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We propose a novel scheduling scheme that determines the instant operation modes of multiple tasks. The tasks have probabilistic execution times and are executed on discrete operation modes providing different utilities with different energy consumptions. We first design an optimal offline scheduling scheme that stochastically maximizes the cumulative utility of the tasks under energy constraints, at the cost of heavy computational overhead. Next, the optimal offline scheme is modified to an approximate online scheduling scheme. The online scheme has little runtime overhead and yields almost the maximum utility, with an energy budget that is given at runtime. The difference between the maximum utility and the output utility of the online scheme is bounded by a controllable input value. Extensive evaluation shows that the output utility of the online scheme approaches the maximum utility in most cases, and is much higher than that of existing methods by up to 50% of the largest utility difference among available operation modes.