Short-term hydro-thermal scheduling aims to obtain optimal generation scheduling of hydro and thermal units for a one-day or a one-week scheduling time horizon. The main goal of the problem is to minimize total operational cost considering a series of equality and inequality constraints. The problem is considered as a non-linear and complex problem involving the valve-point loading effect of conventional thermal units, the water transport delay between connected reservoirs, and transmission loss with a set of equality and inequality constraints such as power balance, water dynamic balance, water discharge, initial and end reservoir storage volume, reservoir volume limits and the operation limits of hydro and thermal plants. A solution methodology to the short-term hydro-thermal scheduling problem with continuous and non-smooth/non-convex cost function is introduced in this research applying dynamic non-linear programming. In this study, the proposed approach is applied to two test systems with different characteristics. The simulation results obtained in this paper are compared with those reported in recent research studies, which show the effectiveness of the presented technique in terms of total operational cost. In addition, the obtained results ensure the capability of the proposed optimization procedure for solving short-term hydro-thermal scheduling problem with transmission losses and valve-point effects.