Network utility maximization (NUM) addresses the problem of allocating resources fairly within a network and explores the ways to achieve optimal allocation in real-world networks. Although extensively studied in classical networks, NUM is an emerging area of research in the context of quantum networks. In this work, we consider the quantum network utility maximization (QNUM) problem in a static setting, where a user’s utility takes into account the assigned quantum quality (fidelity) via a generic entanglement measure, as well as the corresponding rate of entanglement generation.