Demand Response Management Systems (DRMS) in microgrid environment have been widely investigated during these last ten years. In this matter, numerous optimization models, based either on exact or approximate techniques, have been proposed in the literature to facilitate a transient energy independence of the private premises from the public grid. Three factors may either impose or motivate such an autonomy: a breakdown of a public electricity generator, a dysfunction in the distribution network or the hourly price of a KWh on the market. Service continuity in case of islanding of the private premises necessitates three types of equipment: a DRMS, one or several local energy sources and a set of stationary batteries. On the basis of the hourly day-ahead price of public electricity, the end-user may disconnect transiently his equipment from the public grid in order to reduce his energy expenses. The contribution of this paper is twofold. In a first step, we propose an original classification of the various electric loads that can be activated within a microgrid. We then propose a DRMS based on an exact formulation of this optimization problem.