Demand side management (DSM) programs aim at reducing energy consumption on the demand side, which benefits both consumers and utilities. These programs could also help maintain the critical balance between generation and demand in isolated microgrids. In this case, demand is a treated as a significant uncertainty in the context of dispatching the power resources of a microgrid. Thus, in this paper the uncertainty of consumer response to DSM signals are treated as intervals to represent the corresponding range of variation based on affine arithmetic. The total range of total grid consumption is taken as the sum of intervals in each house, using data obtained through surveys regarding usage of appliances to obtain the individual consumer intervals. The proposed affine arithmetic model is then applied to the prediction of possible range variation in a one-day ahead load forecast. Finally, the presented technique is demonstrated using data obtained in an actual microgrid deployed in Huatacondo, Chile.