O²RDL-net for joint risk classification and delay forecasting in logistics systems using interaction amplified deep

Abstract

Transportation and logistics systems face frequent delays and operational risks due to congestion, human factors, and rapidly changing conditions. Predicting delays and identifying risk levels in advance is therefore essential for reliable logistics planning. Most existing methods handle delay forecasting and risk classification separately and often fail to capture complex temporal and interaction-driven patterns. To overcome these limitations, this study proposes O²RDL-Net, a load-aware and interaction-amplified deep learning framework for joint risk classification and delay forecasting. The proposed model integrates higher-order operational indicators, including the Risk Accumulation Index, Delay Sensitivity Indicator, Human–Operational Interaction Score, and Logistics System Representation, to capture cumulative risk, short-term sensitivity, and system-level interactions. A spatio-temporal attention encoder with risk regime modulation is used to improve learning stability and generalization. Experimental results show that O²RDL-Net achieves superior performance compared to baseline models, with a mean absolute error of 2.05, RMSE of 3.01, and R² of 0.91 for delay forecasting. For risk classification, the model reaches an accuracy of 92%, precision of 91%, recall of 92%, and F1-score of 91%. Interpretability analysis using SHAP and local explanations confirms that the model relies on meaningful and domain-consistent features. Overall, O²RDL-Net provides an accurate, stable, and interpretable solution for real-world logistics risk and delay management.

Introduction

Transportation and logistics networks play a vital role in modern economies by enabling the timely movement of goods across regions and markets. However, these networks operate under increasing pressure due to rising demand, congestion, limited infrastructure capacity, and human–system dependencies¹. As a result, delivery delays and operational risks have become frequent and costly, affecting service reliability, customer satisfaction, and overall supply chain efficiency. Accurately predicting delays and identifying risk conditions in advance is therefore a critical challenge for logistics planners and decision-makers².

In recent years, data-driven and machine learning-based approaches have been widely adopted for logistics analytics, including travel time prediction, delay estimation, and disruption detection³. While traditional statistical and machine learning models provide useful baseline insights, they often struggle to capture non-linear relationships, temporal dependencies, and interaction effects among heterogeneous operational factors^4,5. Moreover, many existing studies treat delay forecasting and risk classification as separate problems, even though both are driven by shared underlying dynamics such as congestion buildup⁶, operational overload, and human performance variability⁷. Recurrent networks, as well as transformer-based frameworks based on deep learning, have demonstrated potential in the logistics forecasting of sequential and temporal logistics data even though other applications such as agriculture targets⁸. Under complicated conditions, attention mechanisms help models to pay attention to important steps and features to enhance accuracy in prediction⁹. Nonetheless, most deep learning techniques have a strong dependence on raw input characteristics and do not have explicit ways to capture cumulative risk, sensitivity to short-term variations, and higher-order interactions between the operation subsystems and human factors¹⁰. Moreover, these models have a black-box character that prevents their implementation in the real logistics setting where explainability and trust are crucial¹¹.

Another important limitation in existing work is the lack of joint learning models that explicitly and jointly consider the issue of risk classification and delay prediction¹². The risk states and the delay magnitude are also closely related because the increasing operational risk can be a precursor of serious delays, whereas ongoing delays may indicate the occurrence of risk conditions¹³. Not taking this relationship into account will lead to disjointed predictions and interventions. Also, not many studies directly deal with the issue of temporal stability and calibration, which is essential to achieve the credibility of usage in dynamical logistics systems¹⁴.

To address these challenges, this study proposes O²RDL-Net, an Operational Overload-Responsive and Load-Aware Interaction-Amplified Deep Learning model to address these issues to perform joint risk classification and delay prediction. The developed strategy presents the higher-order constructed indicators, such as the Risk Accumulation Index (RAI), Delay Sensitivity Indicator (DSI), Human-Operational Interaction Score (HOIS), and the Logistics System Representation (LSR), to reflect the cumulative, short-term, and interaction-driven effects. Modeling the complex dependencies among the elements involves using a spatio-temporal attention encoder, interaction-aware cross-attention and risk regime modulation, and a temporal consistency constraint is adopted to ensure the stability of prediction results. The three-fold main contributions of this work are to be appreciated. First, a joint deep learning architecture is defined for predicting the risk level and delay magnitude, providing uniform and coordinated decision support. Secondly, two feature representations, namely load-aware and interaction-amplified, are proposed to reflect the real-world dynamics in logistics. Third, the model’s performance is widely analyzed in comparison with other models by experimental studies and the post-hoc interpretability analysis demonstrates that the proposed model can provide better performance, stable generalization and transparency in decision making compared with other models. All these ideas together present a feasible and reasonable way to deal with logistics issues with risk-problem consciousness and delay-consciousness.

State-of-the-art techniques in predictive risk assessment for supply chains

Initial research had determined that ML could be used to do such tasks, with classical algorithms as a starting point and more complex deep neural networks and hybrid models over time¹⁵. The research was initially done on classifying deliveries as on-time and delayed instead of predicting the degree of delay. The study noted that performance can be enhanced by integrating the data of enterprise logistics with external data (e.g. weather, location), but most models do not take into consideration the environmental factors that can be easily integrated. This gap highlights the development of simple predictive models to more holistic models in recent years¹⁶. Predicting delays ML was already used early in its development to demonstrate the worth of data-driven approaches. The regression and tree-based model on more than 1 million U.S. flights gave an R² of 0.94 and RMSE around 12.5 min when the feature such as a late arrival or carrier and weather delays are taken into consideration¹⁷. Likewise, another study examined the aspects of flight delays and achieved 84.5% accuracy with the help of a Gradient Boosting classifier. These works, however, did not completely consider class imbalance in data of delay, which the subsequent works tried to eliminate¹⁸. Coming to an airline dataset, comparing 11 algorithms and discovering that k-NN and CART classifiers performed best still, the authors also found that their models were limited because of the lack of feature engineering and imbalanced classes¹⁹. Advances in this area soon added more substantial architecture and imbalance repair to enhance predictive capacity²⁰.

The emergence of deep learning prompted scientists to use neural networks to make more precise and less sensitive predictions. The FCF-Net proposed which is a cost-sensitive deep model that was used to identify the patterns of train delay propagation using CNN and fully connected networks. They successfully applied CNN images and class weighted training to their model to surpass the traditional models in performance²¹. Advanced deep models have also come out in the air transport industry. In literature, a delay-propagation network is used in conjunction with a multi-label Random Forest, achieving a higher rate of prediction of the arrival delay (86.7%) due to an explicit concurrent delay cascading model across flights²². Going even more, with hybrid CNN-LSTM models that can learn spatio-temporal relations within flight networks with an accuracy of about 90%²³. These deep learning methods signaled a change to networks of intricate interdependencies in logistic networks to graph structures in airline hubs to spatiotemporal dynamics in railway systems. Worth noting, numerous recent works are not only focused on accuracy, but also interpretability and compatibility with other methods. As an example, the interpretable deep learning-based supply chain demand forecasting with self-organizing maps with ANN and SHAP analysis to explain their results. This gave precise forecasts as well as pointing out macroeconomic and demand conditions that encouraged delivery delays²⁴. The other trend is the combination of ML and the metaheuristics or optimization. Using a hybrid method, which is a Decision Tree regressor and Firefly Algorithm to select the features and optimize the hyperparameters. They used a large Dataco supply chain dataset (180k records) to model shipment delay durations and the results obtained a very high R² which was significantly higher than the baseline regressors²⁵. Application of Firefly Algorithm enhanced the generalizability as it reduced overfitting. This shows the advantage of hybrid ML methods in dealing with logistics data complexity²⁶.

The integration of deep learning with other innovative approaches has been shown to be useful in real-time and proactive risk management. Introducing a hybrid model which combines deep neural networks and reinforcement learning to classify supply chain delivery risk²⁷. The study initially optimized CNN, LSTM, Bi-LSTM and XGBoost models and discovered stacked and bidirectional LSTMs to be generalized well when optimizing predictive late orders. Based on them, they launched a proximal policy optimization agent that considers the output of the deep model as its state. The resulting DL-RL hybrid obtained higher F1-score in differentiating between on-time and late deliveries, which is far higher than in individual learners²⁸. Logistic areas and stress situations have also been implemented using deep learning. To predict risks in shipments during COVID-19 disruptions, we examined different DL models. They trained recurrent networks (LSTM, BiLSTM, GRU) and a Temporal Convolutional Network (TCN) on binary risk classification and evaluated six classifiers on the classifier trained features²⁹. The TCN-based model on an export dataset of the pandemic era was able to predict with success rates of close to 100% whether a shipment would leave under restrictions. This level of performance, although potentially resilient, begs the question of overfitting to the exceptional circumstances of COVID³⁰. Elsewhere, not to mention the crucial area, ML automated to anticipate seaport disruption threats caused by natural hazards. They tested 24 AutoML pipelines on a global port dataset of 2010–2019 and discovered that wide neural networks achieved the highest accuracy. Their model emphasized their key features of hazard severity, recovery time which determines whether port operations will experience big delays or not. This is useful information with regards to port resilience; however, the researchers acknowledge that the data is not detailed enough and suggest that using a more detailed and comprehensive multi-port interaction data³¹. would be helpful.

These collectively show that deep models can effectively predict the risk of disruption of a transport network and supply chain when trained on data relevant to a particular domain, such as a representation of extreme events. It has also been observed that there is a rise in the research on delay prediction in different modes of transport. In this research, the authors present a visual servo predictive control (VSPC) scheme based on neurodynamic for omnidirectional logistics robots to solve the nonlinearities and physical/visual constraints. The approach enables smooth motion and constraint satisfaction with quasi-min–max MPC with LMI optimization, which has been validated by experiments conducted on the real world. The approach allows for smooth motion and constraint satisfaction, with the help of quasi-min–max MPC with LMI optimization and has been validated through experiments on the real world³². ML in the context of the public transit of ferry boats, combining weather and ridership data with general transit feed specification schedules. On two case studies (Sydney and NYC) they discovered that, although both SVR and deep neural nets were good in city-specific tasks, the Gradient Boosting machines had the best tradeoff between accuracy and efficiency³³. A multi-task Temporal CNN (MT2CN) in the roads to simultaneously forecast traffic emissions and travel delays on the intersections of urban areas. Their model outdid single-output models because the interdependent nature of congestion on delay and pollution was learnt, to ensure more precise and comprehensive predictions to traffic management. They also used SHAP explainability to enable traffic engineers to learn about contributing factors³⁴.

Recent developments in the railway field address the problem of delay propagation on the network level. Multivariate Event Hypergraph Diffusion to predict the delay of trains in regions. Through their representation of coordinated train schedules as a mixed hypergraph and diffusion convolution-based approach, they were able to model high-order spatiotemporal correlation between multiple lines of train schedules³⁵. Evidently, in all types of transport, including the air, sea, road, and rail, society has been shifting towards the more customized deep learning techniques that consider the specifics of each of the networks. Supply chain resilience and risk mitigation through predictive analytics is also another direction worth mentioning. The case studies in the fields of Ecommerce³⁶, pharmaceuticals, agriculture³⁷, automotives³⁸ and energy³⁹ with five deep learning models (ANN, CNN, RNN, LSTM, GRU)⁴⁰. DL models forecasted demand or logistics risks within each industry, and they were frequently more accurate than the conventional ones⁴¹. An example is that CNN had 89.3% accuracy in a pharmaceutical logistics case (avoiding stock-outs), and GRUs reduced errors in forecasts of food and automotive supply. These outcomes reveal the flexibility of DL in any supply chain setting⁴². Nevertheless, both models were fitted to a given industry dataset, hence there might be a lack of generalization. A big data strategy, developing a unified ML pipeline of supplier delay risk to a multinational manufacturer. These researchers used a combination of big data architecture and ML models to make predictions of late deliveries of supplies in an electronics supply chain. They did not only report the accuracy but also predicted the financial implications of errors in the predictions on the cost of inventory. They tested their model with real factory data to provide realistic risk estimation without the need for the conventional, yet unrealistic assumption of fixed lead times⁴³. The practical orientation (predictions/expenditure) is a sign of maturity of the discipline to be used in decision-making.

Limitation of existing studies and motivation for the proposed method

As demonstrated in the literature, the previous machine learning models were supplanted by the more advanced deep learning models and various hybrid frameworks to predict risk assessment and delay forecasting in the logistics network⁴⁴. Initial research mainly used classical models including the decision trees and the regression methods that did not work well to explain complicated temporal dynamics and contextual relationships as seen in Table 1.

Table 1.

Comparative Summary of Existing Studies of recent benchmark approaches highlighting key models, techniques, datasets, reported performance metrics, core strengths, and notable limitations, to contextualize the contributions of the proposed O²RDL-Net.

Refs.	Approach	Technique & features	Dataset	Results (metric)	Strength	Limitation	Research focus
17	RF vs. regression & tree models	Multi-factor delay model (315 features); classical ML (regression, CART, RF)	1 M US domestic flights (2018)	R² = 0.04, RMSE = 12.5	High accuracy; identified key delay causes (late aircraft, weather)	No imbalance handling; not a deep model	Flight departure delay prediction
21	FCF-Net (CNN + FCNN) with cost-sensitive loss	Treat timetable as image (CNN); fully-connected nets for metadata; class-weighted training	China HSR (2 lines, delays)	F1 gain: 78.28	Captures high-order train interactions; mitigates class imbalance	Needs large historical data; specific to railway timetables	Train delay propagation pattern recognition
22	Multi-Label RF + Propagation model	Random Forest with delay-propagation links; optimized feature selection	Chinese civil aviation data (multi-flight connections)	Acc: 86.7%	Models knock-on delays between flights; improved accuracy over single-flight models	Complexity in labeling multi-flight delays; moderate gain vs. simpler models	Flight delay prediction with propagation effects
23	CBAM-CondenseNet & SimAM-CNN-MLSTM	Deep CNNs with attention + LSTM; capture spatial-temporal dependencies	Multi-airport flight network (China)	Acc: 89.8%	Captures complex spatial-temporal patterns; high predictive accuracy	High model complexity; requires extensive training data	Flight delay forecasting
15	Hybrid RNN-ANN + Gradient Boosting	RNN and ANN ensemble; GB regression fusion; compare LSTM, SARIMA, etc.	Automotive demand data (Morocco)	R² ≈ 0.75	Combines statistical and DL strengths; improved demand forecast accuracy	Focused on demand uncertainty (indirect delay risk); not tested for delivery delays	Supply chain risk mitigation via demand forecasting
42	Comparative DL models (ANN, CNN, RNN, LSTM, GRU)	Trained five DL architectures across four sectors; case-specific tuning	Multi-industry supply chains (pharma, agro, auto, energy)	Acc: 79.3%	Showed DL superiority over traditional ML in diverse SCM contexts; improved resilience (fewer stockouts)	Case studies isolated by sector (models not generalizable across domains); lacks unified metric of risk	Predictive risk analytics for supply chain resilience
30	Hybrid Deep Learning + RL (PPO agent)	Bi-LSTM and Stacked LSTM for delay classification; RL agent refines decisions under dynamics	Retail supply chain orders (on-time vs. late labels)	F1: 73.3	Extremely high accuracy; adaptive to changing conditions; addresses class imbalance via DL features	PPO alone struggled with minority class; complexity in training RL + DL	Real-time order delay prediction with adaptive decision-making
33	Gradient Boosting, SVR, DNN (with XAI)	Merged GTFS transit data, weather, and operations; SHAP for feature importance	Ferry transit delays (Sydney & NYC open-data)	Acc: 82.3%	Showcased value of open data fusion; provided explainable insights (schedule factors most critical)	Limited to ferries; moderate accuracy (ferries inherently variable); city-specific models	Ferry delay prediction via open data analytics and explainable ML
35	MEHD: Mixed Event Hypergraph Diffusion (with Attention Denoising)	Hypergraph convolution to model multi-train interactions; diffusion for temporal event propagation	Regional high-speed rail network (multiple lines, China)	MAE: 8.2	First end-to-end model for multi-train delay propagation; captures high-order dependencies	Complex model, computationally heavy; requires granular train event data; new approach (needs replication)	Regional train delay prediction
43	Big Data ML Pipeline (ensemble)	Integrated data lake + ML models; evaluated cost impact of delay predictions	Automotive electronics supply chain (Bosch)	RMSE: 3.29	Big-data architecture for real-time risk prediction; connects predictive accuracy with business impact	Industry-specific solution; results not reported in standard metrics; complex deployment	Real-time supply delay risk prediction in manufacturing

To address these shortcomings, more modern studies have turned to the use of more advanced architecture such as recurrent neural networks (RNNs), convolutional neural networks (CNNs), attention-based transformers, graph neural networks and even AutoML systems. These new approaches improve predictive accuracy through directly incorporating the domain specific knowledge like transport schedules, supply chain structures and operational interactions among different modes into models⁴⁵. Through this technical development there has come an increased focus on practical usefulness, especially about model interpretability. Model decisions based on trust, SHAP and LIME have become popular techniques to make more transparent decisions about the model, and to make the model more reliable⁴⁶.

Despite these advances, however, there are several critical issues that remain to be addressed. Much of the literature available either discusses the detection of a delay or considers only simple regression problems, without considering the severity of the risk or quantifying the amount of uncertainty, considering the differences by aspects that are displayed in Table 2. While several models distinguish between late and on-time deliveries, relatively few are attempting to predict the actual number of delays and the impact downstream. Moreover, other factors, such as weather and economic variables, are not commonly applied and their addition could significantly improve prediction accuracy⁴⁷. The problem of event class imbalance is still present, though these techniques like resampling and cost-sensitive learning have been adopted, they are not always implemented, thus causing bias prediction. Some hybrid and attention-based models which are domain-specific without features of interaction consciousness, and without time consistency. Also, interpretability is often viewed as a post-hoc procedure and not as a part of the modeling procedure. There are new avenues that are beginning to incorporate explainability and causal reasoning, but it’s not something that’s done regularly in business.

Table 2.

Key differences between existing models and proposed.

Aspect	Existing studies	Proposed
Task Design	Mostly single-task models focusing on either delay prediction or risk analysis separately17,21–23,30,33,35	Unified dual-task framework for joint risk classification and delay prediction
Feature Modeling	Generic features or limited domain-specific inputs; weak representation of operational load and interactions15,17,42	Load-aware and interaction-amplified features using RAI, DSI, HOIS, and LSR
Temporal Modeling	RNN/CNN-based or implicit temporal modeling; lacks consistency enforcement23,30,35	Spatio-temporal self-attention encoder with temporal consistency constraint
Interaction Handling	Limited modeling of interdependencies (e.g., propagation links or static relationships)22,35	Interaction-aware cross-attention mechanism capturing dynamic dependencies
Class Imbalance Handling	Addressed partially via cost-sensitive learning or resampling21,30	Robust dual-task learning with attention modulation improving minority sensitivity
Interpretability	Post-hoc or limited explainability (e.g., SHAP in isolated models)33	Integrated SHAP + LIME for transparent and explainable predictions
Generalization & Scalability	Often domain-specific and not easily transferable across logistics systems42,43	Scalable and adaptable framework suitable for dynamic logistics environments
Overall Capability	High performance in specific tasks but lacks unified, interaction-aware, and consistent modeling	Comprehensive framework integrating performance, interpretability, and temporal stability

Despite the progress in existing studies, a clear research gap remains. As summarized in Table 2, most prior works focus on either delay prediction or risk analysis as separate tasks, using classical machine learning¹⁷, deep learning architectures²³, or hybrid models³⁰, without explicitly modeling their interdependence. Additionally, existing attention-based and graph-driven approaches capture temporal or propagation patterns but lack load-aware and interaction-sensitive feature representations, limiting their ability to reflect real-world logistics dynamics^22,35. Furthermore, temporal modeling is often implicit and does not enforce consistency across time steps. In contrast, the proposed O²RDL-Net introduces:

• A unified dual-task learning framework that jointly predicts risk levels and delay magnitude.

• Integration of load-aware indicators (RAI, DSI, HOIS, LSR) for domain-driven feature representation.

• An interaction-aware cross-attention mechanism to capture complex operational dependencies.

• A temporal consistency constraint to ensure stable and coherent predictions over time.

• A comprehensive design that combines joint learning, domain-aware feature construction, and temporally consistent interaction modeling within a scalable framework.

• A fundamental advancement over existing deep learning, attention-based, and hybrid models in logistics risk–delay prediction.

Overall, the field has shown a good level of technical innovation though there are yet to be any comprehensive solutions that cover the aspect of real deployment issues such as data latency, changing operational trends, and the human factor of decision making. It is evident that there is a need to have common frameworks that may model risk, delay, and at the same time maintain the generalizability, temporal coherence, and interpretability⁴⁸. To fill these gaps, the proposed study provides a context-sensitive dual-task deep learning model that combines temporal attention with risk-sensitive modules, namely, RAI, DSI, HOIS, and LSR. The model is also built-in interpretable with LIME and SHAP which guarantees predictive accuracy as well as operation transparency. Proposed model provides a scalable and trustworthy risk-delay forecasting tool in a dynamic logistics setting by filling the gap between explainability and performance.

Proposed research methodology

This study proposes a Load-Aware Interaction-Amplified Deep Learning framework (O²RDL-Net) for joint risk classification and delay forecasting in logistics networks. The framework shown in Fig. 1, is designed to capture operational overload dynamics, temporal propagation effects, and human–system interactions within a unified architecture.

Fig. 1.

Methodological Framework Overview of the proposed architecture integrates risk-relevant inputs to dual prediction heads for risk classification and delay estimation.

Unlike conventional pipelines that treat risk and delay as independent problems, the proposed model jointly learns both tasks by integrating shared spatio-temporal representations and task-specific output heads. As illustrated in the proposed architecture, raw operational signals are first transformed into load-aware embeddings, which are subsequently processed through spatio-temporal self-attention and interaction-aware cross-attention mechanisms. A risk regime modulation module further adapts internal representations to different operational states, while a temporal consistency constraint enforces stability across time. Finally, post-hoc interpretability modules (LIME and SHAP) are employed to ensure transparent decision support for both classification and regression outputs.

Data preprocessing and input representation

The data that was utilized in this research based on real-world logistics processes that were recorded off an integrated logistics network that was happening in Southern California. It covers a period of three years between January 2021 and January 2024 and represents multifaceted dynamics in surfaces with high traffic and multimodality in the transport path. It is obtained at an hourly resolution and is provided using GPS trackers, IoT sensors, warehouse management systems, and external providers and covers the modes of trucking, rail and drone-delivery. Overall, the dataset consists of more than 210,000 shipment-level records containing telemetry of vehicles, their working condition, environmental conditions, and human behavior. Data has all been anonymized to ensure sensitive data has been saved without compromising the richness of analysis.

A time-based data splitting strategy was used on all modeling tasks to maintain the temporal integrity and ensure that there is no leakage of information. The data was chronologically divided into three subsets: training set contained the data between January 2021 and December 2022 (70% of the data was used to learn the model), the validation set covered January 2023-June 2023 (15%), and the testing set was July 2023 to January 2024 (15%), which is chronologically consistent, without the risk of temporal leakage. This sequential splitting can provide that the models are trained on past events and assessed on future time intervals, which is in line with the real-life deployment setting. Some of the most important target variables considered in the dataset are the Delivery Time Deviation, the probability of delay, likelihood of disruption, and risk classification, as reported in Table 3, which could be used to run both a regression and a classification activity. Multimodal and multi-source character of it improves the broadening of findings and predetermines its suitability in predictive modeling in the logistics risk and delay forecasting.

Table 3.

Summary of key features in the logistics dataset, including operational, environmental, temporal, and behavioral indicators used for modeling delay and risk.

Feature name	Description	Type	Unit
Timestamp	Date and time of record (hourly granularity)	Temporal	YYYY-MM-DD HH: MM
Vehicle GPS Latitude	Latitude coordinate of vehicle	Spatial	Decimal degrees
Vehicle GPS Longitude	Longitude coordinate of vehicle	Spatial	Decimal degrees
Fuel Consumption Rate	Fuel usage rate per hour	Operational	Liters/hour
ETA Variation (hours)	Deviation between estimated and actual arrival time	Operational	Hours
Traffic Congestion Level	Level of congestion on route	Environmental	0–10 scale
Warehouse Inventory Level	Current inventory at warehouse	Operational	Units
Loading/Unloading Time	Time taken for material handling	Operational	Hours
Handling Equipment Availability	Forklift/equipment availability	Binary	0 = No, 1 = Yes
Order Fulfillment Status	Order fulfillment success	Binary	0 = Not fulfilled, 1 = Yes
Weather Condition Severity	Intensity of weather disruptions	Environmental	0–1 scale
Port Congestion Level	Port congestion status	Environmental	0–10 scale
Shipping Costs	Cost associated with shipment	Economic	USD
Supplier Reliability Score	Reliability of upstream supplier	Behavioral	0–1 score
Lead Time (days)	Average supplier delivery time	Temporal	Days
Historical Demand	Previous demand volume for logistics services	Operational	Units
IoT Temperature	Sensor-based cargo temperature	Environmental	°C
Cargo Condition Status	Status of cargo quality	Binary	0 = Poor, 1 = Good
Route Risk Level	Risk associated with selected route	Risk Indicator	0–10 scale
Customs Clearance Time	Time taken at customs	Temporal	Hours
Driver Behavior Score	Driver performance quality	Behavioral	0–1 score
Fatigue Monitoring Score	Estimated driver fatigue	Behavioral	0–1 score

To process this input representation, thorough preprocessing is necessary to clean raw data into one standard form. Let the raw logistics dataset be defined as

1

where denotes the multivariate operational input at time step \:t, represents the discrete risk label, and denotes the continuous delay value.

Class distribution & imbalance handling

The distribution of the sample size was also extremely skewed with 75% of the samples in the High-Risk category, 15% in the Moderate Risk category, and 10% in the Low-Risk category. This is likely to be a bias in the prediction towards the dominant class, and it was challenging model training with such a skewed distribution. To address this a preprocessing approach was used which entailed class-balancing by means of random under sampling of the majority class and oversampling the minority classes⁴⁹. This resulted in an even distribution among the three risk groups (~ 33% in each group) as illustrated in Fig. 2. This enabled the model to learn uniformly in all the classes, improve the generalization and make equitable decisions in various levels of risk.

Fig. 2.

Class distribution before and after processing. The left pie chart shows the original imbalanced distribution with a dominant High Risk class (75%). The right chart presents the balanced distribution (~ 33% per class) achieved through preprocessing techniques to support fair and effective multi-class learning.

Feature normalization

Each numerical feature is normalized using z-score normalization to ensure scale consistency:

2

where and are the mean and standard deviation of feature \:i, computed from the training set only.

Load-aware input embedding

The normalized features are grouped into semantically meaningful subsets representing operational load and interactions including RAI, DSI, HOIS, and LSR. These features are concatenated to form the load-aware input vector:

3

A linear embedding layer projects the input into a latent space:

4

followed by layer normalization:

5

The resulting embedding sequence

6

serves as the input to the spatio-temporal attention encoder.

Feature construction and selection strategy

Instead of relying solely on raw operational variables, the proposed framework constructs higher-order derived indicators to capture systemic behavior, instability, and interaction effects, reported in Table 4.

Table 4.

Feature construction selection strategies designed to capture systemic risk behavior and delay dynamics in transportation and logistics networks.

Component	Indicator	Input features used	Purpose
Risk Accumulation Index (RAI)	Aggregated operational stress	Traffic congestion level; Route risk level; Disruption likelihood score; Weather severity; Port congestion level	Captures cumulative system stress over time instead of isolated risk factors
Delay Sensitivity Indicator (DSI)	Delay responsiveness	Delivery time deviation; ETA variation hours	Identifies instability regions where small ETA changes cause large delivery delays
Human–Operational Interaction Score (HOIS)	Human–system coupling	Driver behavior score; Fatigue monitoring score	Models human influence as an interaction rather than an independent factor
Logistics Stress Representation (LSR)	Structured subsystem encoding	Warehouse; port congestion level; Transport (fuel consumption rate, traffic congestion, route risk)	Enables structured learning across logistics subsystems instead of flat feature concatenation

Risk accumulation index (RAI)

The Risk Accumulation Index models cumulative operational pressure over time and is defined as:

7

Where are normalized risk-related features (e.g., congestion, disruption likelihood), are learnable importance weights. This formulation allows the model to adaptively emphasize dominant risk contributors.

Delay sensitivity indicator (DSI)

To capture delay instability, the Delay Sensitivity Indicator is defined as:

8

Where denotes the change in delivery time deviation, represents short-term ETA variation. High DSI values indicate regions where small ETA changes lead to disproportionately large delays.

Human–operational interaction score (HOIS)

Human factors are modeled as interactive rather than independent variables:

9

This multiplicative formulation explicitly captures coupling between human performance and operational load.

Logistics subsystem representation (LSR)

Operational subsystems are encoded as structured vectors:

10

Where, : warehouse indicators, : port indicators, : transport indicators.

This preserves subsystem semantics and avoids information loss caused by flat feature concatenation.

Feature selection and stability filtering

A stability-driven filtering mechanism removes features with high variance but low temporal consistency⁵⁰. For a feature , a rolling stability score is computed as:

11

Features exceeding a predefined instability threshold are excluded.

Additionally, contribution-weighted selection is applied using prediction perturbation:

12

Features causing significant output deviation are retained, while interaction-dependent features are preserved even if their individual importance is low.

Model operation

The proposed architecture considers the combined model of risk classification and delay forecasting based on a common spatio-temporal representation. This model works by encoding heterogeneous operational inputs into load-sensitive embeddings, then propagating temporal dependencies using attention-based networks, enhancing significant interaction of features, and finally making task-specific predictions by using two output heads⁵¹. In contrast to traditional deep learning pipelines, the given architecture incorporates explicit interaction-aware attention, risk regime modulation, and temporal consistency regularization, which provides strong prediction in the conditions of changing and overloaded logistics. The entire working process is depicted in architectural design shown in Fig. 3.

Fig. 3.

Scientific architectural breakdown of the proposed model from input to final layers route predictions to interpretable heads supported by LIME and SHAP, ensuring explainability and reliability across temporal dynamics.

Block 1- spatio-temporal self-attention encoder

Multi-head temporal attention

The input feature vector at time step \:t utilized to capture temporal propagation of operational load, multi-head self-attention is applied over the embedding sequence⁵², which is forwarded to the spatio-temporal attention encoder. Query, key, and value matrices are computed as:

13

The attention operation is defined as:

14

Multiple attention heads operate in parallel and are concatenated to form the temporal representation:

15

Residual connections and layer normalization are applied:

16

Interaction-aware cross attention

To explicitly model dependencies between operational load and human-system interactions, an interaction-aware cross-attention mechanism is introduced⁵³. The attention inputs are defined as:

17

Cross-attention is computed as:

18

A gated fusion mechanism amplifies critical interactions:

19

This allows the model to selectively enhance feature interactions that contribute disproportionately to risk escalation or delay realization.

Position-wise feed-forward network

The fused representation is refined using a position-wise feed-forward network:

20

Dropout and residual normalization are applied:

21

The resulting tensor represents the spatio-temporal interaction representation.

Block 2: risk regime modulation module

To adapt predictions to different operational regimes, a risk modulation mechanism is applied. Attention pooling computes regime weights:

22

The representation is modulated as:

23

This step enables the model to distinguish between stable, transitional, and high-risk operating regimes before task-specific prediction.

Block 3: dual-task prediction heads

Risk classification head

Risk prediction is formulated as a multi-class classification task:

24

where the output corresponds to Low, Moderate, and High-risk classes.

Delay forecasting head

Delay prediction is modeled as a regression task:

25

The shared representation allows mutual learning between risk and delay tasks while preserving task-specific objectives.

Block 4: temporal consistency regularization

To prevent unstable temporal predictions, a consistency constraint is imposed:

26

This regularization encourages smooth transitions in both risk and delay outputs across time.

Block 5: interpretability module

Finally, LIME and SHAP are applied post-hoc to extract local and global explanations for both outputs, enabling transparent assessment of feature contributions and model decisions.

Model optimization and training strategy

The proposed O²RDL-Net is trained using a joint multi-task optimization objective that simultaneously minimizes risk classification loss, delay forecasting error, and temporal inconsistency, measures are reported in Table 5. The overall loss function is defined as:

27

Table 5.

Hyperparameter configuration of the proposed O²RDL-Net.

Category	Hyperparameter	Value
Input & Embedding	Embedding dimension	128
	Input projection dropout	0.10
Attention Encoder	Number of attention heads	8
	Key/Query dimension	16
	Attention dropout	0.10
Feed-Forward Network	FFN hidden dimension	256
	FFN activation	ReLU
	FFN dropout	0.20
Interaction Amplification	Gating activation	Sigmoid
Risk Regime Modulation	Attention pooling dimension	64
Output Heads	Risk classes	3
	Risk head activation	SoftMax
	Delay head activation	Linear
Training	Optimizer	AdamW
	Learning rate	1e-4
	Weight decay	1e-5
	Batch size	64
	Epochs	20
Regularization	Temporal consistency weight	0.2
Early Stopping	Patience	8

Where is the categorical cross-entropy loss for risk classification, is the mean absolute error (MAE) for delay forecasting, enforces temporal smoothness between consecutive predictions, and control task balancing and temporal regularization, respectively.

The network parameters are optimized using the AdamW optimizer, which decouples weight decay from gradient updates to improve generalization. A learning rate of is employed with early stopping based on validation loss to prevent overfitting. Dropout is applied across embedding, attention, and feed-forward layers to further enhance robustness under fluctuating operational conditions.

Comparison based models

To develop a universal performance standard, a portfolio of baseline models in terms of both classical and deep learning paradigms. In the case of regression exercises, the fundamental model was Linear Regression, which was not regularized, and the Ridge Regression had the regularization of L2 to prevent overfitting and enhance generalization⁵⁴. The TCN was used because it can model long-range dependencies on a dilated convolution and causality of time data. Logistic Regression was applied in the classification field as a probabilistic linear classifier and the Random Forest offered a strong ensemble-based model that had the ability to deal with non-linear relationships by aggregating decision trees⁵⁵. In the case of models that tackle regression and classification simultaneously, an Attention-based LSTM is used, that is like standard LSTMs with an additional temporal attention mechanism to highlight steps that have the greatest impact⁵⁶. Transformer Encoder architecture was added since it has a parallelizable self-attention mechanism and proved successful in time-series modeling⁵⁷.

To have stringent benchmarking, the training of all models was conducted on the same data splits and early stopping policies. In simpler models such as Linear and Ridge Regression, the hyperparameters were either defaulted or grid-searched, as is common in practice⁵⁸. The more complicated models like the Random Forest, TCN and LSTM were grid or manually tuned to basic architectural parameters. Transformer Encoder and the proposed model used more sophisticated models such as AdamW optimization with dropout and regularization and early stopping (patience = 8). The design of the proposed model as outlined in Table 6 shows its architectural depth and specialized heads and thus requires an intensive training program. This standardized design would allow a fair comparison and underline the added value of the suggested design dual-task learning.

Table 6.

Hyperparameter configuration and optimization strategy used across baseline and comparison with proposed models to ensure fair benchmarking and evaluation.

Model	Key hyperparameters
Linear Regression	Regularization: None, Optimizer: Normal Equation/OLS
Ridge Regression	Regularization Strength (α): 1.0, Solver: auto
Logistic Regression	Penalty: L2, Solver: liblinear, Max Iter: 1000
Random Forest	Trees: 100, Max Depth: 10, Criterion: Gini, Min Samples Leaf: 2
Temporal CNN (TCN)	Kernel Size: 3, Filters: 64, Dilation: [1, 2, 4], Dropout: 0.2
Attention-based LSTM	Layers: 2, Hidden Units: 128, Attention: Scaled Dot Product, Dropout: 0.2
Transformer Encoder	Heads: 4, Hidden Size: 128, FFN Dim: 256, Dropout: 0.1, Layers: 2, Optimizer: Adam

Performance evaluation measures

The proposed model is evaluated based on task specific metrics that would be suitable towards the objective of classification of risks and prediction of delays. The classification task model performances that can capture the level of overall correctness, class-specific reliability and robustness in the presence of imbalance between classes are Accuracy, Precision, Recall and F1-score. For regression tasks, the Mean Absolute Error (MAE) is used to estimate the absolute error of prediction, while the Root Mean Square Error (RMSE) is used to estimate the error in predicting variance, and in the process, goodness of fit is tested using the coefficient of determination (R2). For the sake of further gauging the reliability of a delay forecasting in case of the presence of operational variability, both Mean Absolute Percentage Error (MAPE) and symmetric MAPE (sMAPE) are added, which provides an error interpretation without scale⁵⁹. All metrics are generated on held out test data, are unbiased and can be compared with baseline models.

Results and discussion

In this section, the experimental results of the proposed joint risk classification and delay forecasting model in logistics networks are presented. The results of the proposed framework are compared with well-known baseline models using measures of standard classification and regression. Analysis of the results is performed to evaluate the predictive accuracy, temporal stability and the effectiveness of the interaction-aware and load-aware modeling components. The benefits of the proposed architecture in terms of better risk discrimination and delay estimation in different operational scenarios are discussed and implications for logistics decision-making are explored.

Proposed framework is compared to the standard classification and regression variables on the basement models in terms of efficiency. Results analysis is conducted to check the predictive accuracy, temporal stability, interaction and load component effectiveness of the model. In particular the capacity to understand how the proposed architecture can improve the risk discrimination and delay estimation in the scenarios of change of the operational conditions, and practical impacts of these improvements in logistics decision-making. The outcomes of the experiment show that the model is more effective on both delay prediction and risk classification problems in comparison to traditional machine learning models and advanced deep learning baselines. Traditional linear regression models like Linear and Ridge Regression have relatively large error values (MAE > 3.7, RMSE > 5.2) which implies that they are not very good in reflecting non-linear and time-dependent logistics dynamics. Even though TCN is more effective in sequential patterns modeling compared to attention-based architecture, its performance remains worse, which supports the significance of adaptive dependency modeling in logistics settings, reported in Table 7. To illustrate the classification task, the traditional classifiers like the Logistic Regression and the Random Forest are reasonable in terms of their baseline performance yet they are unable to maintain high score on recall and F1-scores especially when operating in complex and overlapping risk environment, reported in Table 8.

Table 7.

Results analysis in regression modeling for delay forecasting. Evaluation across various benchmark and proposed models, highlighting predictive precision and error reduction.

Model	MAE	RMSE	R²	MAPE (%)	sMAPE (%)
Linear Regression	3.92	5.48	0.61	28.6	26.4
Ridge Regression	3.75	5.21	0.64	26.9	24.8
Temporal Convolutional Network (TCN)	2.89	4.12	0.78	19.4	18.1

Table 8.

Results analysis in classification modeling for risk assessment. Performance metrics are reported to demonstrate each model’s discriminative power and reliability.

Model	Accuracy	Precision	Recall	F1
Logistic Regression	0.78	0.76	0.74	0.75
Random Forest Classifier	0.83	0.82	0.81	0.81

However, models with shared representations using deep learning are significantly more accurate, the Transformer Encoder having an accuracy of 0.89. Prediction errors are also decreased by attention-based LSTM and Transformer Encoder models, which proves the presence of effective temporal attention mechanisms. Nonetheless, the proposal offers the lowest MAE (2.05) and RMSE (3.01) and the highest R (0.91), and thus, it has a greater level of accuracy and stability in prediction of delays. The further decrease in MAPE and sMAPE hints at the fact that the suggested model is not merely valid in absolute terms, but also strong and stable with respect to the different scales of delay, which is indispensable to operational planning and service-level agreement (SLA) compliance in the real-world logistics systems.

The suggested model demonstrates even better performance in classification, with an accuracy of 0.92, balanced precision-recall rates, which shows the high credibility of this method in distinguishing between low, moderate, and high-risk operational states. the outcomes are indicative of the viability of the suggested structure of real-time logistics decision support, reported in Table 9. Concurrent risk and delay learning allows the model to predict the disruption of operations and measure the impact of such disruptions in terms of time. Additionally, the use of interaction-aware attention and modulation of risk regime enables the model to logically respond to changing load conditions and, therefore, can be used in transportation and logistics networks that are dynamic in nature. These good performance gains coupled with readable outputs make the model even more practical to us since the model aids in making informed decisions by the logistics managers.

Table 9.

Joint results analysis using the proposed unified model. Combined regression and classification metrics are presented to reflect the effectiveness of dual-task learning in transportation and logistics networks.

Model	MAE	RMSE	R²	MAPE (%)	sMAPE (%)	Accuracy	Precision	Recall	F1
Attention-based LSTM	2.63	3.84	0.82	16.8	15.6	0.86	0.85	0.84	0.85
Transformer Encoder	2.41	3.52	0.86	14.9	13.8	0.89	0.88	0.87	0.88
Proposed O²RDL-Net	2.05	3.01	0.91	11.7	10.9	0.92	0.91	0.92	0.91

The comparative analysis shows clearly that the proposed model has better performance than the baseline methods in regression and classification procedures. Proposed model has the best MAE (2.05) and RMSE (3.01) in regression-based delay forecasting as demonstrated in Fig. 4, significantly outperforming both classical models, Linear Regression (MAE: 3.92, RMSE: 5.48) and Ridge Regression (MAE: 3.75, RMSE: 5.21), and deep-temporal models, including TCN (MAE: 2.89, RMSE: 4.1. This shows its improved predictive accuracy and minimized error values in modeling complicated operation delays. When viewed on the classification provided in Fig. 5, proposed model has the best Accuracy (92) and F1-score (91) and significantly outperforms Logistic Regression (Accuracy: 78, F1: 75) and Random Forest (Accuracy: 83, F1: 81). Despite the depth of learning models, including attention-based LSTM and Transformer encoders, proposed model still has a consistent advantage in discriminatory power and generalization. These findings validate the usefulness of the proposed model in terms of capturing operational dynamics and interdependences between risks and delay as well as providing robust and reliable predictions. This proves the feasibility and efficiency of the suggested approach, in practice, as a logistics forecasting model. At the same time the result of the proposed model gives rich interpretative information along with the metrics of accuracy.

Fig. 4.

Evaluation comparison of regression error metrics in term of MAE and RMSE across baseline and proposed models for delay forecasting.

Fig. 5.

Comparative analysis of classification performance for risk prediction models with traditional classifiers and proposed model in both accuracy and F1-score, demonstrating its effectiveness in balanced risk classification.

The epoch-varying trends of MAE depict a distinct variance in learning behavior, stability of convergence and ability to generalize across the comparable regression models, shown in Fig. 6. Phase I (epochs 1–4) shows that all models have fast error reduction as first pattern recognition by the training data occurs. Nonetheless, linear regression does not improve significantly even at early epochs, suggesting that it cannot save non-linear and time-dependence traits of logistics delay dynamics.

Fig. 6.

Regression Performance Analysis Training and Validation w.r.t MAE of all models.

The increasing discrepancy between its training and validation curves also indicates a lack of generalization and sensitivity to difference in data. Phase II (epochs 5–12) The deep learning models are more controlled in their learning behavior. The TCN obtains persistent error decrease, but it has moderate variability in validation MAE, suggesting that it is a bit sensitive to noise in time and fixed receptive fields. Attention-based LSTM is a better generalizer because the long-term dependencies are adaptively represented but still, the train-validation divergence is vivid in the middle of the epoch, which suggests that the underlying instability continues to exist under varying conditions of operation. This gap is further reduced by the Transformer Encoder which enjoys the self-attention mechanisms that are more effective in capturing the global temporal relationships, although a small oscillation in validation continues. The proposed model in Phase III (epochs 13–20) has the lowest and most consistent MAE of training and validation. It is remarkable that the training and validation curves are separated by a small distance, which indicates high levels of generalization and good regularization. The interaction-conscious attention and risk regime modulation and the temporal consistency constraint of the model are credited to this stability, which in combination inhibits overfitting and at the same time maintains predictive sensitivity. Conversely, baseline models, especially linear regression, retain a broader error margin during training, which justifies their inability to be used in real world logistics forecasting. The regression analysis proves that the proposed model not only converges at a faster pace, but it also has better stability and strength between the epochs.

According to the feature impact analysis as shown in Fig. 7, the DSI and LSR have the highest impact on the delay prediction as compared to the RAI. This shows that short-term responsiveness in ETA changes and system-wide patterns of congestion are the dominant factors in establishing delays in deliveries, although cumulative risk is also a stabilizing long-term effect. Conversely, other features like HOIS and Weather Severity exhibit a moderately strong influence and this implies that human system interplay and environmental factors influence delays through its interaction with operational load and not as independent agents.

Fig. 7.

The feature impact analysis for delay forecasting using O²RDL-Net, showing the relative contribution of constructed and operational features to predicted delivery delay.

A feature effect analysis with sparse confidence indicators is given in Fig. 8 to further comprehend individual features effect on delay results on their own value ranges. This monotonic increase of DSI, and its smooth increase, respectively, prove a high-sensitivity regime, in which slight changes of DSI cause disproportionately large changes in predicted delay. This behavior is consistent with the real-life logistical cases where even small ETA changes may create large-scale delivery problems. The RAI curve shows a slow but steady growth which is characteristic of the cumulative nature of the operational risk with time. On the contrary, HOIS portrays a limited contribution pattern which means that, though human-system interactions do affect delay, the impact of these interactions becomes saturated at some point. The confidence indicators also demonstrate that in areas of high impact, the level of prediction uncertainty is higher, which supports the significance of modeling variability explicitly due to interactions. The interaction between accumulated risk and delay sensitivity is represented jointly in Fig. 9 that shows the surface of interaction between RAI and DSI. Out of this surface two separate operational regimes can be identified. The area to the lower-left translates to low-impact operating zone, both accumulated risk and sensitivity are low, and therefore delay behavior is predictable and stable. On the other hand, the upper-right area underscores a high delay interaction regime, in which a concomitant rise in both RAI and DSI results in a steep rise in delay intensity. Such non-linear interaction indicates that delay escalation is not caused by either of the isolated factors but the interaction between the factors has been amplified, so the design of the interaction-awareness attention and risk regime modulation layers in the proposed model is supported.

Fig. 8.

Feature effect analysis with sparse confidence indicators, illustrating how normalized feature values influence predicted delay and associated uncertainty across different operating ranges.

Fig. 9.

Interaction surface of RAI and DSI, highlighting low-impact and high-delay operational regimes and their combined effect on delay intensity.

In the case of enhancing transparency and realistic trustworthiness, post-hoc interpretability measures were utilized to understand both global feature impact and instance-level decision making of the proposed model. The analysis is a hybrid of SHAP-driven global explanations and local contribution visualization, which allows one to understand fully how the operational features produce the model predictions.

As illustrated in Fig. 10, SHAP summary plot displays the total contribution of input features and the directional effect of the input features on the model output. The most influential factors are the RAI and the DSI with the most extended distributions of SHAP values. An increase in values of RAI and DSI (in lighter colors) is also linked mainly to positive values of SHAP, which imply that there is a significant contribution to higher predicted delay or higher risk. This verifies that cumulative operational exposure and sensitivity to ETA changes in the short run are the main factors in the decision-making process of the model. Conversely, other features like Port Congestion and Weather Severity exhibit relatively slim SHAP distributions with most of the values near zero, and hence, their effect can be more context-dependent and in most cases, the effect may be mediated by the higher-level indicators. HOIS and the Transport Load show some moderate yet consistent contributions with the SHAP values showing that an increase in human-systems interaction and transport use is more likely to take the predictions to higher delay or risky states. Notably, the two-way propagation of SHAP values of these features underscores the fact that the model has non-linear and conditional effects, as opposed to monotonic assumptions.

Fig. 10.

SHAP summary plot of the global feature importance and directional influence on output of the proposed model. The intensity of the color indicates the size of the features, and the horizontal dispersion indicates the stability and variation of the contribution of each feature.

To complement the analysis done on a global scale, Fig. 11 (a) provides a local explanation of a representative prediction based on a contribution breakdown. This visualization breaks down the output of the model into terms of positive and negative contribution of features to the predicted value. A high value of RAI in this case has the biggest contribution in the positive shift of prediction, with DSI and HOIS having a supportive effect. On the contrary, smaller values of Port Congestion and Transport Load have a slight offsetting effect on the prediction; this demonstrates that the model combines conflicting signals, not equalizing all features equally. The feature-value further bases the explanation on actual measures of operation, which adds to its interpretability by practitioners, as in Fig. 11 (b). Collectively, these post-hoc explanations show that proposed model is a consistent decision maker, which focuses on the accumulation of risk and sensitivity-based dynamics and consider human and environmental factors in a subtle way. This clarity is essential especially when dealing with the applied logistics systems, where stakeholders need more than just the correct prediction, but also justifiable reasons as to why risk warning signals and delaying forecasts so that they can make informed operational intervention.

Fig. 11.

Local, post-hoc explanation of individual prediction: (a) LIME-type contribution-style analysis (b) displaying both positive and negative influences of features on the output as well as associated feature values.

The comparison of the epoch-wise classification shows that there are different learning styles and discriminatory abilities of the assessed models through the three training stages, shown in Fig. 12. Phase I (epochs 1–4) All models demonstrate the rapid gains in their performance, which is the initial learning of the patterns based on the data. Nevertheless, conventional algorithms like Logistic Regression exhibit premature saturation and low accuracy and F1-scores, which implies poor discriminative ability in the context of overlapping and non-linear risk patterns. This is in line with the linear decision boundaries used by such models which are inadequate in complex classification of logistics risks. In Phase II (epochs 5–12), ensemble and deep learning models show better feature refinement and generalization. Random Forest classifier generates moderate gains as it can capture non-linear relationships, but its results vary across epochs, implying that it is susceptible to the noise of features and poor time information. The Attention-based LSTM has a smoother improvement, as it has the advantage of sequentially modelling temporal dependencies, but the oscillation in validation accuracy and F1-score is still evident, and it suggests that it is partially unstable across different regimes of operation.

Fig. 12.

Comparison between models of classification based on their epoch-wise performance in terms of accuracy and F1-score. The plot brings to the fore three learning stages, namely, a rapid gain in discrimination, feature refinement, and decision stability, which demonstrate the better convergence, stability, and the ability to separate different classes that the proposed attains as opposed to the base models.

Transformer Encoder is an additional feature that improves classification by using global self-attention, which makes the learning curves smoother and the overall accuracy of the model higher than that of the LSTM-based models. During Phase III (epochs 13–20), the suggested model shows significant and steadiest validation accuracy and F1-score. The low distance between epochs and the lack of drastic variations imply high generalization and stability of the decision. This high performance may be due to the interaction-aware attention of the model, modulation of risk regime and the common representation learning which together contribute to increasing the separability of classes between low, moderate, and high-risk states. It is worth noting that it demonstrates balanced accuracy and recall during training, which is the presence of competent recognition of risk-full situations that are of higher importance without generating too many false alarms. The results of the classification suggest that it can be used to monitor operational risk in logistics networks. Its capability of early discrimination, which is then followed by converging stabilization, makes it appropriate to be deployed in real time where consistent and interpretable risk notifications are needed. By contrast, baseline models either converge too soon or have unstable decision boundaries, which restricts their capability to work in high load and dynamic logistics.

The classification-oriented interpretability analysis supports well the fact that the proposed acquires meaningful and operationally consistent decision boundaries to categorize risks. As shown in Fig. 13, the feature importance analysis reveals that the most effective contributors to predicting risk classes are the DSI and LSR and the third and fourth most influential factors are RAI. This ranking indicates that both temporary fluctuations in the delivery schedules and systemwide patterns of congestion can be decisive in defining the presence of risk conditions, whereas the cumulative exposure serves as a reinforcement contextual phenomenon.

Fig. 13.

Feature importance of risk classification provides the proportion of constructed and operational features which are significant in predicting risk classes.

Other features like HOIS, Traffic Load and Port Congestion have a moderate contribution of features, as they have an indirect but not negligible impact on operational risk. The fact that the classes of risks can be separated in different operational regimes is also demonstrated in Fig. 14, which shows a distinct and progressive rise in the mean class confidence between stable and escalated regimes. At low RAI DSI, low confidence values of low, medium, and high risks are close hence there is an overlap in the operating state. But, as the system moves towards mid and high RAI -DSI regimes, the separation of classes in terms of confidence is more pronounced, especially about the high-risk category. This practice underscores the fact that the uncertainty in alerting risks in stressful conditions due to its dynamic adjustment of classification confidence to changing operational conditions.

Fig. 14.

Separability of risk classes between operational regimes induced by RAI and DSI, which shows confidence of mean classes with low, medium, and high risk with standard deviation.

Human-system interaction has been directly captured in risk escalation since the surface of interaction between the HOIS is visually represented in Fig. 15, where driver behavior and fatigue monitoring scores are visualized. Interaction areas where the risk is low and high can be observed on the surface, and the risk level grows non-linearly with the behavioral deviation and fatigue. It is also possible to consider the fact that the alignment of the areas implies that the given model is not based on rigid boundaries but rather learns continuous interaction impacts, which will enable the early detection of new human-made risk patterns. This is especially critical with real world logistics systems, where human factors tend to increase the operational risks in small but compounding ways.

Fig. 15.

HOIS Interaction surface to identify risk classification, and the low-risk and high-risk areas of human-system coupling by driver behavior and fatigue monitoring scores.

The subsystem level analysis presented in Fig. 16 gives more information on how various logistics elements can play a role in classifying risks in various operational regimes. The findings suggest that the contribution of the subsystem by stable to escalated regimes increases steadily, which proves that the hypothesized model to explain the amplification of risk according to the regimes. Transport is the subsystem with the most significant and vivid rise in contribution, especially in escalated circumstances, which identifies it as the core of contributing to risk as logistics processes approach capacity constraints. The increase in the Warehouse subsystem is moderately but steadily growing, which indicates gradual build-up of inner operational pressure whereas Port contributions are relatively smaller and yet steadily increasing, which represents their designation as secondary bottlenecks. The addition of the uncertainty bands and distributional dispersion also proves that although the mean trends are monotonically rising, the variability is the greatest in the transition regime, where the operational states are not completely separated, and risk boundaries are not so clear. This action is consistent with a real-life logistics environment, where intermediate congestion usually gives unclear risk indicators. The fact that proposed model can maintain the stability of mean trends amidst uncertainty is an indication of its strength in terms of being able to cope with the heterogeneity of the subsystem dynamics. To build upon the insights provided at the subsystem level, Fig. 17 examines how prediction confidence, empirical accuracy and calibration gap varies throughout the training process. In the initial periods, it is observed that the model develops the prediction confidence very quickly as indicated by sharp increase in the mean confidence.

Fig. 16.

Subsystem-level influence of the LSR on the risk classification in all operational regimes in terms of the mean contributions along with the uncertainty distributions of warehouse, port and transport subsystems.

Fig. 17.

Change in prediction confidence and empirical accuracy with training era as well as uncertainty and calibration gap, depicting confidence building, calibration correspondence, and predictive consistency.

This stage is associated with first feature discrimination when the uncertainty is still rather large. Under the calibration alignment stage, both confidence and empirical accuracy will meet, whereas the calibration gap will consistently fall showing that there was an enhancement in the alignment between the forecasted probabilities and the actual results. It is important to note that the uncertainty region with hues becomes increasingly smaller as time goes on implying that the predictions of the model will be more stable. During its last training stage, the model is stable and reliable in predictions, which are highly confident, high empirical accuracy and the calibration gap is low. The results of these analyses, along with other findings, confirm the applicability of the proposed model to real-world situations in transportation and logistics decision support, by supporting the following findings: it successfully differentiates risk across subsystems and regimes, and it offers reliable prediction and uncertainty sensitive and calibrated prediction.

To ensure transparency and trust in the proposed O²RDL-Net, post-hoc interpretability techniques were used to study the global decision behavior as well as the predictions on per-instance basis for the risk classification task. This dual level analysis provides insights into what features are most important in general, but also to the extent that each feature is important to a particular risk decision. Figure 18 depicts the worldwide SHAP-based feature prominence analysis which demonstrated that RAI and the DSI provide the greatest effect in risk class decisions. Their mean absolute SHAP values are higher which implies that accumulated operational exposure and short-term delay volatility is regularly determinant in the risk discrimination of the model. HOIS plays a moderate role and emphasizes the importance of human-system coupling in the determination of the risk outcomes. On the other hand, the value of SHAP of Transport Load, Port Congestion and Weather Severity is relatively smaller, indicating that these variables affect the risk factor not as the predictors themselves but as the factors that interact with other higher-level predictors. This level corresponds perfectly to the knowledge of the logistics domain, in which systemic and temporal aspects often surpass the single signals of the environment.

Fig. 18.

Global feature importance to risk classification with SHAP, displaying the mean absolute contribution of constructed and operating features to the predictions.

In addition to the global view, Fig. 19 (a) gives a local account of a representative prediction in the form of a contribution breakdown as in LIME-style. In this case, the Moderate Risk category receives the most significant probability due to the increased values of RAI and HOIS, and other positive values of DSI contribute to this probability. Meanwhile, comparatively lower values of Port Congestion and Weather Severity have a moderate effect on the predictive, not allowing it to go to the classification of high risk. This balance pattern of contribution shows that model combines antagonistic signals instead of enhancing all the high-valued features equally, leading to subtle and context-sensitive risk decisions, as shown in Fig. 19 (b). The post-hoc interpretability test verifies that the suggested model relies on its predictions based on the meaningful feature relationships that can be implemented in a domain. The consistency of global significance tendencies with local decision rationale augurs well with the suitability of the model to actual-life logistics risks surveillance, where the explainability and justification of risk warning is critical to the operational decision-making process.

Fig. 19.

Local post-hoc model of a typical risk classification choice (a) showing the probability of the classes and (b) the contribution of positive/negative features to the desired outcome.

In general, both experimental and interpretability findings can be collectively used to show that the suggested model is a powerful and practically feasible solution to joint delay forecasting and risk classification in transportation and logistics networks. In regression tasks, the model has the fewest prediction errors and most robust training-validation behavior, which means that it has great generalization in dynamic operational scenarios. At the same time, it has better classification performance indicating apparent risk class separability, robust-calibrated confidences, and stable decision stability over the training stages. The interpretability analyses also display that models are premised on meaningful, domain-consistent feature relationships and that RAI and DSI are dominating predictors, while human system and subsystem relationships are adaptive amplifiers and not initiating factors. Notably, the model can be used to describe non-linear interactions and regime-dependent behavior and is thus capable of early identifying growing risk and predicting the delay adequately. Combined, these results prove that the proposed architecture is not only better at making predictions but also provides transparent, stable and operationally actionable insights, which is why it is most effectively applicable to the real-life implementation in complex logistics and transportation systems.

Figure 20 of the reliability diagram is a valuable indicator of the calibration behavior of the proposed model in all the three categories of risks. The curve of the High-Risk class is in close relation to the diagonal line which means good calibration and good probability measures. Conversely, the category of Moderate Risk demonstrates a slightly negative under-confidence pattern, that is, the predicted frequencies of the classes are slightly lower than the real frequencies of those classes. This is an indication of guarded enthusiasm, which can possibly be tolerated in risk-averse applications. The Low-Risk classification, however, has a uniform deviation on the side of the ideal calibration line, suggesting overconfidence, that is, the model is more confident in its decisions of low risk than it should. This is one of the ways in which the model could be improved with post-training calibration methods including temperature scaling or focal loss to address the misclassification confidence. Overall, the figure confirms the fact that the model is more calibrated on high-risk situations that are usually urgent in operational logistics decisions.

Fig. 20.

Reliability diagram showing calibration performance across High Risk, Moderate Risk, and Low Risk classes. The dashed diagonal line indicates perfect calibration, where predicted probability equals observed accuracy.

The architectural integrity and synergistic design of proposed model is highlighted by the ablation results in Table 10. The overall model is the most optimal in terms of both regression and classification, and its MAE is 2.05, RMSE is 3.01, R2 is 0.91 and its classification accuracy is 92%, which makes it the most robust model. The marginalization of individual modules brings out acute degradations. It should be noted that in the absence of the RAI or DSI, the performance drops drastically (R2 0.87–0.88) and these two indicators form part of the operational risk indicators that relate to domain awareness. Their effects on the temporal coherence and uncertainty reduction are reflected in the instability of the predictions due to the loss of the Risk Regime Modulation Layer or Temporal Consistency Loss, which is also attributed to a decrease in accuracy (89–90%) and F1-scores. Removing Interaction-Aware Cross Attention leads to substantial variability in delay forecasting as well as class discrimination, showing its importance in the establishment of spatio-interaction dynamics. In sum, this discussion confirms the additivity of each element as well as the recognition that it is the combination of each element that makes the proposed model successful in generalizing and predicting in complex logistics environments, but not their individual innovativeness.

Table 10.

Ablation study evaluating the marginal impact of each proposed component in the O²RDL-Net model. Regression and classification performance metrics are reported after individually removing architectural modules to assess their contribution to the overall model effectiveness in percentage.

Variant	MAE	RMSE	R²	MAPE	sMAPE	Accuracy	Precision	Recall	F1
Full O²RDL-Net Model	2.05	3.01	0.91	11.7	10.9	92	91	92	91
– RAI	2.29	3.35	0.88	13.5	12.7	89	87	88	87
– DSI	2.22	3.26	0.89	12.8	12.0	90	88	89	88
– HOIS	2.18	3.19	0.89	12.6	11.8	90	89	89	89
– LSR	2.14	3.12	0.90	12.2	11.3	91	90	90	0.90
– Risk Regime Modulation	2.30	3.37	0.88	13.6	12.8	88	86	87	0.86
– Interaction-aware Cross Attention	2.20	3.18	0.89	12.5	11.5	89	88	89	0.88
– Temporal Consistency Loss	2.25	3.24	0.89	13.0	12.1	90	88	89	0.89

The outcomes of the simulations of the regression and classification tasks prove the ability of the proposed model to be a better predictor than all the baseline methods. The model had the lowest MAE of 2.05 and the highest R2 of 0.91, which points to the high degree of accuracy and correlation with the deviations of the ground-truth delays. These advantages can be explained by the incorporation of domain-specific capabilities such as the RAI and DSI, spatiotemporal encoding layers, and attention-based architecture. To classify the model achieved 92% accuracy and F1-score of 91, substantially better than the traditional models Logistic Regression and Random Forest, especially in the high-risk cases of prediction. These performance benefits were consistently evident both at validation and test stages with low variance margins, indicating high generalization and consistency.

These findings could be used in the real world. With a correct estimate of the delay, planners of logistics decisions have the means to optimize the delay buffers, and to avoid disturbances in the handling. The ablation experiments further validate that each architectural component (e.g., risk modulation and loss of temporal consistency) adds a real value. Results confirm the proposed dual-task framework as an alternative solution to the traditional ones, and to integrate the domain knowledge in the field of supply chain forecasting, which will aid in the construction of more resilient and responsive logistic networks. To achieve a comprehensive comparison of contemporary models, a visualization of the results of the logistic and supply chain models on the logistic models data set and the supply chain data set is shown in Fig. 11, which shows significant findings of disparity in the sophistication of architecture, feature engineering and predictive performance as reported in Table 11. Moderate accuracy (F1: 82%, R2: 0.67) was provided by classical and shallow models such as MLP and decision tree hybrids, but they failed to offer strong learning in terms of temporal or risk-sensitivity. Deep temporal models including TCNs and LSTMs also outperformed by capturing temporal features more effectively (Acc: 8488, R2: 0.71), but they were restricted in their interpretability because they depended on standard operational variables. Recent literature that included explainability and hybrid attention mechanisms added interpretative value to the results but did not perform as well with increased error (MAE: 3.83). The proposed model, conversely, demonstrated much better accuracy (Acc: 92, F1: 91), regression strength (R2: 0.91, MAE: 2.05) due to its dual-task design and the presence of such special features as DSI, RAI, HOIS. These results put proposed model as a better predictor and interpretative framework of delay and risk prediction in cases of operational complexity.

Table 11.

Comparative Summary of Existing Approaches and the Proposed O²RDL-Net for Risk and Delay Forecasting in Logistics and Supply Chains.

Refs.	Year	Model/Approach	Technique & Features	Dataset	Results (Metric)
40	2022	MLP Neural Network vs. classical ML	Compared MLP, DT, RF, NB, LR for delay classification; CRISP-DM pipeline	Quarry production line	F1: 82%
30	2023	Temporal CNN vs. RNN + ensemble classifiers	Two-stage: DL feature extractor + six ML classifiers	COVID-19 shipment	Acc: 88%
37	2024	Deep LSTM with macro features	LSTM capturing autocorrelation; macroeconomic indicators	Automotive supply chain	Acc: 84%
26	2025	Decision Tree + Firefly Algorithm (hybrid)	DT regression for transit time; Firefly metaheuristic for feature selection & hyper-param tuning	Smart Supply Chain dataset	R2=0.67
38	2025	A-LSTM Autoencoder + Attention (A-LAPPM)	Hybrid LSTM autoencoder for anomaly detection + attention mechanism for risk features	Logistics and supply chain	MAE: 3.83
34	2025	Multi-Task Temporal CNN (MT2CN) + SHAP	Joint prediction of emissions & delays; TCN captures congestion’s dual impact	Logistics and supply chain	R2=0.71 MAE: 5.24 RMSE: 5.03
20	2026	Ensemble Tree models + LIME XAI	Engineered features from flight + weather data	Logistics and supply chain	R2=0.48 MAE: 7.64 RMSE: 8.53
This Study		Proposed O²RDL-Net	LSR, RAI, DSI, HOIS	Logistics and supply chain	R2=0.91, MAE: 2.05, RMSE: 3.01 Acc: 92%, F1: 91%

Conclusion

In this study, O²RDL-Net, a load-aware and interaction-amplified deep learning approach for joint risk classification and delay forecasting in transportation and logistics networks is presented. The proposed model incorporates constructed indicators like the Risk Accumulation Index, Delay Sensitivity Indicator, Human–Operational Interaction Score and Logistics System Representation to effectively capture both the short and long-term operational dynamics. The experimental results show that O²RDL-Net is always more accurate in predicting, stable and well calibrated when compared to traditional machine learning models and advanced deep learning baselines for both regression and classification. The simultaneous learning of risk states and delays in the model facilitates more intelligent and timely decision making in dynamic and congested operations. In addition to the performance, detailed interpretability studies were conducted via SHAP and local contribution explanations, which also validate that the model is based on meaningful feature interactions and domain consistent feature relationships. By doing this, transparency increases trust and practical applicability, enabling logistics stakeholders not only to be able to see what the model predicts but also to see why this prediction is made. This study has the following limitations. The model has been tested on a given logistics data environment and may not perform the same way in a different region that may have different logistic aspects. Furthermore, the external effects like regulatory changes or extreme disruption events were not considered explicitly. Future efforts will involve extension of the framework to multi-region and real-time streaming datasets, addition of graph-based spatial dependencies, and adaptation to provide proactive decision optimization and adaptive intervention strategies.

Author contributions

The sole author Xiao Yang has fully contributed to this study.

Funding

Acknowledgements of Research Funding Grants: The study was supported by “Research on the Coupled and Coordinated Development of Transportation and Modern Industrial System in Shaanxi Province, (Grant2025YB0214)”.

Data availability

The dataset is freely available at: [https://www.kaggle.com/datasets/datasetengineer/logistics-and-supply-chain-dataset/data].

Declarations

Competing interests

The authors declare no competing interests.