  The sum-utility maximization problem is known to be important in the energy
systems literature. The conventional assumption to address this problem is that
the utility is concave. But for some key applications, such an assumption is
not reasonable and does not reflect well the actual behavior of the consumer.
To address this issue, the authors pose and address a more general optimization
problem, namely by assuming the consumer's utility to be sigmoidal and in a
given class of functions. The considered class of functions is very attractive
for at least two reasons. First, the classical NP-hardness issue associated
with sum-utility maximization is circumvented. Second, the considered class of
functions encompasses well-known performance metrics used to analyze the
problems of pricing and energy-efficiency. This allows one to design a new and
optimal inclining block rates (IBR) pricing policy which also has the virtue of
flattening the power consumption and reducing the peak power. We also show how
to maximize the energy-efficiency by a low-complexity algorithm. When compared
to existing policies, simulations fully support the benefit from using the
proposed approach.
