Offline preemptive bottom left decreasing height scheduling of power loads in smart grids

We are considering the scheduling of flexible preemptable electric loads in a smart grid so as to minimize peak load when all loads have the same earliest start time and deadline. We show that when this scheduling is done using the bottom left decreasing height heuristic, the ratio of the peak load of the schedule generated by this heuristic and the optimal peak load has the tight bound 4 / 3 - 1 / ( 3 D ) , where D is the duration of the scheduling interval. This settles an outstanding conjecture regarding the worst-case performance of this heuristic. Our experiments indicate a reduction in peak load of up to 45% using the bottom left decreasing height heuristic and benchmark data.