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We study the problem of optimising the provisioning of collections of virtual machines (VMs) having different placement constraints (e.g., security and anti-collocation) and characteristics (e.g., memory and disk capacity), given a set of physical machines (PMs) with known specifications, in order to achieve the objective of maximising an IaaS cloud provider's revenue. We propose two approaches. The first is based on the formulation of the problem as an integer linear programming (ILP) problem, the solution to which provides an optimal VM placement. The second approach is a heuristic based on classifying the requests into different categories and satisfying the constraints in a particular order using a first lit decreasing (FFD) algorithm for multi-dimensional vector bin packing problem. Given a model of VM placement constraints, offered resources and requests with multiple VM types, both approaches devise a …