A Decomposed Fourier-Motzkin Elimination Framework to Derive Capacity Models of Container Vessels

Accurate capacity models 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 fine-grained linear Vessel Stowage Models (VSMs), they 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 Vessel Capacity Models (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 20-35 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.