Approximation Methods for the Uncapacitated Dynamic Lot Size Problem

We provide worst case error bounds for several approximation methods (heuristics, product aggregation, and partitioning of the planning horizon) for the uncapacitated dynamic lot size problem. We propose two managerially oriented heuristics and show that they have a relative wont case error bound equal to two, and develop similar analyses for methods known as the least cost per unit heuristic, the part period balancing heuristic, and an economic order quantity heuristic (expressed in terms of a time supply of demand). We also show how errors introduced by partitioning of the planning horizon in multi-product multi-facility problems are bounded by product set-up costs, and how errors introduced by product aggregation are bounded by set-up costs, holding costs, and demands. The latter results suggest methods for product aggregation that minimize the worst case error bounds.