We study the important and challenging problem of virtualized radio access network (vRAN) design in its most general form. We develop an optimization framework that decides the number and deployment locations of central/cloud units (CUs); which distributed units (DUs) each of them will serve; the functional split that each BS will implement; and the network paths for routing the traffic to CUs and the network core... Our design criterion is to minimize the operator's expenditures while serving the expected traffic. To this end, we combine a linearization technique with a cutting-planes method in order to expedite the exact solution of the formulated problem. We evaluate our framework using real operational networks and system measurements, and follow an exhaustive parameter-sensitivity analysis. We find that the benefits when departing from single-CU deployments can be as high as 30% for our networks, but these gains diminish with the further addition of CUs. Our work sheds light on the vRAN design from a new angle, highlights the importance of deploying multiple CUs, and offers a rigorous framework for optimizing the costs of Multi-CUs vRAN. (read more)