Online Allocation with Unknown Shared Supply

TL;DR

This paper introduces the OSSA problem, a new online resource allocation model for prepositioning limited supply across multiple sites with unknown demand, and proposes a near-optimal policy with a learning extension.

Contribution

It formulates the OSSA problem, develops a deterministic threshold policy with proven approximation bounds, and extends it with a learning-augmented approach for practical demand forecasting.

Findings

GPA achieves a 4/3-approximation to the offline optimum.

The 4/3 ratio is proven to be tight, with unavoidable additive errors.

The learning-augmented extension effectively utilizes imperfect forecasts.

Abstract

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.