  The ever increasing adoption of mobile devices with limited energy storage
capacity, on the one hand, and more awareness of the environmental impact of
massive data centres and server pools, on the other hand, have both led to an
increased interest in energy management algorithms.
  The main contribution of this paper is to present several new constant factor
approximation algorithms for energy aware scheduling problems where the
objective is to minimize weighted completion time plus the cost of the energy
consumed, in the one machine non-preemptive setting, while allowing release
dates and deadlines.Unlike previous known algorithms these new algorithms can
handle general job-dependent energy cost functions, extending the application
of these algorithms to settings outside the typical CPU-energy one. These new
settings include problems where in addition, or instead, of energy costs we
also have maintenance costs, wear and tear, replacement costs, etc., which in
general depend on the speed at which the machine runs but also depend on the
types of jobs processed. Our algorithms also extend to approximating weighted
tardiness plus energy cost, an inherently more difficult problem that has not
been addressed in the literature.
