We introduce a new problem inspired by energy pricing schemes in which a client is billed
for peak usage. At each timeslot the system meets an energy demand through a
combination of a new request, an unreliable amount of free source energy (eg solar or wind
power), and previously received energy. The added piece of infrastructure is the battery,
which can store surplus energy for future use, and is initially assumed to be perfectly efficient
or lossless. In a feasible solution, each demand must be supplied on time, through a …