A robust optimization approach to synchromodal container transportation

Abstract

This thesis addresses synchromodal planning at operational level from the perspective of a logistics service provider. The existing infrastructure and the transportation activities are studied and modeled as an optimization problem with simultaneous vehicle routing and container-to-mode assignment. A special characteristic of this problem is the uncertain data. In other words, it is assumed that the release times of the containers belong to an uncertainty interval, and no further statistical information is available. The problem is then classified according to an extensive framework previously developed within the project. An extensive body of literature is reviewed to identify current modeling approaches and their theoretical and practical limitations. This literature study shows that, although discrete time models have been intensively investigated, there are few studies which propose continuous modeling of time. The container routing problem is modeled 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 optimization solver, robust solutions are obtained corresponding to transportation plans which remain feasible for any realization 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 modeled 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. The computational results show that the adjustable robust model yields on the one hand, route-dependent adjusted solutions for the case of penalized lateness, and on the other hand, a direct improvement of the objective function for the case of tolerated lateness. The results suggest that the adjustable robust optimization framework has sufficient potential to model the synchromodal container routing problem. This thesis concludes with addressing some of the limitations of the proposed model and indicating concrete approaches for countering them.