Most important large-scale surveys carried out by national statistical institutes are the repeated survey type, typically intended to produce estimates for several parameters of the whole population, as well as parameters related to some subpopulations. Small area estimation techniques are becoming more and more important for the production of official statistics where direct estimators are not able to produce reliable estimates. In order to exploit data from different survey cycles, unit-level linear mixed models with area and time random effects can be considered. However, the large amount of data to be processed may cause computational problems. To overcome the computational issues, a reformulation of predictors and the correspondent mean cross product estimator is given. The R code based on the new formulation enables the elaboration of about 7.2 millions of data records in a matter of minutes.