An efficient design of in-bound transport systems is crucial to meet the challenges of performance and reliability facing logistics, as they represent a central part of production and distribution systems. Moreover, these systems often consist of a heterogeneous fleet of vehicles, e.g., forklifts, tugger trains, and automated guided vehicles. Besides the vehicles' different technical and physical aspects, control strategies also significantly impact the system performance. Therefore, order assignment, i.e., how transport orders are distributed among the vehicles, is of primary importance. This work presents a new method based on the Hungarian algorithm for dynamically solving the transport-order assignment problem. For an exemplary transport system, we then use discrete event simulation to study the impact of different assignment strategies on the system performance.