In a cloud data center, servers are always over-provisioned in an active state to meet the peak demand of requests, wasting a large amount of energy as a result. One of the options to reduce the power utilization of server farms is to diminish the quantity of sit still servers or to switch idle servers into a low-power sleep states. Notwithstanding, the servers can’t process the requests quickly when transiting to the active state. There are delays and extra power consumption during progress. In this project, we consider utilizing state of the art servers with multi-sleep modes. The sleep modes with smaller transition delays, usually consume more power when sleeping. Given the arrival of incoming requests, our goal is to limit the power utilization of the cloud data center by the planning of servers with multi-sleep modes. We formulate the issue as an integer linear programming (ILP) issue during the whole period of time with millions of decision variables. To solve this issue, we divide it into sub-issues with the smaller period while ensuring the feasibility and each transition continuity for each sub-issues through a Backtrack-and-Update technique. Experiments demonstrate that our technique can significantly decrease the power utilization for a cloud data center.