June 4, 2024
Virgile Galle and Tom Tangl, Software Engineers, Operations Research Team, Google Research
We present a previously unknown solution to the Liner Shipping Network Design and Scheduling Problem, which is part of our new Shipping Network Design API.
Background
Look around you. Chances are that something in your line of sight sailed on a cargo ship. 90% of the world's goods travel over the ocean, often on cargo vessels mammoth in scale: a quarter mile long, weighing 250,000 tons, holding 12,000 containers of goods collectively worth a billion dollars. Unlike airplanes, trains, and trucks, cargo ships are in nearly constant operation, following cyclical routes across oceans.
But what are the best, most efficient routes for these ships? To a computer scientist, this is a graph theory problem; to a business analyst, a supply chain problem. Done poorly, containers linger at ports, ships idle offshore unable to berth, and ultimately, products become pricier as the flow of physical items becomes slower and unpredictable.
Every container shipping company needs to solve these challenges, but they are typically solved separately. Combining them multiplies the complexity, and, to the best of our knowledge, is a problem that has never been solved at the scale required by the largest container operations (500 vessels and 1500 ports). Google's Operations Research team is proud to announce the Shipping Network Design API, which implements a new solution to this problem. Our approach scales better, enabling solutions to world-scale supply chain problems, while being faster than any known previous attempts. It is able to double the profit of a container shipper, deliver 13% more containers, and do so with 15% fewer vessels. Read on to see how we did it.
Methods
There are three components to the Liner Shipping Network Design and Scheduling Problem (LSNDSP). Network design determines the order in which vessels visit ports, network scheduling determines the times they arrive and leave, and container routing chooses the journey that containers take from origin to destination.
Solving them all simultaneously is more difficult but is also more likely to discover better solutions. Solutions to network design create service lines that a small set of vessels follow. Container vessels can't dock at ports whenever they like; they have pre-arranged berthing slots. As they approach a port, they linger at an anchorage area. When a port is congested, vessels may end up staying in the anchorage area for hours or days. The precise network schedule of the vessels becomes important: not just what day to dock, but what hour, and whether to increase velocity to arrive at a particular time (or conversely, to decrease velocity to save fuel).
Results and Optimization
Every optimization problem has three components: variables (e.g., ships and ports), constraints on those variables (e.g., a ship can fit only so many containers onboard), and an objective function to be minimized or maximized (e.g., maximize the number of containers shipped). The variables and constraints are often represented as a matrix in which the columns are the variables and the rows are the constraints.
A common technique to decompose such large problems is column generation, in which only a subset of the variables are considered at first, and then new variables — that is, new columns — are generated to more closely approximate the original problem. To help manage this, we developed a software library that analyzes the problem and predicts which columns are best to generate. This library will be open-sourced via MathOpt, our mathematical programming framework.
Similarly, we used local search heuristic strategies to scale the problem to larger sizes effectively. Finally, incorporating transit times significantly improved the quality of solutions. Our methods proved powerful, improving throughput and profit margins dramatically compared to previous approaches.
Example of Heuristic Strategy
A small modification to the network discovered with neighborhood search can affect shipping profits. For example, the model might suggest a new connection that makes it possible to ship containers between ports that previously weren't connected.
To quantify the performance of our solutions, we used LINERLIB, an industry benchmark for shipping network design problems. We tested our solution on three scenarios: WorldSmall, EuropeAsia, and WorldLarge.
Our method was able to route more containers with fewer vessels compared to the baseline. For each scenario, our solutions improved overall efficiency, increasing throughput while using fewer vessels, which also improved projected profit margins considerably.
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Conclusion
Our advanced optimization techniques have a remarkable effect on the efficiency of shipping networks. We believe our method is the first able to solve the network design and scheduling problem at the scale of WorldLarge. We hope that this work will inspire additional research into this domain with the goal of building more efficient and smooth global supply chains. The Shipping Network Design API is part of a set of Operations Research APIs that we will be adding to in the future as we look for other industries to optimize.
Remember these 3 key ideas for your startup:
- Enhanced Efficiency: Implementing advanced optimization techniques can double the profit of a container shipper, provide more container throughput, and reduce the number of vessels required.
- Innovative Solutions: Utilize new tools like the Shipping Network Design API to solve complex logistical problems that combine network design, scheduling, and routing with superior scalability and speed.
- Open-source Advantage: Leverage open-source libraries such as MathOpt to benefit from powerful data-driven predictions and optimized operations.
Read more about the Shipping Network Design API and our research.
