model framework and path planning. The assumption of deterministic transport time is reflected in parameter setting and scheduling optimization. The assumption of sufficient material reserves at SPs is used in constraint modeling to prevent shortages from interfering with the scheduling process. Single-planning-cycle scheduling is assumed in model solving and simulation. A fixed urgency level is assumed throughout the ELA and priority mapping process. Furthermore, the assumption of multiple transport modes available with fixed capacities and costs supports transport mode selection and resource allocation, enabling the coordinated optimization of multiple transport modes.
3.2 TOPSIS-based emergency level analysis
In cross-regional emergency rescue, the imbalance between the DPs and rescue supplies leads to low rescue efficiency [14]. To maximize the effectiveness of rescue, the study firstly conducted ELA. In the context of emergency rescue occurrence, information communication and transportation are the key facilities for rescue. Therefore, the study mainly focuses on the related departments to conduct ELA. The specific process is shown in Fig 2.
Disaster cases are analyzed to estimate emergency material demand and support allocation from supply points to demand points. SP and DP denote supply point and demand point, respectively.
In Fig 2, denotes the SP.
denotes the DP. The overall analysis process of this study includes data collection and processing, ELA, priority mapping, DM construction, solver configuration with baseline settings, and result validation. Among these steps, ELA serves as the core component for achieving cross-regional emergency dispatch by comprehensively assessing the urgency level of DPs through multiple indicators. The determination of urgency is mainly based on the material shortage at the rescue site, the number of casualties and the proportion of the affected population, as well as the economic losses caused to social production activities. Material shortages are the key factor driving cross-regional rescue. Casualties directly reflect the threat emergencies pose to human life and safety. The impact on social production represents the disruption to economic activities [15]. Meanwhile, the study mainly assesses the social production functioning from two levels: transportation and business transit. Therefore, the evaluation system of rescue demand level under emergency is shown in Fig 3.
The system includes material gaps, personnel casualties, and socio-productive impacts, evaluated using deterministic and fuzzy indicators.
From Fig 3, the study divides the hierarchical evaluation system into two levels. The first-level indicators are the material demand gap, human casualties and the impact on social production, as proposed earlier. The material shortage rate is the second-level indicator that corresponds to the gap in the material demand, and the number of injuries, deaths, and the ratio of the affected population to the total population comprise the second-level indicator that corresponds to the casualty situation. The secondary indicators corresponding to the first-level indicator of social production impact are transportation impact and enterprise impact. Traffic impact and enterprise impact are fuzzy indicators, and the study introduces Triangular Fuzzy Number (TFN) to calculate them. TFN offers significant advantages when it comes to handling ambiguity and uncertainty. It can accurately represent data that is difficult to characterize with exact numerical values. Its membership function adopts a commonly used standard form, as shown in Equation (1) [16].
In Equation (1), denotes a fuzzy number.
denotes an evaluation index.
denotes the affiliation function of fuzzy number
.
,
and
denote the most pessimistic, probable and optimistic number, respectively. When the three are equal, the fuzzy number
is real. In the TFN, the degree of impact of transportation and business is categorized into five linguistic variables, namely, “very severe”, “severe”, “fair”, “mild”, and “very mild”. The five linguistic variables correspond to the TFN numbers (0.7,1.0,1.0), (0.5,0.7,0.9), (0.3,0.5,0.7), (0.1,0.3,0.5), and (0.0,0.0,0.3), respectively. This study uses the TFN values of five linguistic variables to parameterize the corresponding variable weights at their maximum possible values. The method estimates the most probable value from the observations, as shown in Equation (2) [17].
In Equation (2), ,
, and
denote the weights corresponding to TFN numbers
,
, and
, respectively. The five linguistic variable weights are further derived from Equation (2) as 0.95, 0.7, 0.5, 0.3, and 0.05, respectively. Multiple attribute decision-making studies have clearly identified language variables and their TFN weights [18]. These values are widely applicable in contexts such as disaster management and emergency logistics. The study also assesses the impact on transportation and commerce. The same classification system is highly appropriate. The study introduces the TOPSIS method of ELA to construct a rescue demand level analysis model. ELA and TOPSIS can achieve efficient and transparent urgency quantification and priority sorting using multiple indicators [19,20]. In the cross-regional emergency rescue evaluation process, the first relevant rescue strategy is made by the relevant organizations such as the emergency department in the event of emergencies to the urgency of the rescue needs of the affected location. Therefore, the initial rescue decision matrix expression is shown in Equation (3).
In Equation (3), denotes the initial decision matrix.
denotes the fuzzy number of qualitative indicators.
denotes the material DPs, and
denotes the evaluation indicators. The qualitative indicators are processed using TFN to further obtain a clear
. Meanwhile,
is normalized, and the final
is updated, as shown in Equation (4).
In Equation (4), denotes
after normalization,
denotes fuzzy number after normalization, and
. The study calculates each afflicted point’s objective weight using the EW approach since the disaster information that each DP transmits during an emergency is unique, as shown in Equation (5).
In Equation (5), is the contribution of the
th indicator to the
th DP, where
,
.
is the information entropy of the
th indicator.
is the weight of the
th indicator. Simultaneously, the EW approach and hierarchical analysis are combined to calculate the overall weight of the indicators, as shown in Equation (6).
In Equation (6), is the combined weight of the
th indicator.
is the preference coefficient, calculated using the analytic hierarchy process. The study draws on existing research experience in the field of emergency dispatch and sets it at 0.5 [21,22]. According to the determined weights of each influencing factor in the decision-making judgment, the weighted normalization matrix can be further obtained, as shown in Equation (7).
In Equation (7), denotes the weighted normalization matrix and
denotes the reference sample vector. The maximum and minimum values in the reference sample constitute the positive and negative ideal solutions of the evaluation indexes. The specific expression is shown in Equation (8).
In Equation (8), and
denote the positive and negative ideal solutions, respectively. On this basis, the matrix of Gray Correlation Coefficient (GCC) is calculated using gray correlation theory to calculate the GCC and correlation degree of DPs and positive ideal solutions. In this case, the matrix of GCC expression is shown in Equation (9).
In Equation (9), represents the matrix of strength and closeness coefficients used to quantitatively describe and compare the relationship between factors in one system or between two systems.
denotes the coefficient of strength and closeness used to quantitatively describe and compare the relationship between factors in one system or between two systems. The formula for calculating
and correlation between a DP and the corresponding indicator is shown in Equation (10).
In Equation (10), is the GCC of the
th indicator.
is the positive ideal gray correlation.
is the resolution coefficient, which takes the value of 0.5. The relative closeness of the gray correlation of the DP is shown in Equation (11).
In Equation (11), denotes the relative closeness of the gray correlation.
denotes negative ideal gray correlation. The implementation steps of ELA based on the TOPSIS method are shown in Table 1.
3.3. PED model based on emergency level analysis and transportation planning
Based on the ELA approach in the previous section, the study further combines TP for PED model construction. PED model is an optimisation framework for the allocation of police resources in emergency situations. The model comprehensively considers the urgency level of the incident, traffic conditions in the target area, and resource availability to construct a dispatch priority function, and on this basis, it realises resource path optimisation and minimisation of response time. The PED model is designed by leveraging artificial intelligence technology. Transportation and distribution of materials are the key aspects of emergency rescue. Therefore, the PED model is mainly designed around ES in emergency. Since emergency dispatching includes multiple materials, multiple origins and destinations, and multiple transports in cross-regional emergency rescue [23,24], the study describes it as a network topology, as shown in Fig 4.
Supply, transfer, and demand points are connected through differentiated dispatch routes, with colored arrows indicating different emergency levels and transportation schemes.
In Fig 4, the study divides the scheduling process into a three-level network, in which the first level is mainly responsible for supplying the materials needed at the DPs, which are produced and raised by the relevant departments, enterprises, etc., and transported to the material CDPs through a variety of means of transportation. The second-level network is the material CDPs, which are mainly responsible for receiving and transferring the materials transported by the SPs and distributing them to the sites in need of materials. The tertiary network is the DPs, which are mainly responsible for receiving materials from the while network and then distributing the materials in the vicinity through helicopters and land transportation [25,26]. Meanwhile, the study divides the network for transportation dispatched across the region, as shown in Fig 5.
Supply, transfer, and demand points are connected by railway, road, and airline routes, with orange links indicating intermodal transfers. a, b, and c denote SP, CDP, and DP, respectively.
In Fig 5, the study divides the transportation network into three layers: railroad, road, and airline. The material CDP in each layer should have the following principles: convenient transportation, perfect scale of equipment and facilities, high social impact situation and advantageous natural conditions. Combined with the above, the PED model is shown in Equation (12).
In Equation (12), denotes the PED model.
denotes the timeliness OF of rescue and
denotes the economy OF of rescue.
denotes the utility OF of rescue.
denotes a CDP.
denotes a certain type of supplies.
denotes the number of planned routes for transportation of supplies.
denotes the transportation of relief supplies from
to
, and takes a value equal to 1 when the transportation strategy chosen by
is the
strategy, or 0 when the opposite is applied.
denotes the transportation volume of
, and
denotes the time overhead spent on transportation by
.
denotes the time overhead spent on distribution and transshipment of supplies at
.
denotes the transportation of relief supplies from
to
.
denotes the transportation volume of
, and
denotes the transportation time of
.
and
denote the distance and cost of transportation for the
transportation method planned from
to
, respectively.
denotes the unit transit cost of material
except at CDP
.
and
denote the transportation mileage and transportation cost of the
kind of transportation method selected by material
from CDP
to DP
, respectively.
denotes the lack of quantity of the material at the DP.
denotes the emergency relief demand level of
after the occurrence of emergencies.
denotes the correction factor that sets the premium or discount cost for the benefit of relief material
to the ER. The urgency level obtained from ELA is normalized and incorporated into the correction factor in Equation (12), which serves as the priority weight for each DP. Higher urgency levels lead to higher correction factors, thereby increasing their weight in the allocation objective. The study focuses on the determination of the OF of the PED model in terms of timeliness of rescue, economy of rescue and utility of rescue. Consequently, the study imposes pertinent constraints on the PED model. Less material than the amount of reserve at the SP must be carried from the SP to the CDP. In a similar vein, less material must be provided to the DP from the CDP than must be requested at the CDP. Additionally, the amount of goods conveyed at the CDP cannot be greater than the amount of stuff requested at the CDP. The specific expression is shown in Equation (13).
In Equation (13), denotes the SP’s reserve on material
.
denotes the total amount of materiel
accepted by the CDP.
denotes the amount of demand for material
at the DP. To ensure the fairness of ER, it is necessary to ensure that the amount of material transported to the disaster site meets the minimum level of material demand service. Furthermore, the original storage quantity of the material at the CDP and the quantity transported to the CDP by the SP should be equal to the quantity of the substance delivered to the DP. The specific expression is shown in Equation (14).
In Equation (14), denotes the reserve at the CDP with respect to material
, and
denotes the minimum demand rate. The sum of the transportation volume of the CDP should be lower than the throughput capacity of the CDP, and the number of transportation means should be lower than the transportation reserve capacity. The specific expression is shown in Equation (15).
In Equation (15), denotes the throughput capacity of the CDP, and
denotes the number of means of transportation of
.
denotes the number of transportation means of
.
denote the reserved transportation capacity from SP to CDP, and
denote the reserved transportation capacity from CDP to DP.
represents the unit carrying capacity of transportation mode
. Transportation capacity is determined by the number of transportation vehicles and their unit carrying capacity. Since different transportation modes have different carrying capacity parameters
, this model can describe emergency dispatching problems under heterogeneous transportation resources. To effectively solve the model, the study first performs multi-objective processing on the model, determines the priority of the OF
according to the principle of human-centeredness, and takes it as the constraint of the model. It then performs weighted single-objective processing. Compared to methods based on the Pareto frontier, the weighted summation method is more computationally efficient and better suited to the requirements of solution speed and decision certainty in emergency scheduling problems. The processing formula is shown in Equation (16) [27].
In Equation (16), and
denote the different weight coefficients of the OF, and
denotes the optimal solution. According to Equation (16), the study utilizes the IPSO algorithm to compute the better solution of the model. The IPSO algorithm is obtained by introducing the Beetle Antennae Search (BAS) algorithm for optimization based on the PSO algorithm [28,29]. The BAS algorithm can improve the optimization rate of the PSO algorithm during the goal search process, increasing the efficiency with which the algorithm finds an optimal solution [30–32]. In the IPSO algorithm, the PED model is mainly transported from two routes (SP-CDPs, and CDPs-DPs) and provides corresponding transportation strategies for various types of materials. It is assumed that there are two supplies to be transported and five sites (a1, a2, a3, a4, and a5) capable of supplying both. There are 2 sites (b1 and b2) that distribute the supplies. There are 4 sites (c1, c2, c3, and c4) that need to receive supplies. The specific particle codes for the two phases are specified in Table 2.
In Table 2, the SP-CDP transportation scheme is 20-dimensional. The CDP-DP transportation scheme is 16-dimensional. p denotes the random number carrying the transportation volume and transportation mode, which takes the value range of [0,1]. Therefore, Fig 6 depicts the IPSO algorithm’s solution flow in accordance with the particle coding approach.
The algorithm iteratively evaluates particle fitness, updates the global optimum, velocity, position, and particle state until the termination condition is satisfied. BAS denotes beetle antennae search, and IPSO denotes improved particle swarm optimization.
In Fig 6, the IPSO algorithm first sets the relevant parameters to set the specific information about the size of the particle swarm at the very beginning, the update speed and the position [33,34]. The adaptation degree is calculated according to the adaptation function, which is shown in Equation (17).
In Equation (17), denotes the fitness function. According to the particle adaptation degree, the positions of individual particles and the global optimum are determined, and the particle positions are updated according to the BAS algorithm. The specific update is shown in Equation (18).
In Equation (18), is the ion update velocity and
is the particle update position.
represents the particle position.
is the inertia factor, and
and
are the particle movement acceleration.
and
are uniformly distributed random numbers with values in the range of [0,1].
is the Historical Optimal Position (HOP) of a single particle.
is the HOP of all particles of the population.
and
are the target values of left whisker and right whisker respectively. To ascertain whether the maximum iteration has been achieved, the particle state is updated at the end. The scheduling scheme’s output will be executed if the condition is met. Otherwise the adaptation will be brought in with new particles to recalculate until the condition is satisfied and the optimal scheduling scheme is output. To enhance the global search capability of PSOA and avoid premature convergence, this paper constructs a collaborative mechanism between BASA and IPSOA. In each iteration, the position and velocity of the particles are first updated using standard PSOA. The BASA tentacles search mechanism is introduced to evaluate the objective function of the particle’s current position neighborhood and determine the search direction based on the comparison results, thereby enhancing the local search capability. IPSOA introduces a conditional triggering mechanism: when the global optimal solution is not updated in K consecutive iterations, the particle swarm is considered to have entered a stagnant state. At this time, BASA is triggered to perform local perturbation to escape the local optimum and improve the diversity of solutions. The parameter K is used to balance the relationship between global search and local search. When K is too small, local search is triggered frequently, while when K is too large, it will weaken the role of local search. Therefore, the parameter is set to 10 through preliminary experiments. Overall, BASA provides a neighborhood search supplement to PSOA, and the two achieve collaborative updates through Equation (18). Based on the above, the pseudo-code of the PED model implementation is shown in Table 3.
4. Results
To verify the effectiveness of the PED method using the emergence class and TP proposed in this study, PSO algorithm and BAS algorithm are first presented and their solutions to the PED model are compared with IPSO algorithm. Secondly, the scheduling method validation is carried out with two different emergency instances.
4.1. Experimental design and data sources
The two typical case studies correspond to the large-scale material dispatch scenario of the 2019 COVID-19 pandemic (instance 1) and the emergency rescue scenario following the 2008 Wenchuan earthquake (instance 2). Data sources include emergency drills, historical public data, transportation information platforms, and supplementary simulation-based data based on characteristics of real-world scenarios. The data is a mix of real-world and simulated data. Real-world data is used to simulate typical cross-regional emergency dispatch scenarios for major public health events and earthquakes. Simulated data supplements the scale and complexity of nodes. Simulated data is generated based on real data through random perturbation and parameter expansion, so that the expanded data maintains similar statistical characteristics to the original data in terms of demand scale and transportation distance. Data collection primarily focuses on emergency transportation records during the 2019–2020 pandemic and public case data from the 2008 Wenchuan earthquake rescue. Data collection methods include systematic data collection, historical data collation, and simulation expansion. Data is used in the experiments after passing scientific research project registration and open data authorization. All data is standardized before using, including distance matrix normalization, transportation time standardization, and material demand smoothing.
In terms of the feasibility of transportation methods, the transportation routes for all scenarios are set based on the actual transportation network or post-disaster transportation recovery capabilities: In the epidemic scenario, the focus is on the regular allocation of materials by railways and highways and emergency air transport channels. In the earthquake scenario, blocked roads and interrupted lines are taken into consideration. Routes that cannot be used are closed or assigned high penalty costs.
4.2. Validation of PED instance 1
To verify the effectiveness of the proposed PED model based on ELA and TP for transportation scheduling in emergency, the study firstly validates the results of performance comparison between artificial intelligence optimization algorithms PSO, BAS, and the proposed IPSO in solving the PED model. Based on the typicality and operability principles of PED, the transportation and material hub areas most affected by the epidemic in instance 1 are selected. A public health event at a location with five SPs (a1, a2, a3, a4, and a5), two CDPs (b1 and b2), and four DPs (c1, c2, c3, and c4) are set up. ES is medical protective gear and vegetables. The combination ratio of protective gear is protective clothing: goggles: mask = 1:1:2. The weight of one protective clothing is 0.5 kg, the weight of goggles is 0.03 kg, and the weight of mask is 0.02 kg. The weight of 10,000 sets of medical protective gear is 5.7 t. The set of material transportation modes include air, rail and road. Specific transportation-related information is shown in Table 4.
In Table 4, the study sets the average speed of air transportation as 600 km/h, the average speed of railroad as 75 km/h, and the average speed of road as 100 km/h. By programming in Matlab r2019b software, the particles are set to be 100, and the number of iteration of the three algorithms is 500. The final obtained iteration curves of the three algorithms for solving the PED model are compared. The results are shown in Fig 7.
(a) Comparison of iterative convergence curves of three algorithms. (b) Comparison of the iteration time curves of the three algorithms. PSO, BAS, and IPSO denote particle swarm optimization, beetle antennae search, and improved particle swarm optimization, respectively.
Fig 7(a) displays the iterative convergence curves of the three algorithms. The updated IPSO algorithm achieves a lower optimal solution value of 0.17 and converges more quickly. The iterative convergence time of the three methods is shown in Fig 7(b). Each algorithm’s time overhead rises with the number of rounds. The PSO algorithm takes the most time, followed by the BAS algorithm. This indicates that the study to improve the PSO algorithm using the BAS algorithm is reliable and reasonable, and the improved IPSO algorithm is more superior in convergence speed as well as model solving. The algorithm converges quickly in the initial stage. This is mainly because the constraints on transportation capacity, demand, and transportation network structure in the model impose certain limitations on the feasible solution space, enabling the algorithm to quickly approach the optimal solution within a relatively small number of iterations. Simultaneously, IPSOA introduces the BAS local search mechanism on top of particle swarm optimization, which enhances the solution space exploration capability and reduces the risk of getting trapped in local optima. Therefore, this rapid convergence process mainly stems from the combined effect of model constraints and the algorithm’s search mechanism, rather than premature convergence. The scheduling results under different weight coefficients of the PED model obtained by solving according to the IPSO algorithm are shown in Fig 8.
(a) Rescue response time solution results with different weights. (b) Rescue transportation cost solution results with different weights.
From the optimal value and rescue response time obtained by solving under different weighting parameters in Fig 8(a), the PED model solves the smallest optimal value of 0.17, and the smallest rescue response time of 459.73 min. Combined with the results of solving the rescue transportation cost in Fig 8(b), the IPSO algorithm solves the smallest rescue transportation cost of Rmb14.86 million. As the rescue time decreases, the rescue transportation cost increases. This indicates that the decision maker can choose the appropriate weighting system for the determination of the scheduling scheme at different rescue stages. The study also calculates the urgency score of each DP using the TOPSIS comprehensive evaluation model. Then, it normalized the
to obtain the priority weight of each DP and introduced this weight as a node-level parameter into the PED scheduling model. By converting urgency scores into priority weights through a linear mapping method, consistency between urgency evaluation results and scheduling models is maintained, and the relative urgency of different demand nodes is reflected in the scheduling optimization process. The details are shown in Table 5.
Table 5 showed that c1 and c4 had the highest ELA urgency scores and corresponding priority weights, resulting in relatively high resource allocation and satisfaction rates during the scheduling process. In contrast, c2 had a priority weight of 0.70, but its satisfaction rate was 80%. This result is obtained by optimizing the overall objective function of the PED model using the IPSO algorithm, taking into account factors such as transportation capacity constraints, supply node inventory limitations, and transportation path costs. The model achieves global optimum by optimizing overall response time and transportation costs while ensuring that each demand node meets the minimum service level constraint, reflecting the trade-off between efficiency and fairness in emergency scheduling during resource allocation. Therefore, based on the above solution results, the study further obtains the optimal scheduling scheme based on the material transportation and the transportation means, as shown in Fig 9.
(a) Scheduling results for medical protective gear. (b) Schematic diagram of the quantity of material transported versus the two-dimensional coordinates of the means of transport.
In Fig 9(a), in the PED model solved by IPSO algorithm, the optimal SP to CDP scheduling schemes are a1-b2, a2-b1, a4-b1, and a5-b1 for air transportation of supplies, and a3-b2 for rail transportation of supplies. In addition, in CDP to DP of medical protective gear scheduling, the optimal scheme is b1-c1, b1-c2, b2-c4 for railroad transportation of materials, b2-c3 for road transportation of materials. The results of the two-dimensional coordinate system, as depicted in Fig 9(b), indicate that the number of required air, railroad, and road means of transportation is 56, 65, and 73, respectively. The scheduling scheme for the rescue materials and vegetables is shown in Fig 10.
(a) Dispatch results for vegetables. (b) Schematic diagram of the quantity of material transported versus the two-dimensional coordinates of the means of transport.
In Fig 10(a), in the PED model, the transportation means for scheduling relief materials and vegetables are mainly railroads. Combined with Fig 10(b) the transportation means required for each planning dispatch and the quantity of transported materials, in larger distances or requiring larger materials, railroad transportation with low transportation cost and large transportation quantity is more favored by DM. According to this scheduling scheme, the study further analyzes the changes in the when adjusting the quantity of materials at the four DPs for the two materials to meet the demand rate and the quantity of materials at the DPs under the situation of constant supply of materials, as shown in Fig 11.
(a) Point-of-need material satisfaction rate under the movement control programme. (b) Variation of f3 under different scenarios of medical protective gears.
In Fig 11(a), the medical protective gear and vegetable scheduling scheme obtained from the PED model. All four DPs have a 100% material satisfaction rate for vegetables. The material satisfaction rate for medical protective gear is 80% for DP c2 and 99.74% for DP c4. This is mainly due to the fact that the current model does not set clear priority strategies for resource allocation. All types of demand are optimized uniformly according to the objective function, resulting in some delays in the response to medical supplies during certain periods. Vegetables have relatively small demand quantities, more concentrated DP, and lower transportation weights, so they are given priority. Combining the five scheduling scenarios of medical protective gear in Fig 11(b), the minimum material satisfaction rate of all scenarios is 80% and above, which meets the actual rescue needs. In addition, from the changes of the under the five scenarios,
under scenario 1 takes the smallest value. When combined with the rescue response time and transportation cost under the different weight parameters of the OF from the previous section, it can be concluded that the rescue loss is lowest when the OF is small. Therefore, it is feasible and reasonable to study the PED of this emergency according to scheme 1.
4.3. Validation of PED instance 2
To further verify the effectiveness of the proposed PED model scheduling method, experiments are conducted using a strong earthquake event as an example. The most representative disaster-stricken points and emergency material nodes for post-disaster emergency rescue are selected. Six SPs (a1, a2, a3, a4, a5, and a6), two CDPs (b1 and b2), and five DPs (c1, c2, c3, c4, and c5) are set. The required relief materials are tents and drinking bottled water. The results of scheduling calculations under different weight values are shown in Fig 12.
The bars represent the optimal solution and scheduling cost, while the green markers indicate activation time.
In Fig 12, the scheduling transportation time is inversely proportional to the transportation cost for different values of weights. This indicates that the weight setting sensitivity of the proposed PED model is more desirable. Based on the above results, the IPSO algorithm is further utilized to solve the PED model, and the obtained scheduling scheme is shown in Fig 13.
(a) Results of the movement of tents for relief supplies. (b) Results of the movement of relief supplies of drink water.
In Fig 13(a), in the scheduling scheme of relief material tents, the transportation modes from the SP to the CDP are mostly railroad transportation and air transportation, while the road transportation is less. This may be because the PED model model takes into account that the example is an earthquake event and the efficiency of road transportation is slow. Combined with the transportation distribution of rescue material drinking water in Fig 13(b), the effectiveness of the proposed PED method can be observed. Therefore, the study further analyzes the quantity of material transported and the demand satisfaction rate under this scheduling scheme, as shown in Fig 14.
(a) Quantity of relief supplies dispatched. (b) Material satisfaction rate.
Fig 14(a) shows the results of scheduling the quantity of relief supplies at SP-CDP and CDP-DP. The horizontal coordinate indicates the quantity of drinking water and the vertical coordinate indicates the quantity of tents. Combined with the demand fulfillment rate of the two kinds of materials in Fig 14(b), all the supplied quantities of rescue materials tents exceed the actual demanded quantities, and therefore the demands of all demanded sites are fulfilled. The minimum demand fulfillment rate for all DPs in the dispatch result of rescue supplies drinking water is 91.3%. This may be due to the urgency evaluation index of each DP resulting in a lower supply of potable water at DP c1. However, overall, the PED model scheduling method satisfies the minimum demand satisfaction rate, and the scheduling scheme is feasible and reasonable.
4.4. Comprehensive validation and comparative analysis
Based on the aforementioned dataset, this study analyzes the stability and feasibility of the proposed PED model. To reduce the influence of randomness and ensure statistical significance, each set of experiments is independently repeated 30 times. The mean and 95% confidence interval are calculated based on the experimental results. The specific results are shown in Table 6.
Table 6 shows that increasing the number of particles slightly decreases the model’s response time and improves the satisfaction rate. Minimal overall performance fluctuations result from adjusting the TOPSIS weights and values, which has a minimal impact on the cost and satisfaction rate. This demonstrates that the proposed PED model is stable under parameter variations and exhibits strong robustness. Furthermore, the supply-demand balance, throughput constraints, and service-level constraints are met under all perturbation scenarios. No resource allocation imbalances or constraint violations are observed. These results further validate the solution’s feasibility and robustness. To verify the optimization capability of the IPSO algorithm in the path planning subproblem, experiments were conducted using a standard VRP benchmark instance with 50 nodes selected from the standard benchmark library for the Vehicle Routing Problem (VRP). Since the standard VRP instance does not contain node priority information, this experiment is only used to evaluate path optimization performance. Under the same parameters and constraints, the results were compared with those of the GA, the greedy strategy, and the deep reinforcement learning-based path planning method (DRL-based routing). The results are shown in Table 7.
In Table 7, the proposed method achieved a response time of 3.84 h on the VRP benchmark dataset, which was 6.12%, 17.06%, and 3.52% shorter than that of GA, the greedy strategy, and DRL-based routing, respectively. The proposed method also reduced transportation costs by 7.05%, 16.67%, and 3.78% compared to the other three methods. Furthermore, the confidence interval of the proposed model exhibits a narrow fluctuation range, indicating its enhanced stability and robustness. Finally, the study further verified the scalability of the PED emergency scheduling model in large-scale networks. Experiments were conducted with scheduling networks of 100, 200, 300, and 500 nodes, respectively, and the IPSO algorithm was used for solution. The details are shown in Table 8.
As shown in Table 8, as the network size gradually increased from 100 nodes to 500 nodes, the model’s response time and transportation costs increased, but the growth trend remained stable. Meanwhile, the average satisfaction rate of each demand node remained at a high level, indicating that the proposed PED scheduling model can maintain stable scheduling performance even as the network size expands. These results demonstrate that the proposed method has good scalability and application potential in large-scale cross-regional emergency dispatch networks.
This study analyzes the time complexity of the PSO, BAS, and IPSO algorithms. The number of particles is N, the problem dimension is D, and the maximum number of iterations is T. The time complexity of the standard PSO algorithm is O(NDT), and the time complexity of the BAS algorithm is O(DT). The proposed IPSO introduces the BAS local search mechanism into the PSO framework, and its overall time complexity is approximately O(NDT), which is on the same order of magnitude as the PSO algorithm, thus not increasing the computational complexity.
5. Discussion and conclusion
The study’s key contributions included the development of an emergency level assessment and priority emergency dispatch optimization model. This model integrated urgency analysis, transportation priority, artificial intelligence technology, and an IPSO algorithm combined with the beetle antennae search algorithm. The integration was to enhance the efficiency of emergency rescue in cross-regional integrated transportation networks. In PED case 1, the vegetable supply satisfaction rate at all DPs reached 100%, the minimum satisfaction rate for medical protective equipment was 80%, and the average satisfaction rate was 94.94%. In case 2, the tent supply satisfaction rate reached 100%, the average satisfaction rate for drinking water was 98.26%, and the minimum satisfaction rate was 91.30%. On the standard vehicle routing problem benchmark dataset, the response time of the proposed method was reduced by 6.12% and 17.06% compared with the GA and the greedy strategy, and transportation costs were reduced by 7.05% and 16.67%, respectively. Compared to typical algorithms and benchmark methods, the proposed model achieved a more efficient scheduling response and balanced resource allocation [28,29,32].
Theoretically, this study incorporates a dynamic mapping mechanism of urgency and priority into a cross-regional dispatch optimization framework. It also introduces a measurable priority dispatch factor and formalizes equity requirements as model constraints. This enriches the theoretical system of emergency logistics DM. Unlike traditional models, which focus primarily on time or cost, this study balances scheduling efficiency and fairness in resource allocation. This provides a framework that can be used to solve large-scale emergency transportation problems. At the practical level, this model can directly provide auxiliary decision support for actual management entities such as EOCs, public security traffic management departments, and transportation bureaus. For example, in scenarios involving cross-regional allocation of emergency supplies during public health emergencies or disasters, different SPs, CDPs, and DPs need to quickly formulate scheduling plans. Through priority-driven resource allocation and dynamic constraint scheduling, the proposed method can shorten cross-regional material allocation time, reduce transportation costs, and improve the coverage of each demand node. Compared with existing scheduling methods based on PSO or GA, the proposed PED-IPSO model demonstrates superior overall performance in response time and transportation costs, thus providing more efficient decision support for emergency management departments.
Several limitations remain in the modeling process. The main assumptions include deterministic transportation time, static network structure, split deliveries, and fixed fleet capacity. These assumptions are adopted to simplify the computational complexity of the model and ensure tractable optimization in emergency scenarios where rapid decision-making is required. However, they limit the applicability and external validity of the model in highly dynamic, large-scale scenarios. Future work will address these limitations by introducing dynamic and robust routing mechanisms to handle uncertainty and integrate real-time data assimilation to enhance adaptive responses.
Additionally, the scale and heterogeneity of multi-region experiments will be expanded, and governance and handoff constraints will be incorporated to improve applicability in multi-agency coordinated dispatch. Although case studies based on epidemic and earthquake scenarios have demonstrated the effectiveness, the scope of these studies remains limited. They do not represent all emergency dispatch situations. Future research will focus on larger, more complex, and more diverse scenarios to enhance the model’s external validity and generalizability. Future research will introduce demand node priority labels on the existing VRP benchmark dataset to construct an extended test set that better reflects the characteristics of emergency dispatch. Simultaneously, combining traffic simulation tools with digital twin systems can provide real-time perception of road network conditions, thereby achieving dynamic dispatch. Furthermore, cross-regional government collaboration rules will be quantified into model constraints to enhance the model’s practical application value in complex emergency management scenarios.
Supporting information
S1 Dataset. The minimal dataset required to reproduce the figures and results reported in this study is provided as Supporting Information (S1 Dataset).
The dataset contains the original data used to generate the figures and experimental results presented in the manuscript.
https://doi.org/10.1371/journal.pone.0348072.s001
(XLSX)
References
- 1. Chen L, Wang M, Zhang W, Zhang X, Jiao C, Yu Y, et al. The value of inflammatory biomarkers in the occurrence and prognosis of sudden sensorineural hearing loss: a meta-analysis. Eur Arch Otorhinolaryngol. 2023;280(7):3119–29. pmid:36574064
- 2. Preethi P, Mamatha HR. Region-based convolutional neural network for segmenting text in epigraphical images. Artif Intell Appl. 2023;1(2):119–27.
- 3. Liu C, Qian Y. Optimal allocation of material dispatch in emergency events using multi-objective constraint for vehicular networks. Wirel Netw. 2022;28(8):3715–27.
- 4. Kergosien Y, Bélanger V, Ruiz A. A capacity sharing approach to manage jointly transportation and emergency fleets at EMS organisations. Int J Prod Res. 2023;61(3):880–97.
- 5. Ding Z, Xu X, Jiang S, Yan J, Han Y. Emergency logistics scheduling with multiple supply-demand points based on grey interval. JSSR. 2022;3(2):179–88.
- 6. Zhang L, Zhang H, Liu D, Lu Y. Particle swarm algorithm for solving emergency material dispatch considering urgency. J Syst Sim. 2022;34(9):1988–98.
- 7. Wang T, Wu K, Du T, Cheng X. Adaptive weighted dynamic differential evolution algorithm for emergency material allocation and scheduling. Comput Intell. 2022;38(3):714–30.
- 8. Yuan Y, Wang F. An emergency supplies scheduling for chemical industry park: based on super network theory. Environ Sci Pollut Res Int. 2022;29(26):39345–58. pmid:35099704
- 9. Chen J, Li C, Huang L, Zheng W. Tourism demand forecasting: a deep learning model based on spatial-temporal transformer. Tour Rev. 2025;80(3):648–63.
- 10. Shaik T, Tao X, Li L, Xie H, Dai H-N, Zhao F, et al. AI-driven multi-agent reinforcement learning framework for real-time monitoring of physiological signals in stress and depression contexts. Brain Inform. 2025;12(1):14. pmid:40490570
- 11. Li D, Zhang Z, Alizadeh B, Zhang Z, Duffield N, Meyer MA, et al. A reinforcement learning-based routing algorithm for large street networks. Int J Geogr Inf Sci. 2024;38(2):183–215.
- 12. Putri WA, Rachmawati D, Silalahi WS. Sistem pendukung keputusan pemilihan e-wallet menggunakan metode analytic hierarchy process-TOPSIS: E-wallet selection decision support system using analytic hierarchy process-TOPSIS method. MALCOM. 2022;2(1):18–27.
- 13. Saxena P, Kumar V, Ram M. A novel CRITIC-TOPSIS approach for optimal selection of software reliability growth model (SRGM). Qual Reliab Eng Int. 2022;38(5):2501–20.
- 14. Wang Y. Multiperiod optimal allocation of emergency resources in support of cross-regional disaster sustainable rescue. Int J Disaster Risk Sci. 2021;12(3):394–409.
- 15. Bianchi M, Cordella M, Menger P. Regional monitoring frameworks for the circular economy: implications from a territorial perspective. Eur Plan Stud. 2023;31(1):36–54.
- 16. Tešić D, Božanić D, Khalilzadeh M. Enhancing multi-criteria decision-making with fuzzy logic: An advanced defining interrelationships between ranked II method incorporating triangular fuzzy numbers. J Intell Manage Dec. 2024;3(1):56–67.
- 17. Lovell CC, Harrison I, Harikane Y, Tacchella S, Wilkins SM. Extreme value statistics of the halo and stellar mass distributions at high redshift: are JWST results in tension with ΛCDM? Mon Not R Astron Soc. 2022;518(2):2511–20.
- 18. Norouzi MR, Ataei M, Sereshki F. A novel index for shearer system resilience in underground coal mines based on the operational environment. P I Mech Eng O-J Ris. 2024;238(3):475–501.
- 19. Pandey V, Komal, Dincer H. A review on TOPSIS method and its extensions for different applications with recent development. Soft Comput. 2023;27(23):18011–39.
- 20. Susmaga R, Szczȩch I, Zielniewicz P, Brzezinski D. MSD-space: Visualizing the inner-workings of TOPSIS aggregations. Eur J Operat Res. 2023;308(1):229–42.
- 21. Diehlmann F, Hiemsch PS, Wiens M, Lüttenberg M, Schultmann F. Including decision-makers preferences in the cost-deprivation trade-off during disaster interventions. J Eng Des Technol. 2022;20(2):543–65.
- 22. Qiao JM, Li WY. A two-sided matching decision method based on interval triangular fuzzy sets. J Intell Fuzzy Syst. 2023;44(4):5847–57.
- 23. Dawid W, Pokonieczny K, Wyszyński M. The methodology of determining optimum access routes to remote areas for the purposes of crisis management. Int J Digit Earth. 2022;15(1):1905–28.
- 24. Capacci L, Biondini F, Frangopol DM. Resilience of aging structures and infrastructure systems with emphasis on seismic resilience of bridges and road networks. RCS. 2022;1(2):23–41.
- 25. Pouraliakbari-Mamaghani M, Ghodratnama A, Pasandideh SHR, Saif A. A robust possibilistic programming approach for blood supply chain network design in disaster relief considering congestion. Oper Res-Ger. 2022;22(3):1987–2032.
- 26. Ergün S, Usta P, Alparslan Gök SZ, Weber GW. A game theoretical approach to emergency logistics planning in natural disasters. Ann Oper Res. 2021;324(1–2):855–68.
- 27. Calzada I, Pérez-Batlle M, Batlle-Montserrat J. People-centered smart cities: an exploratory action research on the cities’ coalition for digital rights. J Urb Aff. 2023;45(9):1537–62.
- 28. Saha S, Saha A, Roy B, Sarkar R, Bhardwaj D, Kundu B. Integrating the Particle Swarm Optimization (PSO) with machine learning methods for improving the accuracy of the landslide susceptibility model. Earth Sci Inf. 2022;15(4):2637–62.
- 29. Demir S, Sahin EK. Predicting occurrence of liquefaction-induced lateral spreading using gradient boosting algorithms integrated with particle swarm optimization: PSO-XGBoost, PSO-LightGBM, and PSO-CatBoost. Acta Geotech. 2023;18(6):3403–19.
- 30. Fu W, Fang P, Wang K, Li Z, Xiong D, Zhang K. Multi-step ahead short-term wind speed forecasting approach coupling variational mode decomposition, improved beetle antennae search algorithm-based synchronous optimization and Volterra series model. Renew Energy. 2021;179(1):1122–39.
- 31. Gao Z, Liu Y, Li N, Ma K. An enhanced beetle antennae search algorithm based comprehensive water quality index for urban river water quality assessment. Water Resour Manag (Dordr). 2022;36(8):2685–702. pmid:40477984
- 32. Chen D, Li X, Li S. A novel convolutional neural network model based on beetle antennae search optimization algorithm for computerized tomography diagnosis. IEEE Trans Neural Netw Learn Syst. 2023;34(3):1418–29. pmid:34460391
- 33. Ben Regaya C, Hamdi H, Farhani F, Marai A, Zaafouri A, Chaari A. Real-time implementation of a novel MPPT control based on the improved PSO algorithm using an adaptive factor selection strategy for photovoltaic systems. ISA Trans. 2024;146:496–510. pmid:38143223
- 34. Minh HL, Khatir S, Rao RV, Abdel WM, Cuong-Le T. A variable velocity strategy particle swarm optimization algorithm (VVS-PSO) for damage assessment in structures. Eng Compu-Germany. 2023;39(2):1055–84.