In addition to this matching distribution constraint, we also require that the recipient's

In addition to this matching distribution constraint, we also require that the recipient's

Our research addresses the critical challenge of managing blood transfusions and optimizing allocation in resource-constrained regions. We present heuristic matching algorithms for donor-patient and blood bank selection, alongside machine learning methods to analyze blood transfusion acceptance data and predict potential shortages. We developed simulations to optimize blood bank operations, progressing from random allocation to a system incorporating proximity-based selection, blood type compatibility, expiration prioritization, and rarity scores. Moving from blind matching to a heuristic-based approach yielded a 28.6% marginal improvement in blood request acceptance, while a multi-level heuristic matching resulted in a 47.6% improvement. For shortage prediction, we compared Long Short-Term Memory (LSTM) networks, Linear Regression, and AutoRegressive Integrated Moving Average (ARIMA) models, trained on 170 days of historical data. Linear Regression slightly outperformed others with a 1.40% average absolute percentage difference in predictions. Our solution leverages a Cassandra NoSQL database, integrating heuristic optimization and shortage prediction to proactively manage blood resources. This scalable approach, designed for resource-constrained environments, considers factors such as proximity, blood type compatibility, inventory expiration, and rarity. Future developments will incorporate real-world data and additional variables to improve prediction accuracy and optimization performance.

We consider the problem of allocating a distribution of items to $n$ recipients where each recipient has to be allocated a fixed, prespecified fraction of all items, while ensuring that each recipient does not experience too much envy. We show that this problem can be formulated as a variant of the semi-discrete optimal transport (OT) problem, whose solution structure in this case has a concise representation and a simple geometric interpretation. Unlike existing literature that treats envy-freeness as a hard constraint, our formulation allows us to \emph{optimally} trade off efficiency and envy continuously. Additionally, we study the statistical properties of the space of our OT based allocation policies by showing a polynomial bound on the number of samples needed to approximate the optimal solution from samples. Our approach is suitable for large-scale fair allocation problems such as the blood donation matching problem, and we show numerically that it performs well on a prior realistic data simulator.