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When deploying services in a cloud, a balance must be found between performance and capacity of the service, and the memory available on nodes. This is further complicated if the number of replicas of an application is limited, for instance by the available number of licenses. The analysis of interference between services must scale to large numbers of host nodes, applications, replicas of applications, and classes of users. This paper combines a multi-dimensional packing heuristic and network flow optimization to satisfy simultaneous constraints on throughputs, processor utilizations, memory availability and license availability, at a minimum cost and with a minimum of host processors.