In island distribution grids, the increase of renewable generation sources, whose output is stochastic in nature, implies that large amount of operating reserve must be guaranteed during the grid operation. In this paper, a methodology based on predictive optimal dispatch is proposed to optimize the use of energy resources taking into account operating reserve constraints. Reserve constraints are quantified through a probabilistic approach that takes into account the probabilistic distribution of forecasting errors. The methodology is applied to the distribution model of an actual Italyn small island, supplied by a set of conventional diesel generators together with photovoltaic and storage resources. The performance of the proposed predictive approach is assessed considering the response of the system during different load and generation scenarios. The impacts of reserve provision is also studied considering the effect of an open-loop and a closed-loop control strategy.