Online Allocation with Unknown Shared Supply

2026-05-07

AI Summary

This study addresses the online shared resource allocation problem (OSSA) under unknown and non-replenishable total supply, introducing the first formulation and analysis of a no-replenishment setting that incorporates fixed transportation costs and stockout penalties. The authors propose a deterministic threshold-proportional allocation strategy, GPA, which achieves near-optimal performance without relying on historical demand information. They establish that GPA attains a tight 4/3 approximation ratio and demonstrate that an additive error is unavoidable in this setting. Furthermore, they develop a learning-augmented variant of GPA capable of integrating external predictions while preserving both robustness and learnability. Theoretical analysis and empirical experiments confirm that GPA significantly outperforms existing baselines under scarce supply conditions, underscoring the method’s effectiveness and practical relevance.

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.

Problem

• Online Allocation
• Shared Supply
• Unknown Supply
• Lost Sales
• Resource Prepositioning

Innovation

• Online Allocation
• Shared Supply
• Approximation Algorithm
• Learning-Augmented Algorithm
• Lost-Sales Inventory