Observables for single-inclusive hadron productions can be calculated by convolution of process-dependent partonic cross sections and universal fragmentation functions (FFs) at leading power in QCD factorization theory. The FMNLO framework is proposed to perform such calculations in an automated way at next-to-leading order (NLO) in QCD using general-purpose Monte Carlo generators. In this talk, we present the basic idea of FMNLO, which relies on a combination of the phase-space slicing method and local subtraction methods. Additionally, with the help of interpolation techniques, FMNLO is also a promising tool for fits of FFs. We present the outcomes of a new NLO fit of FFs to unidentified charged hadrons using LHC measurements, with particular sensitivity to the gluon FF.