Storage systems and demand-response programs will play a vital role in future energy systems. Batteries, hydrogen or pumped hydro storage systems can be combined to form hybrid storage facilities to not only manage the intermittent behavior of renewable sources, but also to store surplus renewable energy in a practice known as ‘green’ storage. On the other hand, demand-response programs are devoted to encouraging a more active participation of consumers by pursuing a more efficient operation of the system. In this context, proper scheduling tools able to coordinate different storage systems and demand-response programs are essential. This paper presents a stochastic mixed-integer-lineal-logical framework for optimal scheduling of isolated microgrids. In contrast to other works, the present model includes a logical-based formulation to explicitly coordinate batteries and pumped hydro storage units. A case study on a benchmark isolated microgrid serves to validate the developed optimization model and analyze the effect of applying demand-response premises in microgrid operation. The results demonstrate the usefulness of the developed method, and it is found that operation cost and fuel consumption can be reduced by ~38% and ~82% by applying demand-response initiatives.