Energy-efficient control of a vacuum pump having a pump controller integrated in a control and regulation device used in an industrial furnace complex is disclosed. A method and an industrial furnace complex provide incremental deactivation or activation of the vacuum pump depending on whether a vacuum is needed by using a program having one or more program steps, including a first query about whether a heat treatment process is active in the industrial furnace, a second query about whether the vacuum pump is required in a current phase of the heat treatment process, a third query about whether the vacuum pump will be required in a future phase of the heat treatment process, and/or a fourth query about whether a time until the next operation is greater than a required lead time for the vacuum pump to warm up.