In the polymer melt spinning process used to create polymer fibers the macroscopic dynamics is tightly connected to the microscopic state of the polymer chains through the stress and strain-rate fields. To probe the different time- and length-scales in the system, it is necessary to use a combined micro-macro simulation method. In this study, we apply such a multi-scale simulation to study the polymer spinning process. In our multi-scale simulations, we use a microscopic model to describe the entanglement polymer dynamics and a macroscopic model to track the deformation rate imposed at a material point. For the former, we use a slip-link model, for the latter a particle-based Lagrangian model. With this approach, we are able to successfully take into account the memory effects, as well as provide a quantitative evaluation of the polymer dynamics, including the effects of entanglement. We performed extensive simulations to study the relationship between the macroscopic spinning conditions and the microscopic properties of the melt, such as the orientation and level of entanglement of the polymer chains.