We consider fairness scheduling in a user-centric cell-free massive MIMO network, where $L$ remote radio units, each with $M$ antennas, serve $K_{\rm tot} \approx LM$ user equipments (UEs). Recent results show that the maximum network sum throughput is achieved where $K_{\rm act} \approx \frac{LM}{2}$ UEs are simultaneously active in any given time-frequency slots. However, the number of users $K_{\rm tot}$ in the network is usually much larger. This requires that users are scheduled over the time-frequency resource and achieve a certain throughput rate as an average over the slots. We impose throughput fairness among UEs with a scheduling approach aiming to maximize a concave component-wise non-decreasing network utility function of the per-user throughput rates. In cell-free user-centric networks, the pilot and cluster assignment is usually done for a given set of active users. Combined with fairness scheduling, this requires pilot and cluster reassignment at each scheduling slot, involving an enormous overhead of control signaling exchange between network entities. We propose a fixed pilot and cluster assignment scheme (independent of the scheduling decisions), which outperforms the baseline method in terms of UE throughput, while requiring much less control information exchange between network entities.