Switched Ethernet networks rely on the Spanning Tree Protocol (STP) to ensure a cycle-free connectivity between nodes, by reducing the topology of the network to a spanning tree. The Multiple Spanning Tree Protocol (MSTP) allows for the providers to partition the traffic in the network and assign it to different virtual local area networks, each satisfying the STP. In this manner, it is possible to make a more efficient use of the physical resources in the network. In this paper we consider the traffic engineering problem of finding optimal designs of switched Ethernet networks implementing the MSTP, such that the worst-case link utilization is minimized. We show that this problem is N P-hard. We propose three mixed-integer linear programming formulations for this problem. Through a large set of computational experiments, we compare the performance of these formulations. Until now, the problem was almost exclusively solved with heuristics. Our objective here is provide a first comparison of different models that can be used in exact methods.