One of the challenges of cloud computing is to assign virtual machines to physical machines optimally and efficiently. The aim of telecommunication operators is to minimize the mapping cost while respecting constraints regarding location, assignment and capacity. We formulate this problem which appears to be a quadratic constrained non-convex 0-1 program. Then, we propose to lift the problem to a higher dimensional space by classical linearization, thereby handling the problem in the framework of MIP. To improve its computational performance, we employ the Reformulation-Linearization-Technique (RLT) and add valid inequalities to strengthen the model. Some preliminary numerical experiments are conducted to show the effectiveness of these methods