A solution to a variant of a class constrained multiple knapsack problem. Previous solutions require that memory demand of every application be identical and do not consider minimizing placement changes. Previous techniques do not consider optimizing placement to improve load balancing as is described subsequently. Thus, the present invention provides systems, methods and apparatus, encapsulated in software, to provide the dynamic placement of application instances on a heterogeneous cluster of server machines. It depends on the existence of a visible and controllable platform, systems management and other business services that signal events and accept commands. It provides dynamically placing applications on servers such as to maximize a total amount of satisfied application demands, minimize a number of placement changes from a current placement, and minimize imbalance of load distribution of said applications on said at least one server.