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Beyond the Next Port: A Multi-Task Transformer for Forecasting Future Voyage Segment Durations

Nairui Liu, Fang He, Xindi Tang

TL;DR

This work tackles the challenge of forecasting sailing durations for future voyage segments in liner services by reframing ETA prediction as a segment-level time-series problem. It introduces a transformer-based Seq2Seq architecture with causal masking and a multi-task head that jointly predicts segment durations and destination port congestion, leveraging segment-level historical durations, port congestion proxies, and static vessel features. The model demonstrates consistent gains over strong baselines, with notable reductions in MAE and MAPE, and shows robustness across segment frequencies and forecast horizons. The approach enables long-horizon planning for berthing, yard space, and feeder connections, offering a practical decision-support tool for global maritime operations.

Abstract

Accurate forecasts of segment-level sailing durations are fundamental to enhancing maritime schedule reliability and optimizing long-term port operations. However, conventional estimated time of arrival (ETA) models are primarily designed for the immediate next port of call and rely heavily on real-time automatic identification system (AIS) data, which is inherently unavailable for future voyage segments. To address this gap, the study reformulates future-port ETA prediction as a segment-level time-series forecasting problem. We develop a transformer-based architecture that integrates historical sailing durations, destination port congestion proxies, and static vessel descriptors. The proposed framework employs a causally masked attention mechanism to capture long-range temporal dependencies and a multi-task learning head to jointly predict segment sailing durations and port congestion states, leveraging shared latent signals to mitigate high uncertainty. Evaluation on a real-world global dataset from 2021 demonstrates the proposed model consistently outperforms a comprehensive suite of competitive baselines. The result shows a relative reduction of 4.85% in mean absolute error (MAE) and 4.95% in mean absolute percentage error (MAPE) compared with sequence baseline models. The relative reductions with gradient boosting machines are 9.39% in MAE and 52.97% in MAPE. Case studies for the major destination port further illustrate the model's superior accuracy.

Beyond the Next Port: A Multi-Task Transformer for Forecasting Future Voyage Segment Durations

TL;DR

This work tackles the challenge of forecasting sailing durations for future voyage segments in liner services by reframing ETA prediction as a segment-level time-series problem. It introduces a transformer-based Seq2Seq architecture with causal masking and a multi-task head that jointly predicts segment durations and destination port congestion, leveraging segment-level historical durations, port congestion proxies, and static vessel features. The model demonstrates consistent gains over strong baselines, with notable reductions in MAE and MAPE, and shows robustness across segment frequencies and forecast horizons. The approach enables long-horizon planning for berthing, yard space, and feeder connections, offering a practical decision-support tool for global maritime operations.

Abstract

Accurate forecasts of segment-level sailing durations are fundamental to enhancing maritime schedule reliability and optimizing long-term port operations. However, conventional estimated time of arrival (ETA) models are primarily designed for the immediate next port of call and rely heavily on real-time automatic identification system (AIS) data, which is inherently unavailable for future voyage segments. To address this gap, the study reformulates future-port ETA prediction as a segment-level time-series forecasting problem. We develop a transformer-based architecture that integrates historical sailing durations, destination port congestion proxies, and static vessel descriptors. The proposed framework employs a causally masked attention mechanism to capture long-range temporal dependencies and a multi-task learning head to jointly predict segment sailing durations and port congestion states, leveraging shared latent signals to mitigate high uncertainty. Evaluation on a real-world global dataset from 2021 demonstrates the proposed model consistently outperforms a comprehensive suite of competitive baselines. The result shows a relative reduction of 4.85% in mean absolute error (MAE) and 4.95% in mean absolute percentage error (MAPE) compared with sequence baseline models. The relative reductions with gradient boosting machines are 9.39% in MAE and 52.97% in MAPE. Case studies for the major destination port further illustrate the model's superior accuracy.
Paper Structure (32 sections, 39 equations, 11 figures, 20 tables)

This paper contains 32 sections, 39 equations, 11 figures, 20 tables.

Table of Contents

  1. Introduction
  2. Literature Review
  3. Maritime ETA Prediction
  4. Inland ETA Prediction
  5. Research Gap
  6. Method
  7. Problem Definition
  8. Data Preprocessing
  9. Feature Engineering
  10. Temporal Features
  11. Vessel Features
  12. Segment Features
  13. Model Design
  14. Input Representation
  15. Feature Fusion
  16. ...and 17 more sections

Figures (11)

  • Figure 1: The overall architecture of the ETA prediction and evaluation framework.
  • Figure 2: The schematic diagram of vessel departure and arrival process.
  • Figure 3: The overall structure of the proposed model.
  • Figure 4: Sketch of masked multi-head attention mechanism.
  • Figure 5: Distribution of global ports and shipping lines with different frequency.
  • ...and 6 more figures