A Node Flow Model for the Inflexible Visitation Liner Shipping Fleet Repositioning Problem with Cargo Flows

We introduce a novel, node flow based mathematical model
for the fixed-time version of a central problem in the liner shipping industry called the Liner Shipping Fleet Repositioning Problem (LSFRP). We call this version of the problem the Inflexible Visitation LSFRP (IVLSFRP).
During repositioning, vessels are moved between routes in a liner
shipping network. Shipping lines wish to reposition vessels as cheaply as possible without disrupting the cargo flows of the network. The LSFRP is characterized by chains of interacting activities with a multi-commodity flow over paths defined by the activities chosen. We introduce two versions of a node flow based model that exploit the fixed activity times
of the IVLSFRP’s graph to handle cargo demands on the nodes of the graph, instead of the arcs, significantly reducing the number of variables.
Using this model in CPLEX, we are able to solve 12 previously unsolved IVLSFRP instances to optimality. Additionally, we improve the solution time on every instance in the IVLSFRP dataset, sometimes by several orders of magnitude.