Cloud computing is a dynamically evolving computing paradigm. The demand for cloud applications and technologies has especially increased during the CoVID-19 pandemic and martial law in Ukraine. The main purpose of using cloud applications and technologies is to free users of cloud resources from managing hardware and software. One of the challenges in designing a private university cloud is estimating the required number of virtualization cluster nodes. These hosts host virtual machines (VMs) of users. These VMs can be used by students and teachers to complete academic assignments as well as scientific work. The second task is to optimize the placement of VMs in the computer network (CN) of the university, which makes it possible to reduce the number of CN nodes without affecting functionality. And this ultimately helps to reduce the cost of such a solution to deploy a private university cloud, which is not unimportant for Ukrainian universities under martial law. The article proposes a model for estimating the required number of virtualization cluster nodes for a private university cloud. The model is based on a combined approach that involves jointly solving the problem of optimal packing and finding, using a genetic algorithm, the configuration of server platforms of a private university cloud.