This paper presents two exact algorithms for energy efficient scheduling of virtual machines (VMs) in cloud data centers. Modeling of energy aware allocation and consolidation to minimize overall energy consumption leads us to the combination of an optimal allocation algorithm with a consolidation algorithm relying on migration of VMs at service departures. The optimal allocation algorithm is solved as a bin packing problem with a minimum power consumption objective. It is compared with an energy aware best fit algorithm. The exact migration algorithm results from a linear and integer formulation of VM migration to adapt placement when resources are released. Experimental results show benefits of combining the allocation and migration algorithms and demonstrate their ability to achieve significant energy savings while maintaining feasible runtimes when compared with the best fit heuristic.