RoRo stowage planning: a systematic study of mathematical formulations
Abstract
Stowage planning for Roll-On/Roll-Off (RoRo) vessels can be represented with different mathematical formulations for efficient stowage plans: hybrid-slot, grid-based, and lane-based representations. In this work, we implement and compare three formulations equally across a diverse set of instances. We extend these three representations to handle heterogeneous cargo in terms of size and weight, and to address advanced stability requirements, such as centre of gravity limits, stress force limits, and ballast-water adjustments. We evaluate the models in three configurations: cargo placement, simple stability with centres of gravity limits and ballast adjustments, and full stability, which adds shear-force and bending-moment limits. The tests are conducted on three different vessel sizes and solved with a mixed-integer programming solver. The hybrid-slot and grid-based models both perform well finding solutions for 447 out of 486 instances across all configurations; however, the hybrid-slot model placed 8% more cargo than the grid model. By contrast, the lane model only finds solutions for 142 instances and placed 15% less cargo than the grid-based model. The solutions generated by the hybrid-slot model are validated using a commercial vessel-stability software to verify our stability estimations, showing issues in only 24 of 162 instances, which are easily avoided by tightening the stability constraints. Finally, we address the placement of hazardous and refrigerated cargo in an efficient manner for the hybrid-slot model by employing lazy constraints which is shown to solve realistic sized instances.
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BibTeX
@misc{thomsen2026roro,
title = {{RoRo stowage planning: a systematic study of mathematical formulations}},
author = {Oliver Rise Thomsen and Magnus Vilhelm Barrett Levinsen and Dario Pacino and Line Blander Reinhardt},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36879},
eprint = {2610.36879},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36879},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - RoRo stowage planning: a systematic study of mathematical formulations
AU - Oliver Rise Thomsen
AU - Magnus Vilhelm Barrett Levinsen
AU - Dario Pacino
AU - Line Blander Reinhardt
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.36879
UR - https://arxiv.org/abs/2610.36879
AB - Stowage planning for Roll-On/Roll-Off (RoRo) vessels can be represented with different mathematical formulations for efficient stowage plans: hybrid-slot, grid-based, and lane-based representations. In this work, we implement and compare three formulations equally across a diverse set of instances. We extend these three representations to handle heterogeneous cargo in terms of size and weight, and to address advanced stability requirements, such as centre of gravity limits, stress force limits, and ballast-water adjustments. We evaluate the models in three configurations: cargo placement, simple stability with centres of gravity limits and ballast adjustments, and full stability, which adds shear-force and bending-moment limits. The tests are conducted on three different vessel sizes and solved with a mixed-integer programming solver. The hybrid-slot and grid-based models both perform well finding solutions for 447 out of 486 instances across all configurations; however, the hybrid-slot model placed 8% more cargo than the grid model. By contrast, the lane model only finds solutions for 142 instances and placed 15% less cargo than the grid-based model. The solutions generated by the hybrid-slot model are validated using a commercial vessel-stability software to verify our stability estimations, showing issues in only 24 of 162 instances, which are easily avoided by tightening the stability constraints. Finally, we address the placement of hazardous and refrigerated cargo in an efficient manner for the hybrid-slot model by employing lazy constraints which is shown to solve realistic sized instances.
ER -