Dynamic multi-period freight consolidation

Logistic Service Providers (LSPs) o ering hinterland transportation face the trade-o between e ciently using the capacity of long-haul vehicles and minimizing the rst and last-mile costs. To achieve the optimal trade-o , freights have to be consolidated considering the variation in the arrival of freight and their characteristics, the applicable transportation restrictions, and the interdependence of decisions over time. We propose the use of a Markov model and an Approximate Dynamic Programming (ADP) algorithm to consolidate the right freights in such transportation settings. Our model incorporates probabilistic knowledge of the arrival of freights and their characteristics, as well as generic de finitions of transportation restrictions and costs. Using small test instances, we show that our ADP solution provides accurate approximations to the optimal solution of the Markov model. Using a larger problem instance, we show that our modeling approach has signi cant bene ts when compared to common-practice heuristic approaches.