A Hydrostatically Constrained 3D Container Slot-Assignment Heuristic for Feeder Vessels: Mathematical Formulation, Stability Benchmarks, and Open-Source Implementation

Container stowage on feeder vessels requires solving a complex three-dimensional slot-assignment problem that pairs combinatorial cutting-and-packing constraints with continuous naval architectural hydrostatics. Traditional three-dimensional bin packing (3D-BPP) models maximize geometric volume without accounting for vertical center of gravity, metacentric height (GM), or hazardous material segregation, whereas monolithic mixed-integer programming (MIP) formulations scale poorly to operational turnaround windows. This paper develops a hydrostatically constrained 3D container slot-assignment heuristic tailored for cellular feeder vessels. We formulate a reference mixed-integer optimization model enforcing column stack capacity, tier mass stratification, refrigerated power receptacle matching, class-pair International Maritime Dangerous Goods (IMDG) separation distances, and draft-dependent metacentric stability (GM_T >= 0.15 m under IMO regulations, buffered to 0.30 m). To solve the resulting NP-hard problem in real time, we propose an O(n log n + n·M) constructive heuristic that evaluates a multi-criteria scoring function penalizing vertical moment rise and transverse/longitudinal imbalance, paired with an incremental moment-summation stability tracker. Extensive computational experiments across five feeder-vessel benchmark configurations (450–750 containers, mean 600; 520–800 slots, mean 654; 30 random seeds per scenario) demonstrate that the heuristic achieves a mean slot utilization of 83.7% ± 0.9%, an average manifest placement rate of 91.6% (91.1% under top-heavy stress testing), and an optimality gap of 1.42%–2.68% relative to an exact HiGHS mixed-integer linear programming upper bound in 0.98–1.72 s. An open-source Python implementation (py3dbc v1.0.2) and interactive 3D WebGL decision-support dashboard (CargoOptix) are provided to ensure full scientific reproducibility.