In this focused technical paper, we present long-awaited algorithmic advances toward the efficient construction of near-optimal replenishment policies for a true inventory management classic, the economic warehouse lot scheduling problem. While this paradigm has accumulated a massive body of surrounding literature since its inception in the late '50s, we are still very much in the dark as far as basic computational questions are concerned, perhaps due to the intrinsic complexity of dynamic policies in this context. The latter feature forced earlier attempts to either study highly-structured classes of policies or to forgo provably-good performance guarantees altogether; to this day, rigorously analyzable results have been few and far between. The current paper develops novel analytical foundations for directly competing against dynamic policies. Combined with further algorithmic progress and newly-gained insights, these ideas culminate in a polynomial-time approximation scheme for constantly-many commodities. In this regard, the efficient design of $ε$-optimal dynamic policies appeared to have been out of reach, since beyond their inherent algorithmic challenges, even the polynomial-space representation of such policies has been a fundamental open question.

翻译：在这篇聚焦技术性的论文中，我们针对库存管理领域的经典问题——经济仓库批次调度问题，提出了期待已久的算法进展，以实现近最优补货策略的高效构建。尽管该范式自20世纪50年代末提出以来已积累了海量相关文献，但就基本计算问题而言，我们仍处于探索阶段，这或许源于该背景下动态策略的内在复杂性。这一特性迫使早期研究要么局限于高度结构化的策略类别，要么完全放弃可证明的性能保证；时至今日，严格可分析的结果依然寥寥无几。本文为直接与动态策略竞争建立了新的分析基础。结合进一步的算法进展与新获得的洞见，这些思想最终为常数种商品情形提出了多项式时间近似方案。在此背景下，设计具有ε最优性的高效动态策略曾被认为遥不可及，因为除了其固有的算法挑战外，此类策略的多项式空间表示本身一直是一个根本性的开放问题。