Optimizing capacity profiles for effective heating management

We study the capacity planning of a heating plant that supplies multiple buildings in a district heating network. Each flat has specific temperature requirements throughout the day, maintained through radiators fed by hot water from the heating plant. The plant remotely controls water flow rates to the radiators, selecting from a discrete set of options for each flat. Heat is generated by multiple boilers with different capacities and operating costs. The objective is to determine a cost-minimizing heat production plan while ensuring that all temperature requirements are met. We formulate this as a capacitated multi-item lot sizing problem and propose an improved mathematical formulation. We show that the problem is polynomial time solvable when radiators are identical and develop a decomposition based solution methodology for the general case with heterogeneous radiators. Extensive computational experiments demonstrate the effectiveness of the proposed approach in handling instances of varying sizes and cost patterns. We also provide practical insights for real world district heating applications, showing the potential for significant energy savings while maintaining user comfort. The proposed approach can be extended to other energy systems that incorporate heat storage and cogeneration.