When dealing with the tensor network representation of a system interacting with several baths, the actual ordering of the bath modes is arbitrary and often chosen on the grounds of the simplicity of the representation and practicality of the actual numerical implementation. In this chapter we explore the influence of different ordering of the baths modes, and different geometries of the tensor network, on the ressources needed for simulating the time evolution of a quantum system. We show surprising results and empirically demonstrate that the ‘common sense’ physical argument often invoked to motivate the usual tensor network geometry of a system interacting with several environments is wrong.