Uncertainty-Aware Delivery Delay Duration Prediction via Multi-Task Deep Learning

TL;DR

A multi-task deep learning model for delivery delay duration prediction in the presence of significant imbalanced data, where delayed shipments are rare but operationally consequential, and supports probabilistic forecasting for uncertainty-aware decision making is introduced.

Abstract

Accurate delivery delay prediction is critical for maintaining operational efficiency and customer satisfaction across modern supply chains. Yet the increasing complexity of logistics networks, spanning multimodal transportation, cross-country routing, and pronounced regional variability, makes this prediction task inherently challenging. This paper introduces a multi-task deep learning model for delivery delay duration prediction in the presence of significant imbalanced data, where delayed shipments are rare but operationally consequential. The model embeds high-dimensional shipment features with dedicated embedding layers for tabular data, and then uses a classification-then-regression strategy to predict the delivery delay duration for on-time and delayed shipments. Unlike sequential pipelines, this approach enables end-to-end training, improves the detection of delayed cases, and supports probabilistic forecasting for uncertainty-aware decision making. The proposed approach is evaluated on a large-scale real-world dataset from an industrial partner, comprising more than 10 million historical shipment records across four major source locations with distinct regional characteristics. The proposed model is compared with traditional machine learning methods. Experimental results show that the proposed method achieves a mean absolute error of 0.67-0.91 days for delayed-shipment predictions, outperforming single-step tree-based regression baselines by 41-64% and two-step classify-then-regress tree-based models by 15-35%. These gains demonstrate the effectiveness of the proposed model in operational delivery delay forecasting under highly imbalanced and heterogeneous conditions.

Figures (4)

• Figure 1: Logistics network overview. Shipments $s_i \in \mathcal{S}$ flow from origin locations $L_k \in \mathcal{L}$ to destinations $R_j \in \mathcal{R}$, characterized by physical features (weight, volume, items count) and timing information (planned departure/arrival).
• Figure 2: Overview of the multi-task learning model. Input features are processed through dedicated embedding layers (categorical and numerical), concatenated, and passed to a shared MLP backbone that produces a hidden representation $\mathbf{h}_i$. The backbone output feeds into three task-specific heads: a classification head for binary delay prediction, and dual regression heads for duration estimation. The classification probability $\hat{p}_i$ is concatenated with $\mathbf{h}_i$ and passed to both regression heads (dashed arrows). During training, samples are routed to regression heads based on ground truth labels; during inference, routing is determined by the classifier output ($\hat{p}_i > 0.5 \rightarrow$ delayed head). Quantile predictions are calibrated via conformal prediction to produce prediction intervals.
• Figure 3: Delivery time distributions across locations showing distinct patterns of on-time (yellow) and delayed (blue) shipments. Main plots show the overall distribution, while insets focus on the delayed shipment patterns.
• Figure 4: Distribution of shipment volumes across source locations.