An Integrated Approach to Tactical Transportation Planning in Logistics Networks

We propose a new mathematical model for transport optimization in logistics networks on the tactical level. The main features include accurately modeled tariff structures and the integration of spatial and temporal consolidation effects via a cyclic pattern expansion. Using several graph-based gadgets, we are able to formulate our problem as a capacitated network design problem. To solve the model, we propose a local search procedure that reroutes flow of multiple commodities at once. Initial solutions are generated by various heuristics, relying on shortest path augmentations and LP techniques. As an important subproblem we identify the optimization of tariff selection on individual links, which we prove to be NP-hard and for which we derive exact as well as fast greedy approaches. We complement our heuristics by lower bounds from an aggregated mixed-integer programming formulation with strengthened inequalities. In a case study from the automotive, chemical, and retail industries, we prove that most of our solutions are within a single-digit percentage of the optimum.