The economic warehouse lot scheduling problem is a foundational inventory-theory model, capturing computational challenges in dynamically coordinating replenishment decisions for multiple commodities subject to a shared capacity constraint. Even though this model has generated a vast body of literature over the last six decades, our algorithmic understanding has remained surprisingly limited. Indeed, for general problem instances, the best-known approximation guarantees have remained at a factor of $2$ since the mid-1990s. These guarantees were attained by the now-classic work of Anily [Operations Research, 1991] and Gallego, Queyranne, and Simchi-Levi [Operations Research, 1996] via the highly-structured class of "stationary order sizes and stationary intervals" (SOSI) policies, thereby avoiding direct competition against fully dynamic policies. The main contribution of this paper resides in developing new analytical foundations and algorithmic techniques that enable such direct comparisons, leading to the first provable improvement over the $2$-approximation barrier. Leveraging these ideas, we design a constructive approach that allows us to balance cost and capacity at a finer granularity than previously possible via SOSI-based methods. Consequently, given any economic warehouse lot scheduling instance, we present a polynomial-time construction of a random capacity-feasible dynamic policy whose expected long-run average cost is within factor $2-\frac{17}{5000} + ε$ of optimal.

翻译：经济仓库批量调度问题是库存理论中的一个基础模型，它刻画了在共享容量约束下为多种商品动态协调补货决策所涉及的计算挑战。尽管该模型在过去六十年中已产生大量文献，我们对其中算法性质的理解仍惊人地有限。事实上，对于一般问题实例，自上世纪90年代中期以来，已知的最佳近似保证因子始终停留在$2$。这些保证是由Anily [Operations Research, 1991] 以及Gallego、Queyranne和Simchi-Levi [Operations Research, 1996] 的经典工作通过高度结构化的“固定订单量与固定间隔”（SOSI）策略类实现的，从而避免了与完全动态策略的直接竞争。本文的主要贡献在于建立了新的分析基础与算法技术，使得此类直接比较成为可能，并首次实现了对$2$-近似屏障的可证明改进。借助这些思想，我们设计了一种构造性方法，能够以比基于SOSI的方法更精细的粒度平衡成本与容量。因此，对于任意经济仓库批量调度实例，我们提出了一种多项式时间构造的随机容量可行动态策略，其长期平均期望成本与最优解的比值不超过$2-\frac{17}{5000} + ε$。