Online algorithm for battery utilization in electric vehicles

We consider the problem of utilizing the pack of batteries serving current demands in Electric Vehicles. When serving a demand, the current allocation might be split among the batteries in the pack. Due to its internal chemistry structure, a battery's life depends on the discharge current used for supplying the requests. Any deviation from the (a-priori known) optimal discharge-current is associated with a penalty. Thus, the problem is to serve an online sequence of requests for energy, in a way that minimizes the total penalty associated with the service. We first formulate the problem as a combinatorial optimization problem. We show that the problem is strongly NP-hard and is hard to approximate within an additive gap of Ω(m) from the optimum, where m is the number of batteries in the pack. This hardness result is valid even in the offline case, where the sequence of current demands is known in advance. For the online problem, we suggest an algorithm in which the total penalty might be larger than the minimal possible by at most an additive gap of 1.5m - independent of the initial capacity of the batteries and the number of requests in the sequence. Finally, we provide a lower bound of 1.5 for the multiplicative competitive ratio of any online algorithm. To the best of our knowledge, our work is the first to analyze the problem theoretically.