Microgrids are subsystems of the distribution grid which comprises small generation capacities, storage devices and controllable loads, operating as a single controllable system that can operate either connected or isolated from the utility grid. In this paper we present a preliminary study on applying a Model Predictive Control (MPC) approach to the problem of efficiently optimizing microgrid operations while satisfying a time-varying request and operation constraints. The overall problem is formulated using Mixed-Integer Linear Programming (MILP), which can be solved in an efficient way by using commercial solvers without resorting to complex heuristics or decompositions techniques. Then the MILP formulation leads to significant improvements in solution quality and computational burden. A case study of a typical microgrid is employed to assess the performance of the on-line optimization-based control strategy: simulation results show the feasibility and the effectiveness of the proposed approach.