An O(T³) Algorithm for the Economic Lot-Sizing Problem with Constant Capacities

We develop an algorithm that solves the constant capacities economic lot-sizing problem with concave production costs and linear holding in O(T³) time. The algorithm is based on the standard dynamic programming approach which requires the computation of the minimal costs for all possible subplans of the production plan. Instead of computing these costs in a straightforward manner, we use structural properties of optimal subplans to arrive at a more efficient implementation. Our algorithm improves upon the O(T⁴) running time of an earlier algorithm.