A system and method for planning placement of virtual machines VMs in a computing environment comprising a set of hosting machines HM. The method includes constructing a bipartite directed graph-based model that represents both a current and a target placement states, both including virtual machine nodes v in VM and nodes h in HM. Using a technique of graph pruning, the method iteratively generates a plan for achieving a desired target placement starting from the current placement without temporarily violating any policy or resource constraint. The application of the pruning algorithm to VM deployment automation necessarily defines a new model. The methodology employed safely manages concurrent changes in a datacenter, so that the environment can adjust faster to changing constraints. Furthermore, the present invention allows detection of migration cycles, caused by deadlocked combinations of capacity and policy constraints, and resolving them.