The economic dispatch of active power in large-scale power systems is considered and an algorithm for the solution of the problem by means of the sparse dual revised Simplex method is presented. Computational experience with large-scale problems, including dynamic dispatch over several time steps, is given, which indicates that the method has very low memory and processor time requirements and is suitable for implementation on minicomputer systems. The algorithm is extended to allow for hierarchical constraint relaxation and removal in cases where an infeasible problem has been specified inadvertently. The availability of such a constraint relaxation strategy permits the application of approximate methods for the inclusion of transmission losses and spare capacity constraints.