Many real-world resource allocation systems, such as humanitarian logistics and vaccine distribution, must preposition limited supply across multiple locations before demand is realized while stockouts incur irreversible service losses. To study this, we introduce the Online Shared Supply Allocation (OSSA) problem, a stateful online model in which a central hub allocates a finite, unknown supply to multiple sites facing sequential demand under fixed-charge transportation costs and lost-sales penalties. Unlike classical make-to-stock or make-to-order inventory models, OSSA precludes backlogging and replenishment only hedges against future demand. To tackle OSSA, we propose a deterministic threshold-proportional policy GPA and prove that it achieves a $4/3$-approximation to the offline optimum up to an additive term independent of the total supply. We complement this with matching lower bounds showing that the $4/3$ ratio is tight and that the additive-error dependence is unavoidable, even for randomized algorithms that know the total supply upfront. Finally, we develop a learning-augmented extension to GPA that principally incorporates imperfect forecasts (e.g., from human experts or ML models) commonly available in practice, enabling us to exploit high-quality advice while being robust against arbitrary bad ones. Synthetic and real-world experiments show that GPA outperforms natural baselines with global supply is scarce.

翻译：许多现实世界的资源分配系统，例如人道主义物流和疫苗分发，必须在需求实现前将有限的供应预置到多个地点，而缺货会造成不可逆的服务损失。为研究此类问题，我们提出了在线共享供给分配（OSSA）问题。这是一个有状态的在线模型，其中中央枢纽在固定运输成本和缺货惩罚下，将有限且未知的供给分配至面临序列需求的多个站点。与经典的生产-库存或按单生产模型不同，OSSA 不允许延期交货，补货仅用于对冲未来需求。针对 OSSA，我们提出了一种确定性阈值比例策略 GPA，并证明其能够在离线最优解的 $4/3$ 倍近似范围内，加上一个与总供给无关的加性项。我们进一步通过匹配的下界证明 $4/3$ 的比率是紧的，且加性误差的依赖性不可避免，即使对于预先知晓总供给的随机算法也是如此。最后，我们开发了 GPA 的学习增强扩展，该扩展原则上整合了实践中常见的来自人类专家或机器学习模型的不完美预测，使得我们能够在利用高质量建议的同时，对任意劣质建议保持鲁棒性。合成数据与现实世界的实验表明，当全局供给稀缺时，GPA 优于自然基线算法。