In this paper we consider the two-machine ow shop problem with varying machine speeds. We present an algorithm which determines the optimal permutations for all machine speeds in O ( n log n ) time, where n is the number of jobs. To achieve this bound on the running time, the algorithm employs...

We develop an algorithm that solves the constant capacities economic lot-sizing problem with concave production costs and linear holding costs 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...

NP-hard cases of the single-item capacitated lot-sizing problem have been the topic of extensive research and continue to receive considerable attention. However, surprisingly few theoretical results have been published on approximation methods for these problems. To the best of our knowledge,...