The successful launch of electric vehicles (EVs) depends critically on the availability of convenient and economic charging facilities. The problem of scheduling of large-scale charging of EVs by a service provider is considered. A Markov decision process model is introduced in which EVs arrive randomly at a charging facility with random demand and completion deadlines. The service provider faces random charging costs, convex non-completion penalties, and a peak power constraint that limits the maximum number of simultaneous activation of EV chargers. Formulated as a restless multi-armed bandit problem, the EV charging problem is shown to be indexable. A closed-form expression of the Whittle's index is obtained for the case when the charging costs are constant. The Whittle's index policy, however, is not optimal in general. An enhancement of the Whittle's index policy based on spatial interchange according to the less laxity and longer processing time principle is presented. The proposed policy outperforms existing charging algorithms, especially when the charging costs are time varying. learn more on arXiv