This work considers a multi-resource routing problem (MRRP) where drayage orders need to be completed with trucks and trailers from multiple cooperating carriers. The problem contains multiple challenging aspects including a complex pricing model and the need to coordinate cooperating vehicles of several carriers. While the cooperation aspect of the problem can make the overall drayage operation more efficient, it also introduces additional requirements, most notably a cooperation model which respects the individual preferences of carrier companies and customers. In this paper, we first present an efficient way to model this problem and describe a system that collects and analyzes the required data. We then introduce a solution method based on a variable neighborhood search (VNS) metaheuristic, describe our solution representation and discuss the cost function which is specially tailored to the resource sharing aspect of the problem. Finally, we present a scenario-based evaluation of the system based on real-world data and discuss the results.