Aims. We test whether the mass-and σ-[α/Fe] relations in the stellar populations of early-type galaxies can be reproduced by a cosmologically motivated assembly history for spheroids.Methods. We implement a detailed treatment for the chemical evolution of H, He, O, and Fe in GalICS, a semi-analytical model for galaxy formation that successfully reproduces basic low-and high-redshift galaxy properties. We take the contribution of supernovae into account (both type Ia and II), as well as low-and intermediate-mass stars, to chemical feedback. The model predictions are compared with the most recent observational results.Results. We find that the model shows significant improvement at the highest masses with respect to previous work, where the most massive galaxies were also the most α-depleted. In fact the predicted [ α/Fe] ratios in this regime are now marginally consistent with observed values. We show that this result comes from the implementation of AGN quenching of star formation in massive haloes. However, this does not help with the creation of the mass-metallicity relation. Instead, at intermediate masses, the scatter in the predicted [ α/Fe] ratios is much larger than the observed dispersion. This problem is related to inadequacies of the model in treating satellite galaxies. In particular, we find an excess of low-mass strongly α-enhanced satellites.Conclusions. The final stellar [ α/Fe] of a single galaxy is determined by the star formation history summed over all the progenitors. In particular, a longer duration the integrated star formation history leads to a lower α-enhancement, as might be expected from the results of closed box chemical evolution models. However, non-negligible differences between closed box and hierarchical model predictions are found, due to processes such as dry mergers and hot gas-phase metal recycling in the latter case. These processes help to build up the galactic mass while keeping the α element abundance in the stars at a super-solar level. To match the observed mass-[ α/Fe] relation at low and intermediate masses, we suggest that the next generation of semi-analytical model should feature either stellar or AGN feedback schemes that allow galaxies to self-regulate their own star formation history, rather than being crudely linked to the halo mass. At the same time, mechanisms that allow the very old and passively evolving satellite galaxies that do not merge to accrete fresh gas and form stars at later times should be implemented.