Greedy algorithm for local heating problem

This paper studies a planning problem for heating water. Hereby, boilers (e.g. gas or electric boilers, heat pumps or microCHPs) are used to heat the water and store it for domestic demands. We consider a simple boiler which is either turned on or turned off and has a buffer of limited capacity. The energy needed to run the boiler has to be bought on a day-ahead market, so we are interested in a planning which minimizes the cost to supply the boiler with energy. We present a greedy algorithm whose time complexity is O(Tα(T)) where T is the number of time intervals and α is the inverse of Ackermann function.