This paper develops, implements, and applies a mathematical model for economic unit dispatch for a novel cogeneration concept (CHP-HP-FG-CS (CHP with compression heat pump and cold storage using flue gas heat)) that increases the plant's operational flexibility. The CHP-HP-FG-CS concept is a high-efficiency and widely applicable option in distributed cogeneration better supporting the co-existence between cogenerators and intermittent renewables in the energy system. The concept involves integrating an efficient high-temperature compression heat pump that uses only waste heat recovered from flue gases as low-temperature heat source, and an intermediate cold thermal storage allowing for non-concurrent operation of the cogeneration unit and the heat pump unit. The model is applied for a paradigmatic case study that shows how the integration of a heat pump affects the operational strategy of a cogeneration plant. It is found that CHP-HP-FG-CS offers significant reductions in fuel consumption (-8.9%) and operational production costs (-11.4%). The plant's fuel-to-energy efficiency increases from 88.9 to 95.5%, which is state-of-the-art. The plant's intermittency-friendliness coefficient Rc improves only marginally due to the constrained nature of the low-temperature heat source and the associated small capacity of the heat pump unit. Significant improvements in Rc are found when increasing the heat pump capacity assuming the availability of an unconstrained heat source