Combined heat-and-power (CHP) production is an increasingly important technology for its efficient utilization of primary-energy resources and for reducing CO2 emissions. In the CHP plant, the generation of heat-and-power follows a joint characteristic, which makes the determination of both the marginal power production cost (MPPC) and the feasible operating region for the plant more complicated than for the power-only generation plant. Due to the interdependence between heat and power production, the power-ramp constraints, which limit how much the power production of a CHP plant may increase or decrease between two successive periods, may also imply constraints on the heat production. In this paper, we investigate the impact of power-ramp constraints on CHP production planning and develop a robust heuristic for dealing with the power-ramp constraints based on the solution to the problem with relaxed ramp-constraints (RRC). Numerical results based on realistic production models show that the heuristic can generate high-quality solutions efficiently.