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 $\mathcal{O}\left(T\alpha \left(T\right)\right)$ where $T$ is the number of time intervals and $\alpha$ is the inverse of Ackermann function.

中文翻译：

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局部供暖问题的贪婪算法

本文研究了热水的规划问题。因此，锅炉（例如燃气或电锅炉，热泵或微型CHP）用于加热水并将其存储以供家庭使用。我们考虑一个简单的锅炉，该锅炉可以打开或关闭，并具有有限容量的缓冲区。运行锅炉所需的能量必须在日间市场上购买，因此我们对一项计划感兴趣，该计划可最大程度地减少为锅炉提供能源的成本。我们提出一种贪婪算法，其时间复杂度为$\mathcal{Ø}（Ť\alpha （Ť））$ 哪里 $Ť$ 是时间间隔的数量， $\alpha$ 是阿克曼函数的逆函数。