The purpose of this study is to compare two analytical methods with two numerical methods for minimizing the entropy production rate in diabatic distillation columns (i.e., with heat exchangers on all trays). The first analytical method is the equal thermodynamic distance method. The second uses Lagrange minimization on a model derived from irreversible thermodynamics. The numerical methods use Powell's and a Monte Carlo algorithm and gave the same results. Both analytical methods agreed well with the numerical ones for two columns with low separation per tray, while they did not agree well for a column with large separation per tray.