Column Generation and Lazy Constraints for solving the Liner Ship Fleet Repositioning Problem with cargo flows

TL;DR

This paper improves the mathematical modeling of the liner shipping fleet repositioning problem by applying column generation and lazy constraints, enabling optimal solutions for complex instances within minutes.

Contribution

It introduces a novel combination of column generation and lazy constraints to efficiently solve large-scale LSFRP instances to optimality.

Findings

All instances solved to optimality within four minutes.

Column generation significantly reduces model size.

Lazy constraints further improve solution efficiency.

Abstract

We consider an important problem in the shipping industry known as the liner shipping fleet repositioning problem (LSFRP). We examine a public data set for this problem including many instances which have not previously been solved to optimality. We present several improvements on a previous mathematical formulation, however the largest instances still result in models too difficult to solve in reasonable time. The implementation of column generation reduces the model size significantly, allowing all instances to be solved, with some taking two to three hours. A novel application of lazy constraints further reduces the size of the model, and results in all instances being solved to optimality in under four minutes.