Highlights

In brief

A new dual-objective mathematical model for tugboat scheduling uses real-time data and proactive decision systems to better meet highly variable real-world demands while minimising fuel consumption, supporting greener port operations.

Photo by Sung Jin Cho | Unsplash

Tackling tugboat timing woes

6 Oct 2025

Through machine learning, a new mathematical model aims to reduce fuel costs and improve the timeliness of tugboat services in high-traffic ports.

In busy ports such as Singapore, it can be a massive undertaking to coordinate the thousands of different vessels on the move. One aspect of managing traffic in such ports is ensuring that tugboats—small vessels which help larger ships to berth and unberth—are well-scheduled and coordinated.

“A single ship often needs multiple tugboats to work together at specific times and locations,” explained Zhe Xiao, a Research Scientist at the A*STAR Institute of High Performance Computing (A*STAR IHPC). “Tugboats must meet safety and timing constraints, as their actions are interdependent. Depending on the ship’s movement, the services required of them can also change over time.”

As such, fixed tugboat schedules can be difficult to rely on. There’s the fact that requests for tugboats can come in at any time—sometimes just a few hours before their services are needed. Meanwhile, unpredictable weather conditions and port congestion can drastically change tugboat demand. These can also all add to carbon emissions as tugboats are left idly waiting or sent on inefficient routes.

In a project supported by the Singapore Maritime Institute, Xiao, along with A*STAR IHPC Senior Principal Scientist Xiuju Fu and former Scientist Xiaoyang Wei, collaborated with Hoong Chuin Lau from Singapore Management University to tackle the tugboat scheduling puzzle through mathematical modelling.

The team noted that current models aimed at the problem often inadequately accounted for the dynamic nature of tugboat service requests. These models also generally ignored real-world considerations, such as the time a tugboat takes to move to a different location; treated the scheduling problem on an individual level; and were unable to make proactive decisions for the tugboats.

Based on these shortfalls, the team explored a new model that would take in live information, reflect the future uncertainty of real-world operations, and minimise carbon emissions.

“Our model optimises two simultaneous key objectives: tugboat sail cost efficiency through reduced fuel consumption, and service punctuality,” said Fu. “Unlike previous models, it can make both immediate task assignments and predict likely future tasks. This is the first time such a combination has been developed for tugboat operations.”

To develop their model, the team formulated the scheduling problem with real-world parameters, such as time constraints on berthing and unberthing ships, as well as fuel consumption constraints. It also incorporated a proactive decision system, where the model developed plans for tugboats to wait at certain locations in anticipation of future service needs; as well as a method to adjust tugboat speeds for improved efficiency.

“When tested with real data from the Port of Singapore, our model reduced total sail costs by 12.8 percent compared to current practice,” said Fu.

The model also reduced service delays to a minimal level rare in current practice. Given these results, the team is optimistic about the model’s potential to improve decision-making, reduce operational costs and support decarbonisation efforts in the tugboat service industry.

Currently, the team aims to refine their model with feedback from industry partners. “Our future work will explore adding more operational constraints and extending the model to larger-scale port environments,” Xiao added.

The A*STAR-affiliated researchers contributing to this research are from the A*STAR Institute of High Performance Computing (A*STAR IHPC).

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References

Wei, X., Lau, H.C., Xiao, Z., Fu, X., Zhang, X. et al. Bi-objective dynamic tugboat scheduling with speed optimization under stochastic and time-varying service demands. Transportation Research Part E 193, 103876 (2025). | article

About the Researchers

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Xiuju Fu

Director (Maritime AI Research Programme) and Senior Principal Scientist

A*STAR Institute of High Performance Computing (A*STAR IHPC)
Xiuju Fu is the Director of the Maritime Artificial Intelligence (AI) Research Programme and Senior Principal Scientist at the A*STAR Institute of High Performance Computing (A*STAR IHPC) in Singapore. With expertise in AI, big data intelligence, simulation and optimisation techniques, she focuses on advancing complex system management and enhancement. Recognised for her contributions, she was honoured as a Singapore Maritime Institute (SMI) Fellow in 2023. Currently, she spearheads the Maritime AI Research Programme in Singapore, driving research and development initiatives in maritime data excellence, AI modelling excellence, maritime AI computing and application excellence. Her efforts aim to foster the development and application of AI in the maritime industry.
Zhe Xiao is a Research Scientist at the A*STAR Institute of High Performance Computing (A*STAR IHPC), with expertise in intelligent systems, systems science, big data analytics, artificial intelligence and blockchain, and agent-based simulation and modelling systems. His studies align with the emerging trend of information systems being transformed towards better situation awareness and enhanced system intelligence and productivity, especially in the maritime sector. Xiao has co-authored more than 70 papers in top tier journals and conferences. As the Principal Investigator or Co-investigator, he led and engaged in more than 10 industrial projects solving the common challenges in spatiotemporal data quality handling, knowledge extraction and decision support algorithms, together with efficient concurrent computing cluster design to push the models towards real world applications.
Xiaoyang Wei was formerly a Scientist at the A*STAR Institute of High Performance Computing (A*STAR IHPC) in Singapore. He has a PhD degree in Civil and Environmental Engineering from the National University of Singapore. He specialises in operations research, AI and optimisation, with skills spanning mathematical modelling, discrete‐event simulation and supply chain systems. Wei is passionate about using computation to address complex real-world challenges.

This article was made for A*STAR Research by Wildtype Media Group