Smart grid power scheduling via bottom left decreasing height packing

We consider the scheduling of flexible electric power loads so as to minimize the peak load. We settle a conjecture of Alamdari et al.[1] regarding the performance of the bottom left decreasing height heuristic to schedule preemptable loads with known power requirement and duration and having the same earliest start time and the same deadline. Specifically, we show a tight bound of 4/3 - 1/(3D) relative to the minimum peak power load, where D is the duration of the scheduling interval. On benchmark strip packing data, the bottom left decreasing height heuristic generated schedules that required up to 45% less peak power than required by schedules generated using the next fit decreasing height heuristic. On electric and plug-in hybrid electric vehicles data, these two heuristics are very competitive.