<p>In this paper we consider the existence of optimal solutions to dynamic optimization problems in which the decision variables are ordinary controls, a finite sequence of discrete controls giving rise to jump discontinuities in the state variables, and a finite sequence of decision times at which the discrete controls are implemented. The distance between two successive decision times is uniformly bounded below by a positive constant, which allow us to consider the admissible state trajectories as piecewise absolutely continuous functions. We show that for the models considered here the existence of an optimal solution can be obtained under conditions analogous to those in the work of L. Cesari and others for ordinary control problems. Examples arising in the operations research literature are presented to which the existence results apply.</p>