A Robust Optimisation Approach to Synchromodal Container Transportation

This chapter addresses synchromodal planning at operational level from the perspective of a logistics service provider and studies an optimisation problem with simultaneous vehicle routing and container-to-mode assignment, having uncertain data. It is assumed that the release times of the containers belong to an uncertainty interval, and no further statistical information is available. This problem belongs to the fourth quadrant of Fig. 1.4 . The container routing problem is modelled as a mixed integer program with explicit time variables and lateness penalties. A robust formulation is then proposed to eliminate the uncertain parameters from the objective function and constraints. By solving the new model exactly, with the aid of an optimisation solver, robust solutions are obtained corresponding to transportation plans which remain feasible for any realisation of the release times within the pre-specified uncertainty interval. In order to introduce some flexibility in the transportation plan, the continuous time variables are modelled as affine functions of the uncertain parameters. The resulting two-stage decision model is tested for a small-sized instance in both situations, with high and low lateness penalties.