Accurate and robust linear representation for containership stability conditions with ballast water

Abstract

Stowage planning involves optimizing the placement of cargo on a ship while ensuring the ship's stability conditions are met. This optimization problem is typically formulated as a mixed-integer linear programming problem. However, a challenge arises in representing stability conditions as linear constraints since these conditions have non-linear relationships to the decision variables. Although there are methods for linearizing these stability conditions, they lack a systematic modeling approach and numerical verification of accuracy and reliability. In particular, the complex and diverse nature of ballast water contributes to significant non-linearity, posing a considerable challenge in developing an accurate linear approximation. This study proposes linear prediction methods that incorporate ballast water to address major stability conditions such as trim, drafts, shear force, bending moment, torsion, and transverse metacentric height. We introduce a comprehensive training and testing methodology for prediction, and validate the proposed method by comparing it with true values on two ships of different capacities, demonstrating its accuracy and scalability.