A Decomposed Fourier-Motzkin Elimination Framework to Derive Vessel Capacity Models

Accurate Vessel Capacity Models (VCMs) expressing the
trade-off between different container types that can be stowed on container
vessels are required in core liner shipping functions such as uptake-,
capacity-, and network management. Today, simple models based on volume,
weight, and refrigerated container capacity are used for these tasks,
which causes overestimations that hamper decision making. Though previous
work on stowage planning optimization in principle provide finegrained
linear Vessel Stowage Models (VSMs), these are too complex
to be used in the mentioned functions. As an alternative, this paper
contributes a novel framework based on Fourier-Motzkin Elimination
that automatically derives VCMs from VSMs by projecting unneeded
variables. Our results show that the projected VCMs are reduced by
an order of magnitude and can be solved 20–34 times faster than their
corresponding VSMs with only a negligible loss in accuracy. Our framework
is applicable to LP models in general, but are particularly effective
on block-angular structured problems such as VSMs. We show similar
results for a multi-commodity flow problem.