Maxim Dulebenets, Ph.D., poses with a Maersk container and the container vessel the Juan Diego at Port Panama City on August 11, 2026. Dulebenets is part of a team of researchers at FAMU-FSU College of Engineering that is working to improve the efficiency of berth scheduling at global shipping ports. (Scott Holstein/FAMU-FSU College of Engineering)
Key Points
Researchers at the FAMU-FSU College of Engineering developed a new mathematical model to help marine container terminals decide where and when to dock arriving ships, cutting wait times and operating costs.
The study, led by postdoctoral scholar Bokang Li and Associate Professor Maxim A. Dulebenets, was published in IEEE Transactions on Intelligent Transportation Systems in 2026.
The model uses two advanced optimization techniques, Benders decomposition and column generation, to solve scheduling problems for hundreds of vessels faster than existing methods.
The research matters because nearly 80% of world trade moves by sea, and faster berth scheduling can reduce fuel waste, lower shipping costs and ease supply chain disruptions.
The team tested its approach against five leading optimization techniques and three popular metaheuristics, and it outperformed all of them.
At the world’s busiest ports, every minute counts.
As global trade surges and a record number of container ships arrive, the challenge to keep cargo moving swiftly has never been greater. With vessels competing for limited dock space, even minor scheduling errors can cause costly delays and disrupt supply chains worldwide.
A research team at Florida A&M University and the FAMU-FSU College of Engineering is addressing this challenge with a new approach to berth scheduling at marine container terminals. Their goal: a smarter, more efficient solution using a mixed-integer linear programming (MIP) model and advanced decomposition algorithms.
Their work is featured in IEEE Transactions on Intelligent Transportation Systems.
“Our study aims to determine the best way to assign arriving vessels to available docking or berthing positions and the order they are served, so that overall related costs are kept as low as possible,” said Maxim A. Dulebenets, associate professor in the Department of Civil and Environmental Engineering at the FAMU-FSU College of Engineering and a co-author of the study.
How Does the New Optimization Model Work?
The researchers developed an MIP optimization model designed to reduce costs by minimizing ship waiting times, streamlining loading and unloading, ensuring timely departures and assigning vessels to berths as close as possible to their preferred locations.
The model mirrors real-world port operations by simplifying the complex mathematics of scheduling. By leveraging two optimization techniques, Benders decomposition and column generation, the framework can manage hundreds of vessels while delivering results faster than earlier methods.
In simple terms, scheduling hundreds of ships at a busy port is a complex problem that can take computers a long time to solve. Benders decomposition breaks the problem into manageable parts, while column generation narrows the focus to save time and computing power.
What Problem Were the Researchers Trying to Solve?
“In this study, we worked on a planning problem that many marine container terminals face every day: When several vessels are expected to arrive, the terminal needs to decide where each vessel should dock and when it should be served,” said Bokang Li, a postdoctoral research scholar and lead author of the article. “These decisions may sound simple, but they become very difficult when there are many vessels, limited berth space, different handling times and different expected departure times.”
The researchers built a more efficient optimization model that uses key information, including vessel arrival times, service times, preferred berthing locations and delay-related costs, to minimize unnecessary waiting and delays.
“A major part of our work was making the model more compact, so the computer can evaluate scheduling decisions more efficiently than with several earlier approaches,” Li said. “We developed and tested two additional solution methods inspired by Benders decomposition and column generation.”
These methods break down a large, complex scheduling problem into smaller, more manageable parts for the computer to process. This approach helped the team improve the solution process further, particularly for larger and more challenging scenarios, according to Li.
“We tested the proposed model and solution methods using many different problem settings and compared them with existing models and approaches from the literature,” Li said. “The results showed that our approach can find high-quality schedules more efficiently, especially when the number of vessels becomes large.”
Why Does Faster Berth Scheduling Matter for Global Trade?
This research addresses a major challenge facing ports worldwide: efficiently scheduling and managing the arrival and departure of large numbers of container ships. When ships are delayed or ports are congested, it can create a domino effect of slowdowns, leading to higher costs, wasted fuel and disruptions in the global supply chain.
“Maritime transport drives the global movement of goods and forms the backbone of international trade,” Dulebenets said. ”Compared to other transport modes, maritime shipping offers lower costs per unit, greater fuel efficiency and broader geographical reach, making it indispensable for global supply chains. Nearly 80 percent of cargo is shipped by oceangoing vessels, which makes efficient terminal operations vital for international commerce.”
“From my perspective, this work is important because berth scheduling is one of the first major decisions that affects the flow of work inside a marine container terminal,” Li explained. “Once a vessel is assigned to a berth and service order, that schedule can influence the use of cranes, yard space, trucks, labor and other terminal resources. Therefore, a better berth schedule can help the terminal operate more smoothly.”
“Ports often need to make planning decisions under limited time,” Li said. “A model that is easier and faster to solve, together with decomposition-based solution methods such as Benders decomposition and column generation, can help decision-makers compare different scheduling options and respond more effectively when the terminal becomes busy. In that sense, this study is not only about reducing cost in a mathematical model, but also about providing a practical foundation for better operational planning at container terminals.”
Who Contributed to the Research?
Teamwork was key to this project’s success. Lead author Bokang Li worked closely with co-authors and doctoral candidates Fatemeh Shekoohi and Payam Afkhami; Maxim A. Dulebenets; and faculty researchers Amir M. Fathollahi-Fard at Laurentian University and Yui-Yip Lau at Hong Kong Polytechnic University.
By combining their skills and perspectives, the team worked through complex scheduling challenges to develop a solution intended for use at ports worldwide. The researchers generated artificial data using statistical methods, following established approaches from previous studies on berth allocation and scheduling. This use of synthetic data is intended to keep their methods consistent with common practices in the field.
“Marine terminal operators generally do not share their operational data due to privacy and security issues,” Dulebenets explained. “The proposed model and algorithms can be applied for berth scheduling at any marine container terminal in the world by setting the appropriate values of parameters, such as vessel arrival times, vessel handling times and unit waiting and delay costs. Busy terminals that handle hundreds of vessels every day will especially benefit from this work.”
How Well Did the Model Perform in Testing?
The team’s testing didn’t stop at theory. They benchmarked their model against five leading optimization techniques and three popular metaheuristics, and it outperformed them in both speed and solution quality in the researchers’ test scenarios.
According to the researchers, ports using this approach could see reductions in vessel waiting times, faster turnaround and improved operational reliability, though real-world results would depend on how the model is applied at individual terminals.
The model’s performance held up across a variety of test scenarios the researchers designed to reflect the unpredictable and changing realities of global shipping.
“Effective berth scheduling and terminal operations are expected to lower overall supply chain costs,” Dulebenets said. “As a result, consumers would be able to access essential goods at lower prices, especially for imported commodities.”
Editor’s Note: This article was edited with a custom prompt for Claude Sonnet 5, an AI assistant created by Anthropic. The AI optimized the article for SEO/GEO discoverability, improved clarity, structure and readability while preserving the original reporting and factual content. All information and viewpoints remain those of the author and publication. This article was edited and fact-checked by college staff before being published. This disclosure is part of our commitment to transparency in our editorial process. Last edited: 08/26/2026.
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FAQ
Berth scheduling is the process of deciding where an arriving ship will dock at a port and the order in which it will be served relative to other ships. It accounts for factors such as a vessel’s arrival time, the time required to load and unload, and its preferred docking location.
Researchers led by postdoctoral scholar Bokang Li and Associate Professor Maxim A. Dulebenets developed a mixed-integer linear programming (MIP) model paired with two optimization techniques, Benders decomposition and column generation, to schedule ship berths more quickly and accurately, especially at terminals handling hundreds of vessels.
Nearly 80% of the world’s traded goods move by sea, according to the researchers and data from the U.N. Trade and Development agency (UNCTAD). Delays in scheduling ships at ports can cause ripple effects across supply chains, raising costs and creating shortages of goods.
Both are mathematical optimization techniques used to solve large, complex scheduling problems more efficiently. Benders decomposition breaks a large problem into smaller, more manageable parts, while column generation narrows the search process to reduce computing time. Together, they let the researchers’ model schedule hundreds of vessels faster than earlier approaches.
The study’s authors are Bokang Li (lead author and postdoctoral research scholar), Maxim A. Dulebenets (associate professor at the FAMU-FSU College of Engineering), doctoral candidates Fatemeh Shekoohi and Payam Afkhami, Amir M. Fathollahi-Fard of Laurentian University, and Yui-Yip Lau of Hong Kong Polytechnic University.
The study, “An Efficient Mixed-Integer Programming Model and Decomposition Algorithms for Berth Scheduling at Marine Container Terminals,” appears in IEEE Transactions on Intelligent Transportation Systems, a peer-reviewed journal published by IEEE.