  This paper studies planning problems for a group of heating systems which
supply the hot water demand for domestic use in houses. These systems (e.g. gas
or electric boilers, heat pumps or microCHPs) use an external energy source to
heat up water and store this hot water for supplying the domestic demands. The
latter allows to some extent a decoupling of the heat production from the heat
demand. We focus on the situation where each heating system has its own demand
and buffer and the supply of the heating systems is coming from a common
source. In practice, the common source may lead to a coupling of the planning
for the group of heating systems. The bottleneck to supply the energy may be
the capacity of the distribution system (e.g. the electricity networks or the
gas network). As this has to be dimensioned for the maximal consumption, it is
important to minimize the maximal peak. This planning problem is known to be
\NP-hard. We present polynomial-time approximation algorithms for four variants
of peak minimization problems, and we determine the worst-case approximation
error.
