# Stability Constrained Optimal Vessel Loading

## TL;DR

This paper develops a model for optimizing cargo vessel loading to maximize revenue while ensuring stability, incorporating linear and quadratic constraints, and demonstrates its application on a container ship.

## Contribution

It introduces a novel optimization formulation for vessel loading that accounts for stability constraints and demonstrates its practical application with commercial solvers.

## Key findings

- The model effectively balances revenue and stability constraints.
- Application to a 3500 TEU vessel shows practical feasibility.
- Quadratic constraints depend on cargo weight distribution.

## Abstract

We examine the revenue maximizing loading for the single voyage of a cargo vessel where metacentric stability is taken into account. We formulate the problem as a maximization of a linear function with two linear and one quadratic constraint. The quadratic form in the constraint can be definite if heavier loads are to be placed low, but not otherwise. We consider a vessel similar to a 3500 TEU container carrier and perform several calculations using a Generalized Reduced Gradient commercial solver.