# The multi-port berth allocation problem with speed optimization: Exact methods and a cooperative game analysis

arXiv: https://arxiv.org/abs/2011.15085 · HTML: https://mlsanity.com/paper/2011.15085/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Nov 2020.

## Built on by (most cited first, 2 of 2)

- [An adaptive large neighborhood search heuristic for the multi-port continuous berth allocation problem](https://mlsanity.com/paper/2302.02356/) (2023)
- [Navigating Demand Uncertainty in Container Shipping: Deep Reinforcement Learning for Enabling Adaptive and Feasible Master Stowage Planning](https://mlsanity.com/paper/2502.12756/) (2025)

## Abstract (arXiv)

We consider a variant of the berth allocation problem-i.e., the multi-port berth allocation problem-aimed at assigning berthing times and positions to vessels in container terminals. This variant involves optimizing vessel travel speeds between multiple ports, thereby exploiting the potentials of a collaboration between carriers (shipping lines) and terminal operators. Using a graph representation of the problem, we reformulate an existing mixed-integer problem into a generalized set partitioning problem, in which each variable refers to a sequence of feasible berths in the ports that the vessel visits. By integrating column generation and cut separation in a branch-and-cut-and-price procedure, our proposed method is able to outperform commercial solvers in a set of benchmark instances and adapt better to larger instances. In addition, we apply cooperative game theory methods to efficiently distribute the savings resulting from a potential collaboration and show that both carriers and terminal operators would benefit from collaborating.