An approximate dynamic programming approach to urban freight distribution with batch arrivals

We study a dispatch problem with uncontrolled batch arrivals of LTL orders at an urban consolidation center. These arrivals re ect the delivery of goods by independent carriers. The speci c order properties (e.g., destination, size, delivery window) may be highly varying in city logistics, and directly distributing an incoming batch may yield high costs. Instead, the hub operator may decide to wait for incoming batches that allow for more e cient distribution. A waiting policy is required to decide which orders to ship and which orders to hold. We model the dispatching problem as a Markov decision problem. Dynamic Programming (DP) is applied to solve toy-sized instances. To solve realistic instances, we propose an Approximate Dynamic Programming (ADP) approach. Through numerical experiments, we show that the ADP approach closely approximates the optimal values of DP for small instances, and outperforms two benchmark policies for larger instances