Combined heat and power (CHP) production is an important energy production technology which can help to improve the efficiency of energy production and to reduce the emission of CO2. Cost-efficient operation of a CHP system can be planned using an optimisation model based on hourly load forecasts. A long-term planning model decomposes into hourly models, which can be formulated as linear programming (LP) problems. Such problems can be solved efficiently using the specialized Power Simplex algorithm. However, Power Simplex can only manage one heat and one power balance. Since heat cannot be transported over long distances, Power Simplex applies only for local CHP planning. In this paper we formulate the hourly multi-site CHP planning problem with multiple heat balances as an LP model with a special structure. We then develop the Extended Power Simplex (EPS) algorithm for solving such models efficiently. Even though the problem can be quite large as the number of demand sites increases, EPS demonstrates very good efficiency. In test runs with realistic models, EPS is from 29 to 85 times faster than an efficient sparse Simplex code using the product form of inverse (PFI). Furthermore, the relative efficiency of EPS improves as the problem size grows.