Currently, there is serious political support for the decarbonization of transport locally, nationally and even internationally. Public transport operators are focusing on the use of electric buses as an opportunity to reduce greenhouse gas emissions and improve air quality. However, using electric buses requires a functional infrastructure of urban charging points. Fast-charging can be made available thanks to the progress made on the major technological charging devices in recent years. In this study, we consider an optimization problem of the design of an infrastructure for a fast-charge city electric bus service. The decisions which have to be made include determining a mixed fleet of conventional and electric buses, points for electric chargers and power stations, quantities of charging plug devices, a distribution of electric buses between the routes, and matching chargers with power stations. The objective is to maximize the route-weighted total passenger capacity of electric buses. An Integer Linear Programming model has been developed to complement the existing non-linear model. The new model is efficient if the number of possible charging spots is small, which is natural and frequent in practice. Extensive computer experiments demonstrate that our approach delivers near-optimal solutions of the studied problem in ten minutes for real-world instances on a standard PC and it outperforms the earlier approach on every instance.