AI-driven emergency logistics network deployment in dynamic environments

Abstract

Emergency logistics decisions often suffer from inefficiency due to a lack of foresight and robustness in the face of unexpected events. To address this issue, a dynamic deployment model is proposed that combines an Event-Driven Spatio-Temporal Graph Neural Network (STGNN) with Adaptive Robust Optimization (ARO). The Event-Driven STGNN generates probabilistic predictions of logistics network states by integrating historical spatio-temporal data with external event features. The ARO module then converts these uncertain predictions into a structured uncertainty set and solves a two-stage optimization problem to determine emergency resource allocation plans, such as vehicle scheduling, that remain effective even under worst-case scenarios. The model is solved iteratively using a Column-and-Constraint Generation algorithm within a rolling optimization horizon, which allows continuous adaptation to dynamic environments. Model performance is evaluated using the New York City For-Hire Vehicle dataset from 2019 to 2022, which contains more than one billion trip records (https://www.kaggle.com/datasets/jeffsinsel/nyc-fhvhv-data). A simulation environment is created that incorporates real-world events, including the COVID-19 pandemic and severe snowstorms. Results show that, in simulated emergency distribution tasks, the proposed model increases demand fulfillment from 71.3% to 96.5% and reduces average delivery delay from 45.2 minutes to 11.8 minutes compared with a benchmark that combines STGNN prediction with deterministic optimization. When compared with advanced models based on standard Robust Optimization, the proposed model improves emergency fleet resource utilization efficiency by 18.2%. The significant performance improvements primarily stemmed from the ARO framework, which provides performance guarantees under worst-case scenarios. Additionally, the synergistic integration of probabilistic forecasting and optimization-based decision-making prevented the model from becoming overly conservative, thereby enhancing resource efficiency. The core contribution of this study lies in establishing and validating a closed-loop framework that systematically integrates data-driven prediction with risk-averse decision-making. This empirically verified paradigm offers an effective approach to emergency logistics deployment under dynamic and uncertain environments.

Introduction

Public emergencies such as natural disasters, major accidents, and public health crises pose severe threats to social order and public safety due to their unpredictability and destructive impact¹. During these crises, emergency logistics serves as a “lifeline” that ensures the efficient distribution of relief supplies and essential goods. Its response speed and operational efficiency directly affect the success of disaster control and the extent of losses in lives and property^2–4. However, emergency environments are highly dynamic and uncertain. Demand fluctuates dramatically across time and space, while transportation network conditions change rapidly. These characteristics make it difficult for traditional static or reactive logistics decision-making models to cope effectively⁵. Therefore, developing proactive, efficient, and reliable deployment methods for emergency logistics networks under complex and rapidly changing conditions has become a critical scientific challenge in the field of emergency management.

Despite notable progress in existing studies, emergency logistics decision-making still faces two fundamental challenges: limited forecasting foresight and insufficient decision robustness. On one hand, many decision models rely on historical averages or simple trend extrapolations, which fail to capture the nonlinear and dynamic shocks induced by disruptive events such as natural disasters, public health crises, and major infrastructure failures. As a result, prediction distortions occur, leading to a lack of foresight in subsequent decision-making⁶. On the other hand, even when advanced forecasting models are adopted, the ensuing optimization and scheduling processes typically depend directly on deterministic predictions⁷. This simplified “predict-then-optimize” paradigm neglects both forecasting errors and the intrinsic randomness of future states. Consequently, the resulting solutions often exhibit fragility under real-world uncertainty, causing resource misallocation and severe delivery delays, ultimately undermining the overall effectiveness of emergency response systems.

To systematically address these challenges, this study proposes an AI-driven dynamic deployment framework for emergency logistics, which integrates advanced forecasting models with Adaptive Robust Optimization (ARO) theory. This framework aims to bridge critical research gaps in predictive decision-making under uncertainty. The core contributions and innovations of this work are summarized as follows:

• Model innovation: An Event-Driven spatiotemporal graph neural network (STGNN) is developed to integrate external event features with historical spatiotemporal dependencies, generating probabilistic forecasts that accurately quantify future demand uncertainty.

• Framework innovation: A closed-loop framework is constructed to bridge forecasting and decision-making. Probabilistic outputs from the STGNN are seamlessly transformed into uncertainty sets within the ARO model, enabling dynamic adaptation while ensuring solution robustness.

• Empirical validation: Extensive simulations are conducted using large-scale real-world datasets that include disaster scenarios such as COVID-19 outbreaks and snowstorms. Experimental results demonstrate that the proposed method significantly outperforms existing benchmarks in key performance metrics, including demand satisfaction rate, delivery delay, and resource efficiency.

By achieving precise uncertainty characterization and refined risk management, this study provides robust decision support for improving deployment efficiency and system reliability of emergency logistics operations in dynamic and uncertain environments.

Literature review

Emergency logistics optimization has long been a central topic at the intersection of operations research and emergency management. Early studies have made significant contributions to critical problems such as resource allocation and route planning. For example, Zhang et al.⁸ investigated dynamic optimization under major epidemic scenarios by considering the urgency of demand, while Yang et al.⁹ developed and optimized a two-stage earthquake emergency logistics system from the perspective of public psychological risk perception. On the algorithmic side, Yin et al.¹⁰ applied a guided local search approach to optimize the delivery routes of emergency supplies. Some studies have also explored the integration of emerging technologies into optimization, such as Wang et al.¹¹, who examined blockchain-based traceability models and resource optimization strategies for emergency logistics. Although these studies have enriched the methodological toolbox of emergency logistics, their underlying mathematical models often resemble complex nonlinear coupled systems found in other scientific domains. Solving such systems typically requires sophisticated numerical techniques, such as the regional decomposition method analyzed by Aakansha & Das¹² or the high-order convergence analysis for non-smooth data problems developed by Kumar & Das¹³. However, most traditional emergency logistics models are built on deterministic or simplified assumptions about future demand and environmental conditions. This limits their foresight and adaptability when confronted with sudden, severe disruptions.

To overcome the limitations of traditional optimization in forecasting, data-driven AI techniques, particularly machine learning, have been increasingly applied in logistics to achieve more accurate predictions of network states. Liu et al.¹⁴ systematically reviewed AI applications in cyber-physical logistics systems. In specific predictive tasks, Che et al.¹⁵ used deep learning to predict the precise positioning of logistics robots, while Hou & Jia¹⁶ employed graph learning to perform collaborative throughput prediction in logistics networks. These studies demonstrate that AI techniques can significantly enhance the intelligence and forecasting accuracy of logistics systems, providing a solid data foundation for proactive decision-making. This shift toward computationally efficient, data-driven paradigms mirrors trends observed in other complex domains. For instance, Patawari & Das¹⁷ highlighted the potential of advanced algorithms in option pricing, emphasizing their applicability to complex logistics problems. Nonlinear propagation and convective-diffusive phenomena in logistics networks resemble these systems, where obtaining consistently convergent and accurate numerical solutions remains a major challenge, as noted by Kumar & Das¹⁸.

Nevertheless, directly feeding point predictions from machine learning models into optimization frameworks ignores the inherent uncertainty in these forecasts, which can render the resulting solutions highly fragile under real-world fluctuations. Therefore, quantifying and managing predictive uncertainty has become a critical bridge between accurate forecasting and robust decision-making. Recent research on uncertainty quantification has received considerable attention; for example, Tyralis & Papacharalampous¹⁹ provided a comprehensive review of this area. Numerous studies have contributed to this field, such as Khosravi et al.²⁰, who evaluated the performance of hybrid machine learning models in terms of both prediction accuracy and uncertainty estimation. This approach has been successfully applied in diverse domains, including Earth observation and the robustness analysis of photovoltaic power plants, demonstrating its broad applicability and practical value. In the context of dynamic emergency logistics deployment, decision-making under uncertainty remains a core challenge. This aligns with broader theoretical advances, such as stochastic optimal control explored by Anukiruthika, Muthukumar, & Das²¹. Iterative methods that decompose complex problems into manageable subproblems are conceptually related to modern machine learning techniques, including the improved iterative Physics-Informed Neural Network (PINN) algorithms proposed by Patawari, Kumar, & Das²² for solving strongly coupled systems.

In summary, existing research has made significant progress in three areas: emergency logistics optimization, machine learning-based logistics forecasting, and predictive uncertainty quantification. However, a clear research gap remains: few studies have integrated these three dimensions within a unified framework. Specifically, two critical challenges persist: (1) how to construct a probabilistic forecasting model capable of capturing event-driven, dynamically changing environments, and (2) how to transform its structured uncertainty outputs into a ARO framework that supports risk-averse decision-making. Addressing this gap is essential for tackling the dynamic deployment challenges in emergency logistics. This study aims to develop an AI-driven integrated framework that links probabilistic forecasting with ARO, thereby enhancing the foresight, robustness, and efficiency of emergency logistics decisions in dynamic environments.

Methodology for constructing the emergency logistics network model

Overall framework design

In dynamic and uncertain environments, emergency logistics deployment faces challenges such as severe demand fluctuations, diverse event impacts, and decision delays. To address these challenges, this study proposes a closed-loop decision-making framework that integrates event-driven prediction with ARO. The framework follows a continuous cycle of “prediction–optimization–updating.”

In the prediction stage, the model not only captures spatial demand propagation across neighboring regions but also explicitly incorporates external event features. This design ensures that predictions can flexibly reflect demand heterogeneity under event shocks. In the optimization stage, demand variability is represented through a budgeted uncertainty set²³. The model is solved efficiently using a Column-and-Constraint Generation (C&CG) algorithm²⁴, which balances risk aversion with decision flexibility when responding to unexpected events. Finally, the framework continuously incorporates updated information from the environment, enabling adaptive adjustments and optimization of emergency logistics networks. Table 1 summarizes the core modules of the framework and their primary functions.

Table 1.

Core modules of the proposed model framework and their main functions.

Module	Core technique	Main function	Key output
Probabilistic prediction module	Event-driven STGNN	Generate probabilistic forecasts of future logistics network states	Probabilistic distribution parameters of regional demand (mean μ, variance σ2)
Adaptive robust decision-making module	Two-stage adaptive robust optimization (TS-ARO)	Derive resource deployment and scheduling plans with minimal cost under worst-case scenarios	First-stage vehicle pre-deployment plan and second-stage optimal scheduling strategy
Dynamic execution and adaptation module	Rolling horizon and C&CG algorithms	Adjust decisions dynamically based on the latest environmental information to ensure continuous adaptability	A sequence of dynamically updated emergency logistics deployment instructions

The model framework, referred to as Event-Driven Spatio-Temporal Graph Neural Network and Adaptive Robust Optimization (EDSTG-ARO), is illustrated in Figure 1. It operates as a closed loop within a rolling optimization horizon.

Fig. 1.

Framework of the EDSTG-ARO model.

The process begins with the data input layer, where the system continuously collects historical spatio-temporal data (e.g., past demand in each region) along with heterogeneous external event data (e.g., pandemic severity levels, weather warnings). These data are fed into the Event-Driven STGNN module, which functions as the prediction engine. The module outputs probabilistic forecasts of regional demand over the next time window (μ, σ²).

The probabilistic forecasts are then transformed into a structured budgeted uncertainty set, which serves as the critical input for the TS-ARO model. The ARO model is solved using the C&CG algorithm to generate the optimal emergency resource deployment plan for the current decision horizon. After execution of this plan, the system moves forward by one time step and enters the next decision cycle. At this point, the latest observed data are incorporated, and the complete process of “data input → prediction → optimization → decision” is repeated.

This rolling optimization mechanism gives the framework strong adaptive capability. Instead of relying on a fixed static plan, it continuously responds to environmental changes and ensures reliable performance under dynamic conditions.

Event-driven probabilistic spatio-temporal prediction

In dynamic emergency scenarios, sudden events—such as extreme weather, public health crises, or infrastructure failures—can alter demand patterns in nonlinear and temporally heterogeneous ways. These complex interactions often make it difficult for traditional models to capture system dynamics accurately. In some cases, advanced mathematical tools are required, such as fractional partial differential equations, which Saw, Das, and Srivastava²⁵ employed in bio-thermal flow analysis. To address this complexity from a data-driven perspective, the study developed an Event-Driven STGNN. The nonlinear propagation of demand within logistics networks resembles complex convective-diffusive systems, where obtaining consistently convergent and accurate numerical solutions is a significant challenge, as noted by Kumar, Podila, Das, & Ramos²⁶. The approach explicitly integrates historical spatiotemporal sequences with global event features to generate heteroscedastic, multi-step probabilistic forecasts, providing a data-driven quantification of uncertainty for subsequent robust optimization.

The overall framework for event-driven probabilistic spatio-temporal prediction is illustrated in Figure 2.

Fig. 2.

Framework of the event-driven probabilistic spatio-temporal prediction module.

The logistics network in the study area is represented as Equation (1):

1

In Equation (1), represents the graph of the emergency logistics network, where denotes the set of nodes representing geographical partitions (e.g., regions, streets), denotes the set of edges representing physical transportation links between partitions, and is the total number of nodes. is the adjacency matrix, encoding the connectivity or proximity relationships among nodes. The objective of the model is to use historical data from the past time steps to predict demand over the next time steps.

To achieve local-to-global information fusion, this study defines the following key input variables:

• Node Features (): represents a set of dynamic attributes for node at time step , such as historical demand and the number of available vehicles. Here, denotes the total dimension of the node features.

• Event Features (): is a global feature vector shared across all nodes, capturing quantified information about external “unexpected events” occurring at time step , such as epidemic severity levels or blizzard warnings. denotes the total dimension of the event features.

Next, a learnable projection matrix () maps the global event features into a dimension compatible with the node features. As shown in Equation (2), the original node features are concatenated with the projected event features to generate an enhanced feature vector that fuses local and global information. Here, the symbol denotes the concatenation operation, and represents standard matrix-vector multiplication.

2

These inputs are fed into the ST-Block, which alternates spatial and temporal layers to generate hidden representations.

Spatial dependencies

To model time-varying spatial influence under events, a multi-head Graph Attention Network (GAT)²⁷ is employed to model time-varying spatial influence under events. The attention score at layer l and head m at time s is described as Equation (3):

3

In Equation (3), , σ(⋅) is an activation function, and denotes concatenation. The event term allows the attention weights to adapt to event conditions, mapping spatial diffusion paths such as “co-epicenter” or “storm-affected” regions.

Temporal dependencies

Temporal modeling of spatially encoded representations is performed using a Gated Recurrent Unit (GRU) (or stacked GRU)²⁸, which balances long-term inertia and short-term shocks:

4

5

6

7

In the GRU unit described in Equations (4)–(7), the symbols are defined as follows: is the feature vector after modeling spatial dependencies (i.e., the output of the GAT layer) and serves as the primary input to the GRU unit at the current time step . represents the hidden state of node from the previous time step, carrying temporal information. Specifically, and denote the update gate and reset gate, which control the flow of information; is the candidate hidden state; and is the final output, representing the new hidden state that integrates both current input and historical memory. The functions and correspond to the standard sigmoid and hyperbolic tangent activation functions, respectively. denotes element-wise multiplication (Hadamard product). This architecture, through its gating mechanisms, dynamically learns how much long-term historical information (e.g., cyclical demand patterns) to retain and how much short-term shock information (e.g., the impact of sudden events) to incorporate.

Sequence-to-sequence decoding and probabilistic output

The decoder uses an autoregressive GRU. At each step, it takes the previous true or predicted demand and future event features as input to generate distribution parameters for τ=1…, H. Let the decoder hidden state be with input (teacher forcing during training):

8

To achieve heteroscedastic regression, the network outputs both the predicted mean and the log-variance (or soft additive variance) via two separate branches, as shown in Equation (9):

9

In Equation (9), denotes the predicted mean, representing the point forecast of demand at node i for time t+τ, and denotes the predicted variance, which quantifies the uncertainty of the predicted value. The mean and variance together define a Gaussian distribution, forming the probabilistic forecast. represents an intermediate value for variance. The model does not directly predict the variance but instead predicts this intermediate value, which is then passed through a softplus function to ensure that the final σ is positive. , , , and are the weights and biases of the linear layers that map the decoder hidden state g to the predicted mean μ and the intermediate variance s. The softplus function is a smooth activation function that guarantees positive outputs.  is a small constant added to prevent σ from being zero, ensuring numerical stability. The conditional Gaussian assumption is: , where represents all information available up to time t, including historical observations and event features.

The main training objective is the negative log-likelihood over multiple steps of the conditional distribution, as expressed in Equation (10):

10

To enhance distributional calibration, a closed-form Gaussian Continuous Ranked Probability Score term can be added, where Φ and ϕ denote the standard normal cumulative distribution function and probability density function, respectively, as expressed in Equation (11):

11

The total loss L is then defined as Equation (12):

12

In Equation (12), Θ represents all learnable parameters. is a hyperparameter that acts as an adjustable weight, balancing prediction accuracy, distribution calibration, and model generalization. The associated loss function consists of three weighted components, designed to achieve these multiple objectives. The first component, the negative log-likelihood loss, serves as the core training objective. It improves point prediction accuracy by minimizing the discrepancy between the predicted Gaussian distribution and the observed values. The second component, the continuous ranked probability score (CRPS), provides a rigorous evaluation of the calibration and accuracy of the entire predictive distribution, ensuring that the model not only predicts accurately but also reliably estimates its own uncertainty. The final component is an L2 regularization term, which prevents overfitting. Obtaining an optimal error estimate is a fundamental goal in numerical modeling, and several techniques have been developed for this purpose, such as the grid uniform redistribution method explored by Das and Natesan²⁹In this model, end-to-end optimization of this composite loss function enables the neural network to generate high-quality probabilistic forecasts. During training, teacher forcing and scheduled sampling strategies³⁰ are employed to mitigate exposure bias, whereas fully autoregressive inference is applied during the prediction phase.

To convert the probabilistic forecast into an uncertainty set for ARO, the maximum deviation scale for the budgeted uncertainty set is defined as Equation (13):

13

In Equation (13), ∈[-1, 1] is the perturbation factor indicating the degree of deviation of demand from its nominal value. The variance output is explicitly used to construct a data-driven deviation radius Δ, α denotes the confidence level, and Γ represents the uncertainty budget.

TS-ARO

In dynamic emergency logistics network deployment, the propagation of demand and event impacts across network nodes exhibits dynamics similar to those of complex reaction-diffusion systems. Ensuring the convergence of models analyzing such networked systems is critical, as demonstrated by Sarkar, Kumar, Das, & Ramos³¹ in their rigorous analysis of a star-shaped graph network. Traditional stochastic programming approaches often require that uncertainties follow precise probability distributions, which is difficult to satisfy in data-sparse, sudden-event scenarios. To address this challenge, this study adopts a TS-ARO model. This approach offers several key advantages: 1. It does not require exact probabilistic distribution assumptions and only defines an uncertainty set that encompasses all possible realizations, making it more robust under deep uncertainty typical of sudden events. 2. It provides worst-case performance guarantees, which is critical for emergency logistics scenarios where reliability is paramount. 3. Its two-stage decision framework (“deploy first, adjust later”) aligns closely with real-world emergency response operations. The second stage allows for dynamic adjustments, reducing over-conservatism while maintaining robustness, thus achieving a balance between reliability and flexibility.

The decision process of TS-ARO is divided into two stages:

1. First stage (Pre-decision stage): during the initial phase of the disaster, decisions on emergency warehouse locations and initial material allocation are made based on the predicted demand distribution and potential traffic blockage scenarios.

2. Second stage (Post-decision stage): Once the actual demand and traffic accessibility are observed, the initial deployment is dynamically adjusted (e.g., emergency resupply and route replanning) to minimize additional costs and delay risks.

For mathematical formulation, let denote the actual demand at affected node j under scenario ξ; denote the unit transportation cost from warehouse i to node j under scenario ξ; denote the fixed cost of establishing warehouse; denote the maximum storage capacity of warehouse i. The two-stage robust optimization model W can be expressed as Equation (14):

14

It is subject to the constraint shown in Equation (15).

15

The model has a three-layer structure:

1. Outer layer () searches for the optimal first-stage deployment strategy.

2. Middle layer () identifies the worst-case uncertainty scenario (e.g., peak demand or blocked roads).

3. Inner layer () determines the optimal emergency resupply decisions for the given scenario.

To reduce computational complexity, Benders decomposition combined with C&CG is employed, separating the outer and inner layers for iterative solution. A dynamic confidence region adjustment mechanism is introduced to progressively shrink the boundaries of the uncertainty set Ξ, avoiding overly conservative decisions. The procedure is illustrated in Figure 3.

Fig. 3.

Procedure of the TS-ARO algorithm.

In each iteration, an initial uncertainty set is first constructed based on historical disaster data and probabilistic predictions from the event-driven forecasting model. This serves as the confidence region for the optimization. Next, in the master problem, the first-stage decision variables x, y are solved, yielding the current vehicle pre-deployment and facility activation plan.

In the adversarial problem, the worst-case demand scenario ξ_k that maximizes the total system cost is identified from . Then, in the subproblem, the optimal resupply and scheduling plan for scenario ξ_k is computed. Subsequently, the newly generated constraints and columns from this scenario are fed back into the master problem. The uncertainty set is dynamically updated based on real-time predictions and environmental feedback, adjusting its boundaries to control the model’s conservatism. This adaptive adjustment is conceptually similar to adaptive mesh techniques, such as the method developed by Kumar, Das, & Kumar³² for porous media models, which concentrates computational effort on critical regions. The algorithm terminates under either of two conditions: (1) when the improvement in the objective function (i.e., total system cost) between successive iterations falls below a predefined threshold (e.g., 0.5%), or (2) when the algorithm reaches the preset maximum number of iterations. This mechanism ensures convergence and ultimately outputs the optimal adaptive deployment and scheduling plan for the current dynamic environment.

To clearly summarize and present the complete execution process of the proposed model, Figure 4 provides a pseudocode representation of the entire integrated algorithm framework (EDSTG-ARO). The pseudocode illustrates the full closed-loop iterative process, from data input and probabilistic prediction to robust optimization and adaptive decision updates, offering an intuitive view of the model’s dynamic operational mechanism.

Fig. 4.

Code workflow of the model.

Experimental evaluation

To rigorously evaluate the effectiveness of the proposed AI-driven emergency logistics network deployment method under highly dynamic and uncertain conditions, a series of simulation experiments were designed. The experimental data were sourced from the publicly available New York City For-Hire Vehicle (FHV) dataset (2019–2022) (https://www.kaggle.com/datasets/jeffsinsel/nyc-fhvhv-data). Although this dataset reflects the operational patterns of a single megacity, it is unprecedented in scale, containing over one billion trip records. Its high spatiotemporal resolution and inclusion of real, high-impact “unexpected events” make it an ideal and rigorous platform for preliminarily validating the model’s generalization capabilities. To introduce realistic and representative disturbances in the simulation environment, two critical periods were specifically selected and analyzed: the COVID-19 outbreak period (March–May 2020) and the blizzard event (February 2021). The former represents a prolonged public health crisis causing large-scale, sustained fluctuations in demand, while the latter exemplifies short-term, severe disruptions triggered by extreme weather. These real-world disturbance scenarios provide a rigorous testing ground for assessing the model’s robustness and adaptive capacity.

In the simulations, fixed emergency center locations, vehicle capacity, fleet size, and road accessibility constraints are configured. Additionally, event-driven traffic blockage data are introduced to emulate disaster scenarios. The dataset processing pipeline is summarized in Table 2.

Table 2.

Dataset processing steps.

Step	Operation	Description
1	Data filtering	Select New York City FHV records from 2019–2022; remove missing or abnormal entries
2	Spatial aggregation	Map trip coordinates to administrative zones using Taxi Zone shapefile
3	Temporal aggregation	Aggregate trips hourly to obtain zone-level demand
4	Outlier removal	Remove extreme demand peaks using the interquartile range method
5	Scenario construction	Extract data during COVID-19 and blizzard periods; superimpose traffic disruption information
6	Normalization	Apply Min-Max normalization to demand for model training

To ensure experimental transparency and reproducibility, all experiments were conducted in a consistent high-performance computing environment. Table 3 provides a detailed overview of the hardware and software configurations used.

Table 3.

Hardware and software configurations.

Item	Configuration
CPU	Intel Xeon Gold 6226R @ 2.9 GHz × 32 cores
GPU	NVIDIA RTX A6000 48 GB × 2
Memory	256 GB DDR4
Operating system	Ubuntu 20.04 LTS
Deep learning framework	PyTorch 2.0.1
Optimization solver	Gurobi 10.0
Programming language	Python 3.10

Additionally, Table 4 lists all the key hyperparameters of the model. This includes the parameters of the optimization module, such as the rolling horizon and the initial uncertainty set boundaries. It also covers the neural network architecture parameters of the event-driven STGNN prediction module, including the time window length, the number of graph convolution layers, the adjacency matrix construction method, and the learning rate. These parameter settings are designed to ensure that the model achieves robust and generalizable performance across different disaster scenarios.

Table 4.

Hyperparameter settings.

Module	Parameter	Value	Description
Forecasting module	Time window length T	12	Forecasting horizon: 12 hours
	Graph convolution layers	2	Capture spatial dependencies
	Adjacency matrix construction	Road distance threshold = 3 km	Spatial weight matrix WW
	Learning rate	0.001	Adam optimizer
Optimization module	Rolling cycle Δt\Delta t	1 hour	Update deployment every hour
	Initial uncertainty set boundary	±30%	Based on historical volatility
	Convergence threshold	0.50%	Stop when cost improvement < 0.50%

For a comprehensive and multi-dimensional evaluation, the proposed EDSTG-ARO model is compared with the following benchmarks:

• Historical average – Deterministic optimization (HA-Det)³³.

• Event-driven STGNN – Deterministic optimization (STGNN-Det)³⁴.

• Standard robust optimization model (RO-Model)³⁵.

• Event-driven STGNN – Stochastic programming (STGNN-SP)³⁶.

• The recent model proposed by Iwakin & Moazeni (2024) in related domains.

To provide a holistic performance assessment, evaluation is conducted along four key dimensions: service level, response efficiency, resource efficiency, and economic cost. The specific evaluation metrics are defined in Table 5.

Table 5.

Evaluation metrics.

Dimension	Metric	Abbreviation	Definition
Service level	Demand fulfillment rate	DFR	Measures system service coverage and reliability
Response efficiency	Average delivery delay	ADD	Measures system emergency response speed
Resource efficiency	Resource utilization efficiency	RUE	Measures asset input-output efficiency
Economic cost	Total operational cost	TOC	Total costs during the simulation horizon, including fixed deployment costs, variable travel costs, and penalty costs for unmet demand

Results and discussion

System service and response performance analysis

The performance of different algorithms in terms of demand fulfillment rate and average delivery delay under varying rolling decision periods is illustrated in Figures 5 and 6.

Fig. 5.

Demand fulfillment rate of each algorithm under different rolling decision periods.

Fig. 6.

Average delivery delay of each algorithm under different rolling decision periods.

Figure 5 illustrates the performance of each algorithm in terms of demand fulfillment rate (DFR). The results clearly demonstrate the significant superiority of the EDSTG-ARO model. Its DFR steadily increases from 89.8% in the first stage to 96.5% in the sixth stage, markedly higher than all other benchmark algorithms. This advantage is primarily attributed to the core ARO framework proposed in this study. Unlike deterministic methods that directly rely on point predictions (e.g., STGNN-Det, HA-Det), the ARO framework optimizes within an uncertainty set that accounts for worst-case scenarios. This means that when unexpected events cause sharp demand fluctuations, the model pre-deploys resources to cover a broader range of extreme conditions. This prevents the severe service failures that other models encounter due to prediction errors. Even compared with STGNN-SP, which incorporates uncertainty via stochastic programming, ARO’s worst-case guarantee provides a clear reliability advantage. Therefore, the experimental results convincingly answer the key question, “Why choose ARO?” By integrating ARO, the model achieves unmatched robustness, ensuring both high service coverage and system reliability where other benchmark methods fall short.

As shown in Figure 6, the EDSTG-ARO model consistently achieves the lowest average delivery delay across the entire rolling horizon, decreasing from 12.5 minutes in the first period to 11.8 minutes in the sixth period. This performance is notably faster than that of all other algorithms. In comparison, STGNN-SP fluctuates between 14.8 and 16.2 minutes, while the method of Iwakin & Moazeni (2024) records delays of approximately 17–18.2 minutes. The RO-Model, along with the deterministic optimization-based STGNN-Det and HA-Det, performs worse, with delays ranging from 19 to 24 minutes. In summary, by integrating event-driven prediction with ARO, the EDSTG-ARO model significantly reduces delivery time and enhances emergency response efficiency, thereby demonstrating a clear advantage in terms of the ADD metric.

Resource and economic efficiency analysis

This section compares the performance of different algorithms in terms of RUE and TOC under varying rolling horizons and uncertainty budgets (Γ), as shown in Figures 7 and 8.

Fig. 7.

Comparison of RUE across algorithms.

Fig. 8.

Comparison of TOC across algorithms.

Figures 7 and 8 further illustrate the model’s performance from the perspectives of Resource Utilization Efficiency (RUE) and Total Operating Cost (TOC). The EDSTG-ARO model again outperforms all benchmarks, achieving the highest average number of delivery tasks per vehicle throughout the simulation period. Specifically, RUE rises from 6.5 tasks in the initial stage to 7 tasks in the final rolling period. This performance exceeds that of STGNN-SP (6–6.5 tasks) and all other baseline methods. These results strongly demonstrate the economic efficiency and operational effectiveness of the proposed method, challenging the conventional belief that robust optimization inherently leads to excessive conservatism and resource waste. The underlying mechanism lies in the synergy between event-driven probabilistic prediction and ARO’s intelligent scheduling. Accurate predictions provide a compact and realistic uncertainty set for ARO, avoiding redundant resource allocation caused by overly conservative assumptions. Simultaneously, ARO’s two-stage optimization ensures resources are deployed precisely where they are most needed. This prediction–optimization closed-loop enables EDSTG-ARO to achieve high robustness without compromising economic efficiency, leading to an overall optimal balance of performance and cost in emergency logistics.

In terms of economic efficiency, EDSTG-ARO also delivers the best performance. As the uncertainty budget Γ increases, its operating cost rises only slightly, from 1183 USD to 1307 USD. This level is significantly lower than that of traditional methods such as HA-Det, whose costs range from 1651 to 1789 USD. The results demonstrate that EDSTG-ARO effectively controls economic costs while maintaining high service levels and response efficiency.

Overall, EDSTG-ARO outperforms all benchmark algorithms across both dimensions—resource utilization and operating cost—confirming its comprehensive advantage in emergency material distribution.

Algorithm convergence and computational efficiency

To provide detailed empirical evidence of algorithm convergence and highlight its operational characteristics under different decision scenarios, Figure 9 records the sequential changes in total system cost across three representative rolling decision periods using the C&CG algorithm. These three periods correspond to distinct challenges in the simulation: Period 1 represents the initial deployment stage of system operation; Period 2 captures the dramatic demand fluctuations during the COVID-19 scenario; and Period 3 reflects the severe transportation network disruptions caused by a blizzard event.

Fig. 9.

Convergence of the TS-ARO algorithm in representative decision periods.

Figure 9 reveals several key and expected behavioral patterns. First, all decision periods exhibit rapid convergence: total system cost experiences the most significant drop within the first 10 iterations, completing the majority of the optimization process. Second, the figure also highlights the scenario-specific variability of the algorithm. Each decision period differs in its initial cost, convergence speed, and final converged value. For example, Period 2 begins with the highest initial uncertainty (cost = 625.4) but converges relatively quickly in 17 iterations, whereas Period 1 requires 18 iterations to reach stability. These differences are reasonable, as they reflect the unique optimization problem at each time step, influenced by varying demand distributions and event impacts. This detailed numerical evidence is more compelling than idealized smooth curves, demonstrating the robust convergence of our algorithm under diverse real-world scenarios.

Table 6 compares the average computation time of different algorithms within a single decision period. The results show that, due to iterative solving of the master problem and adversarial subproblems, the proposed EDSTG-ARO model incurs higher computational overhead than non-iterative baseline methods. However, this increase in computation is a reasonable trade-off for enhanced decision robustness. Given the extreme reliability requirements in emergency logistics, EDSTG-ARO sacrifices some computation time to achieve significant improvements in demand fulfillment and delivery delay. Therefore, in the context of emergency management, this trade-off between performance and computational cost is both valuable and acceptable.

Table 6.

Average computation time per decision period for different algorithms.

Algorithm model	Average computation time (s)
HA-Det	15.3
STGNN-Det	21.8
RO-Model	115.4
STGNN-SP	132.1
EDSTG-ARO (proposed)	235.6

Conclusion

This study addresses the limitations of traditional emergency logistics decision-making under sudden events, particularly in terms of foresight and robustness, by proposing EDSTG-ARO, an AI-driven dynamic deployment model. The core innovation of this model lies in its systematic, closed-loop framework that integrates event-driven probabilistic prediction with ARO. Specifically, the designed event-driven STGNN precisely quantifies demand uncertainty induced by external events, while the ARO module seamlessly transforms this uncertainty into risk-controlled, robust decisions. Simulation experiments using large-scale, real-world data from New York City show that EDSTG-ARO outperforms existing baseline methods. The model achieves higher demand fulfillment and lower delivery delays, demonstrating its effectiveness in improving both the efficiency and reliability of emergency logistics under dynamic and uncertain conditions.

Despite these promising results, the model has certain limitations, which also suggest directions for future research. First, the computational cost of the model is relatively high, representing a reasonable trade-off for decision robustness; future work could explore more efficient solution algorithms. More importantly, as suggested by reviewers, the generalization capability of the model requires further validation across more diverse geographic contexts (e.g., cities in different countries) and disaster types (e.g., earthquakes, floods). Future research will focus on cross-scenario and cross-regional testing to further enhance the universality and reliability of the framework, ultimately aiming to develop a decision-support tool suitable for broad application in global emergency management practice.

Author contributions

L.M. wrote the main manuscript text, conducted the literature review, and drafted the discussion section. Y.C. collected and analyzed the experimental data, and prepared figures 1-8. S.S. designed the overall research framework, revised the manuscript for intellectual content, and verified the experimental results. All authors reviewed the manuscript and approved the final version for submission.

Funding

This study was supported by the 2021 Special Research Project of the Shaanxi Provincial Department of Education (Project No. 21JK0037), entitled “Research on Emergency Logistics for Uncertain Demand and Road Section Failure.”

Data availability

All data included in this study are available upon request by contact with the corresponding author.

Declarations

Competing interests

The authors declare no competing interests.