Network design, fleet deployment and empty repositioning in liner shipping

We present an integrated modelling framework for the joint problems of network design, fleet deployment and empty repositioning in liner shipping. In our problem the number of service routes and their design are an endogenous part of the problem. The cost of a route is a set function mapping a subset of edges, vessel types and quantities to deploy to the set of non-negative real numbers. Since such cost structures cannot be accommodated in a compact formulation, our modelling framework, which is based on the paradigm of the Benders reformulation, integrates separate problems aiming to obtain a solution to the integrated problem. In this work we look at the Benders approach as a tool for integrating separate optimization problems rather than decomposing an integrated holistic optimization problem. Our numerical experiments show that the method is very efficient in solving instances of this problem with respect to both the problem size and the computational time.