The rapid growth of express business has led to a significant increase in the complexity of sorting, driving the rapid development of automated sorting systems. Therefore, a floor-based sorting system has been developed to enhance the flexibility, economy and scalability of automated sorting systems. In this paper, parcel assignment and conflict-free routing of automated guided vehicles in a floor-based sorting system are studied. Two mixed integer programming models are proposed to minimize the parcel dwell time in the system. To solve the models efficiently, two column generation-based solution algorithms are designed with embedded acceleration techniques such as the variable neighborhood search algorithm and the A* algorithm. Numerous numerical experiments are performed to verify the validity of the models and the efficiency of the algorithms. Sensitivity analysis experiments are also performed to provide some management insights.