An embodiment of the disclosure provides a method, performed by a resource management server, for mapping a plurality of unassigned virtual machines (VMs) to a plurality of physical machines (PMs). The resource management server includes a non-transient computer readable medium and a processor to execute computer executable instructions stored on the non-transient computer readable medium, so that when the instructions are executed, the resource management server performs the method of: (a) obtaining a total resource demand for each dimension requested by the plurality of unassigned VMs; (b) activating at least one PM in the plurality of PMs to create a set of activated PMs; (c) assigning at least one unassigned VM to the set of activated PMs, wherein a VM assigned to a PM has an equal or lower resource demand for each dimension compared to a remaining resource capacity for each respective dimension of the PM; (d) determining whether all unassigned VMs have been assigned to a PM in the set of activated PMs; and (e) conditionally activating one or more PMs when all unassigned VMs have not been assigned to a PM in the set of activated PMs.