The problem is tackled of the allocation of the resources assigned for upgrading an ensemble of buildings or other constructed facilities, whose seismic reliability is not considered sufficient. The resources are allocated in order to minimize the predicted value of either the economic losses, the number of endangered persons or the risk of severance of a network. The optimization procedure, although formulated in general terms, is illustrated with reference to simple examples, in which realistic values are attributed to the relevant parameters. These examples refer to masonry buildings, whose damages can be summed with each other to obtain the total damage of the ensemble, and to a highway network, whose critical elements are reinforced concrete bridges. The presence of several discrete quantities and discontinuous relationships requires the use of specific algorithms, and in particular of dynamic programming.
