A predictive apparatus for controlling or regulating supply values (T_VRL) includes a first data store in which rules, based on a linear consumer model, for calculating process values are stored, a second data store in which rules for restrictions or limit values to be observed for process values and for values derived from process values are stored, and further also means for repeatable optimizing of the energy consumption or of the energy costs with the aid of linear or quadratic programming. The apparatus is configured such that the optimizing can be carried out over a sliding time horizon.