Decomposition techniques for urban consolidation problems

Less-than-truckload deliveries is known to be a source of inefficiency in last-mile logistics leading to high transport costs, environmental pollution, traffic jam, particularly in urban settings. An Urban Consolidation Center (UCC) provides a platform to consolidate freights from various sources before delivering into the city. The operations of UCCs consist of 2 interrelated phases, consolidating freights and scheduling trucks into the city center. This problem is computationally challenging because of large urban freight volumes, which prohibits optimal solutions of conventional integer programming models to be found efficiently. In this paper, we propose two novel decomposition schemes: a vertical decomposition based on dynamic programming can achieve optimal consolidation for the single-period problem, and the horizontal decomposition based on a Lagrangian Relaxation can achieve good approximate solution for the multi-period problem. The combination of these two decompositions yield an efficient approach for dealing with large-scale problems.