Nowadays, end-users can participate in demand response (DR) programs, and even slight load reductions from many houses can add up to major load shifts in the power system. Aggregators, which act as mediators between end-users and distribution system operator (DSO), play an important role here. The aggregator contracts the end-users for DR programs, plans ahead for times when customers should shift their load, and controls the load shifts in the running time. In this paper, our main focus is on planning the end-users for load shifting. Here, we first define and formulate the flexibilities (e.g., Stamina, repetition, and capacity) related to the dynamic loads such as space heating systems (SHSs) in detached houses. Assuming some end-users being contracted for DR program, based on estimation of their house characteristics and load flexibilities, an algorithm is then proposed to plan the SHSs for load shifting. In this algorithm the states in which a flexible load can be planned, kept in backup, or unavailable are considered by the aggregator. Another algorithm has been proposed here to deal with the different sources of uncertainties (which cause some of the planned SHSs to become unavailable). Numerical results are presented at the end, which discuss performance of the proposed strategy in terms of load flexibilities, load shifts in response to DR signals, and sensitivity analysis. Here, how to estimate the houses characteristics is a difficult issue, and we approximate them based on available models in the literature.