  We study the space of optimal schedules for a heat pump with thermal energy
storage used in heating a residential building. We model the heating system as
a Mixed Integer Linear Program with the objective to minimise the cost of
heating. We generate a large number of realistic daily heat demands and
calculate the optimal schedule for the heat pump. In addition to cost savings
stemming from optimal running, we find that the space of optimal schedules is
large in practice, even for the simplest model of the heating system we use,
and that the optimal schedules are difficult to reproduce with statistical
models. These findings strengthen the case for the use of mathematical
optimisation in real-life applications.
