20 / 2024-04-10 19:55:42

Achieving Ex-Ante and Ex-Post Fairness: Design of Allocation Rules for Mobile Food Pantries

Food Bank Operations, Resource Allocation, Ex-Ante Fairness, Ex-Post Fairness

Mobile food pantries (MFPs) have increasingly expanded in recent years to help alleviate world hunger by allocating surplus food to underserved communities that face challenges in accessing conventional food banks. As non-profit programs, MFPs prioritize operational efficiency and minimizing food waste. However, this approach can result in unequal distribution of services among beneficiaries from different communities. To address this issue, we design a sequential food allocation framework that focuses on serving the sequentially revealed demand of each targeted community during the food delivery trip. This framework aims to maximize the expected minimum fill rate across communities (ex-post fairness criteria), while simultaneously meeting the predetermined expected fill rate target (ex-ante fairness requirement) for each community.



We show that this particular type of food allocation problem, constrained by the ex-ante fairness considerations, can be simplified by solving a series of stochastic dynamic program problems with randomized coefficients in the objective function. The online convex optimization tool and Fenchel duality are applied for analysis. Furthermore, we show that the optimal solution to the stochastic dynamic problem, under the ex-post fairness maximization criteria, exhibits a two-threshold structure. This structure explicitly reveals the trade-offs between achieving optimal performance in ex-post fairness while ensuring fair food delivery service to all communities in an ex-ante manner. Extensive numerical experiments with both synthetic data and real-world data showcase the promising benefits of our allocation rules over existing benchmarks.