Distillation columns with multiple feeds are often used in processes for the separation of multicomponent mixtures. The minimum energy demand of such columns is determined via the minimum reflux and reboil, respectively. A novel method for directly calculating the minimum reflux ratio is presented in this paper. Applicable to ideal, nonideal and azeotropic mixtures the method is based merely on the knowledge of vapor-liquid equilibrium of the feed mixtures. This knowledge allows the determination of the internal concentration profile near the feed entry and, in turn, the calculation of both minimum reflux and optimal sequence of feeds. This sequence of feeds depends on feed compositions and product compositions, as well. Surprisingly, sometimes a multiple feed entry requires a higher energy demand than premixing the feed streams.