Dynamic Scheduling for Charging Electric Vehicles: A Priority Rule

We consider the scheduling of multiple tasks with pre-determined deadlines under arbitrarily random processing cost and task arrival. This problem is motivated by the potential of large scale adoption of plug-in (hybrid) electric vehicles (PHEVs) in the near future. We seek to properly schedule the battery charging of multiple PHEVs so as to minimize the overall cost, which is derived from the total charging cost and the penalty for not completing charging before requested deadlines. Through a dynamic programming formulation, we establish the Less Laxity and Longer remaining Processing time (LLLP) principle that improves any charging policy on a sample-path basis, when the non-completion penalty is a convex function of the additional time needed to fulfill the uncompleted request. Specifically, the LLLP principle states that priority should be given to vehicles that have less laxity and longer remaining processing times. Numerical results demonstrate that heuristic policies that violate the LLLP principle, for example, the earliest deadline first policy, can result in significant performance loss.