In this thesis we propose a model for a two-dimensional auction of public service concession agreements. The government design of the auction involves an almost linear scoring rule that evaluates the price charged and the time to start providing the services. The model applies to the public services that improve social welfare by reducing the delivery time of services. Suppliers have private information about their costs and time reduction offer. The proposed scoring rule of each supplier reduces the dimensionality of the bids submitted to a single dimension. The winner is committed to his bid and obliges to provide the required services. The model assists in preparing the design of the auction in order to maximize the preferences of the government given to the strategic behavior of buyers.