Allocating Scarce Resources: Models and Optimization

The question of how to allocate scarce resources amongst a set of recipients is relevant in countless settings around the globe. Cadaver organs must be allocated to patients, public school spaces to students, and public housing to residents who require it. When resources are scarce, it is particularly important to build allocation systems that function efficiently to maximize utility, and fairly to minimize inequity. This thesis contributes several models and tools that assist with both designing new allocation systems and extracting insight from existing systems. In both cases, efficiency and fairness take center stage. Chapter 2 considers the common problem faced by a central authority who allocates resources according to a scoring rule. The scoring rule computes scores for each recipient-resource pair based on some observable properties that relate the pair, and an allocation mechanism then determines the allocation using only the scores. We present a series of optimization models and heuristics that directly optimize over the scoring rule, and demonstrate their effectiveness and ability to scale to practical problem sizes. In a more general setting of allocation, Chapter 3 hypothesizes that the ability for recipients to choose whether to accept or decline the offer of a resource acts as a hidden source of inequity in a system. In particular, we propose several models that show appreciable levels of inequity may arise when segments of a population exhibit different levels of selectiveness. Chapter 4 studies a mass-screening program for SARS-CoV-2 implemented in Greece during 2021, in which the Greek National Health Organization allocated a finite supply of mandatory self-tests amongst different segments of the population. We develop a novel compartmental model to describe the dynamics of the COVID-19 pandemic in Greece, placing particular focus on the testing procedure. We fit the model to detailed historical data to quantify the effectiveness of the program in reducing hospitalizations and deaths, and also to understand whether the observed allocation of tests amongst age groups was an effective choice. We conclude that self-testing is an extremely important intervention to consider for pandemic preparedness.

THESIS COMMITTEE:

Prof. Nikos Trichakis (thesis advisor)

Prof. Patrick Jaillet (thesis advisor)

Prof. Alexandre Jacquillat

Prof. Kimon Drakopoulos