In this 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 evasive nature 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 to a polynomial-time approximation scheme for constantly-many commodities as well as to a proof-of-concept $(2-\frac{17}{5000} + \epsilon)$-approximation for general problem instances. In this regard, the efficient design of $\epsilon$-optimal dynamic policies appeared to have been out of reach, since beyond algorithmic challenges by themselves, even the polynomial-space representation of such policies has been a fundamental open question. On the other front, our sub-$2$-approximation constitutes the first improvement over the performance guarantees achievable via ``stationary order sizes and stationary intervals'' (SOSI) policies, which have been state-of-the-art since the mid-'90s.

翻译：本文针对库存管理领域的经典问题——经济仓库批量调度问题，提出了期待已久的算法进展，实现了近最优补货策略的高效构建。自20世纪50年代末该问题提出以来，虽已积累大量相关文献，但在基础计算问题方面我们仍知之甚少，这或许源于该背景下动态策略难以捉摸的特性。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。本文建立了与动态策略直接竞争的新分析基础，结合进一步的算法进展与新获得的洞见，最终实现了常数种商品情形下的多项式时间近似方案，并为一般问题实例提供了概念验证性的$(2-\frac{17}{5000} + \epsilon)$近似算法。就$\epsilon$最优动态策略的高效设计而言，此前似乎遥不可及——因为除算法挑战本身外，此类策略的多项式空间表示甚至一直是个根本性开放问题。另一方面，我们的次$2$近似算法首次改进了自90年代中期以来保持最优的"固定订单量与固定间隔"策略所能实现的性能保证。