Approximation Formulations for the Single Product Capacitated Lot Size Problem

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

Analysis of the Uncapacitated Dynamic Lot Size Problem

In this paper we provide worst case error bounds for several heuristics for the uncapacitated dynamic lot size problem. We propose two managerially oriented procedures and show that they have a relative worst case error bound equal to two, and develop similar analyses for methods known as the "Silver and Meal" heuristics, the part period balancing heuristics, and economic order quantity heuristics (expressed in terms of a time supply of demand).We also present results on aggregation and partitioning of the planning horizon