We consider the problem of how to place and efficiently utilize resources in network environments. The setting consists of a regionally organized system which must satisfy regionally varying demands for various resources. The operator aims at placing resources in the regions as to minimize the cost of providing the demands. Examples of systems falling under this paradigm are 1) A peer supported Video on Demand service where the problem is how to place various video movies, and 2) A cloud-based system consisting of regional server-farms, where the problem is where to place various contents or end-user services. The main challenge posed by this paradigm is the need to deal with an arbitrary multi-dimensional (high-dimensionality) stochastic demand. We show that, despite this complexity, one can optimize the system operation while accounting for the full demand distribution. We provide algorithms for conducting this optimization and show that their complexity is pretty small, implying they can handle very large systems. The algorithms can be used for: 1) Exact system optimization, 2) deriving lower bounds for heuristic based analysis, and 3) Sensitivity analysis. The importance of the model is demonstrated by showing that an alternative analysis which is based on the demand means only, may, in certain cases, achieve performance that is drastically worse than the optimal one.