Consolidation techniques leverage thresholds to detect overloaded and underloaded hosts that could be vacated to achieve optimal balance between host utilization and energy consumption. Most of existing energy efficiency techniques save energy against the cost on performance degradation. Virtual machine consolidation remains the most deployed strategy to manage both performance and energy consumption.

By extensive computational experiments, we show that (i) the proposed formulation significantly outperforms existing formulations in terms of solution efficiency and (ii) compared with standard MILP solvers, the proposed C&S algorithm is much more efficient.An important issue of energy efficiency in cloud environment is to perform more jobs while consuming less amount of power. The proposed C&S algorithm is based on a novel relaxation of the VMCP that provides a stronger lower bound than the natural continuous relaxation of the VMCP, making a smaller search tree. We then develop a cut-and-solve (C&S) algorithm, a tree search algorithm to efficiently solve the VMCP to optimality. We show that compared with existing formulations, the proposed formulation is much more compact in terms of smaller numbers of variables or constraints, which makes it suitable for solving large-scale problems. In this paper, we first propose a new mixed integer linear programming (MILP) formulation for the VMCP. The virtual machine consolidation problem (VMCP) attempts to determine which servers to be activated, how to allocate virtual machines (VMs) to the activated servers, and how to migrate VMs among servers such that the summation of activated, allocation, and migration costs is minimized subject to the resource constraints of the servers and other practical constraints.