We address the problem of optimally scheduling automated vehicles crossing an urban intersection by assigning vehicles with priorities. We formulate the intersection scheduling problem as a Mixed Integer Programming (MIP) problem which co-designs the priority and traveling speed for each vehicle. The co-design aims to minimize the vehicle waiting time at the intersection area, under a set of safety constraints. To solve the problem, we present a contention-resolving Model Predictive Control (MPC) method to dynamically assign priorities and compute the optimal speed for each vehicle based on the assigned priorities. The optimal priority assignment can be determined using a sampling based approach. The effectiveness of the proposed method is validated through simulation and shows reductions in traveling time.