We consider two approximation formulations for the single product capacitated lot size problem. They correspond respectively to a restriction of the number of production policies and to the rounding of demands up to multiples of a constant. After briefly reviewing the literature within a new % ~ framework, we discuss the relations between these approximation formulations. Next, we provide relative error bounds and algorithms for solving the approximation problems. We demonstrate that these approximation formulations require a significantly smaller number of calculations than the original formulation, and that the relative error bounds are satisfactory for practical purposes.