Energy Aware Scheduling for Weighted Completion Time and Weighted   Tardiness
  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. 
Rodrigo A. Carrasco, Garud Iyengar, Cliff Stein
cs.DM math.CO