In today’s complex and dynamic transportation networks, increasing energy costs and adverse environmental impacts necessitate the efficient transport of goods or raw materials across a network to minimize all related costs through vehicle assignment and routing decisions. Vehicle routing problems under dynamic and stochastic conditions are known to be very challenging in both mathematical modeling and computational complexity. In this study, a special variant of the full-truckload vehicle assignment and routing problem was investigated. First, a detailed analysis of the processes in a liquid transportation logistics firm with a large fleet of tanker trucks was conducted. Then, a new original problem with distinctive features compared with similar studies in the literature was formulated, including pickup/delivery time windows, nodes with different functions (pickup/delivery, washing facilities, and parking), a heterogeneous truck fleet, multiple trips per truck, multiple trailer types, multiple freight types, and setup times between changing freight types. This dynamic optimization problem was solved using an intelligent multi-agent model with agent designs that run on vehicle assignment and routing algorithms. To assess the performance of the proposed approach under varying environmental conditions (e.g., congestion factors and the ratio of orders with multiple trips) and different algorithmic parameter levels (e.g., the latest response time to orders and activating the interchange of trip assignments between vehicles), a detailed scenario analysis was conducted based on a set of designed simulation experiments. The simulation results indicate that the proposed dynamic approach is capable of providing good and efficient solutions in response to dynamic conditions. Furthermore, using longer latest response times and activating the interchange mechanism have significant positive impacts on the relevant costs, profitability, ratios of loaded trips over the total distance traveled, and the acceptance ratios of customer orders.