This letter focuses on the problem of pilot assignment in cell-free massive MIMO systems. Exploiting the well-known Hungarian algorithms, two procedures are proposed, one maximizing the system throughput, and the other one maximizing the fairness across users. The algorithms operate based on the knowledge of large-scale fading coefficients as a proxy for the distances between users in the system and take into account both the uplink and downlink performance. Numerical results show that the proposed pilot assignment algorithms are effective and outperform the many competing alternatives available in the literature.