Sequential Fair Allocation: Achieving the Optimal Envy-Efficiency Trade-off Curve

Optimizing Mobile Food Pantry Operations Under Demand Uncertainty Managing complex systems often involves making trade-offs between different objectives. A common example is seeking fairness guarantees in sequential resource allocation problems. For example, mobile food pantries are tasked with allocating resources under demand uncertainty with the goal of simultaneously minimizing inefficiency (leftover resources) and envy (deviations in allocations). In this work, we tackle a problem established from a partnership with the Food Bank of the Southern Tier in optimizing their mobile food-pantry operations. We provide an exact characterization of the achievable (envy, efficiency) pairs, showing that any algorithm achieving low envy must suffer from poor inefficiency and vice versa. We complement this exact characterization with a simple algorithm capable of achieving any desired point along the trade-off curve.