A Novel exact algorithm for economic lot-sizing with piecewise linear production costs
<|reference_start|>A Novel exact algorithm for economic lot-sizing with piecewise linear production costs: In this paper, we study the single-item economic lot-sizing problem with production cost functions that are piecewise linear. The lot-sizing problem stands as a foundational cornerstone within the domain of lot-sizing problems. It is also applicable to a variety of important production planning problems which are special cases to it according to \cite{ou}. The problem becomes intractable when $m$, the number of different breakpoints of the production-cost function is variable as the problem was proven NP-hard by \cite{Florian1980}. For a fixed $m$ an $O(T^{2m+3})$ time algorithm was given by \cite{Koca2014} which was subsequently improved to $O(T^{m+2}\log(T))$ time by \cite{ou} where $T$ is the number of periods in the planning horizon.\newline We introduce a more efficient $O(T^{m+2})$ time algorithm for this problem which improves upon the previous state-of-the-art algorithm by Ou and which is derived using several novel algorithmic techniques that may be of independent interest.<|reference_end|>
@article{papadopoulos2024a,
    title={A Novel exact algorithm for economic lot-sizing with piecewise linear
  production costs},
    author={Kleitos Papadopoulos},
    journal={arXiv preprint arXiv:2403.16314},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.16314},
    primaryClass={cs.DS}
}