Approximation Formulations for the Single-Product Capacitated Lot Size Problem

We consider two approximation formulations for the single-product capacitated lot size problem. One formulation restricts the number of production policies and the other rounds 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.