As microgrids have gained increasing attention over the last decade, more and more applications have emerged, ranging from islanded remote infrastructures to active building blocks of smart grids. To optimally manage the various microgrid assets towards maximum profit, while taking into account reliability and stability, it is essential to properly schedule the overall operation. To that end, this paper presents an optimal scheduling framework for microgrids both for day-ahead and real-time operation. In terms of real-time, this framework evaluates the real-time operation and, based on deviations, it re-optimises the schedule dynamically in order to continuously provide the best possible solution in terms of economic benefit and energy management. To assess the solution, the designed framework has been deployed to a real-life microgrid establishment consisting of residential loads, a PV array and a storage unit. Results demonstrate not only the benefits of the day-ahead optimal scheduling, but also the importance of dynamic re-optimisation when deviations occur between forecasted and real-time values. Given the intermittency of PV generation as well as the stochastic nature of consumption, real-time adaptation leads to significantly improved results.