Online Fair Allocation of Perishable Resources

We consider a practically motivated variant of the canonical online fair allocation problem: A decision maker has a budget of perishable resources to allocate over a fixed number of rounds. Each round sees a random number of arrivals, and the decision maker must commit to an allocation for these individuals before moving on to the next round. The goal is to construct a sequence of allocations that is envy-free and efficient. Our work makes two important contributions toward this problem: We first derive strong lower bounds on the optimal envy-efficiency tradeoff, demonstrating that a decision maker is fundamentally limited in what they can hope to achieve relative to the no-perishing setting; we then design an algorithm achieving these lower bounds that takes as input (i) a prediction of the perishing order and (ii) a desired bound on envy. Given the remaining budget in each period, the algorithm uses forecasts of future demand and perishing to adaptively choose from one of two carefully constructed guardrail quantities. We demonstrate our algorithm’s strong numerical performance—and state-of-the-art, perishing-agnostic algorithms’ inefficacy—on simulations calibrated to a real-world data set.

Funding: We gratefully acknowledge funding from the National Science Foundation under [Grants ECCS-1847393, DMS1839346, CCF-1948256, CNS-195599, and CNS-1955997], the Air Force Office of Scientific Research under [Grant FA9550-23-1-0068], and the Army Research Laboratory under [Grants W911NF-19-10217 and W911NF-17-1-0094].

Supplemental Material: All supplemental materials, including the code, data, and files required to reproduce the results, are available at https://doi.org/10.1287/opre.2024.0847.