A Mixed-Integer Programming Model for the Container Truck Routing Problem with Net Worth Maximization

We address the container truck routing problem that arises in hinterland logistics, where trucking companies are responsible for transporting empty and loaded containers between various stakeholders in the shipping container supply chain, including consignees, shippers, and others. This problem involves determining efficient routes that balance empty and loaded trips, enabling trucking companies to meet customer transportation requests while optimizing their operations. In this paper, we investigate a variant of the container truck routing problem that focuses on maximizing the net worth of a trucking company by identifying the most profitable set of routes. The model takes into account two types of containers (40-ft and 20-ft) and two types of trucks (long trucks and short trucks). We prove that the problem is NP-hard and propose a compact mixed-integer programming formulation. To evaluate the effectiveness of our approach, we conduct numerical experiments. The results demonstrate that the proposed model delivers optimal solutions for relatively large randomly generated instances. This evidence underscores the practical applicability and efficiency of our proposed approach in solving the container truck routing problem.