Thanks Venkatesh for the reply.
Unfortunately, I can't confirm if your solution works cause in the meantime I managed to process the cube. I'm not sure what exactly worked cause I tried many things, but I think it was something along the lines of the solution described here:
community.dynamics.com/.../129181
So, I logged in as administrator, deleted the cube perspectives (SharedDimensions and ReqDemandPlaningCube), deleted the Visual studio project, compiled everything and tried processing the cube again. And it worked.