Allocating Scarce Resources: Modeling and Optimization

Abstract

There are countless settings in which an authority must choose how to allocate scarce resources among a set of recipients. Deceased-donor organs must be allocated to patients, public school spaces to students, and public housing to residents. When resources are extremely scarce, it is particularly important for the authority to build an allocation system that achieves an acceptable trade-off between efficiency and equity. This thesis contributes several models and tools that both support the design of new allocation systems and extract insight from existing ones. In both cases, efficiency and equity take center stage.

Chapter 2 considers the problem faced by an authority who allocates resources according to a scoring system. A scoring system is based on two foundations: a scoring rule, which is a function that computes scores for each recipient-resource pair based on some observable properties that relate the pair, and an allocation procedure, which determines the allocation using only the scores. We introduce a model that allocates a set of resource types among a set of patient types according to a scoring system, before presenting several optimization formulations and heuristics that directly optimize the scoring rule while scaling to practical problem sizes. We also show how a scoring rule of high quality in the type-based model can fail in a setting where individual recipients and resources exhibit within-type variation in properties, and suggest approaches that perform well when allocating individuals.

Moving away from the specific setting of a scoring system, Chapter 3 shows that the ability for recipients to choose whether to accept or decline the offer of a resource can act as a hidden source of inequity in an allocation system. We formulate several game-theoretic models based on two groups of recipients, selective and non-selective, who display different propensities to accept or decline the offer of a resource. We define the notion of an equilibrium in these models and provide numerical experiments showing that inequity can arise directly as a result of the disparity in selectiveness between recipients.

Chapter 4 studies a mass screening program for SARS-CoV-2 that was implemented in Greece during 2021, in which the Greek National Public Health Organization allocated a finite supply of mandatory self-tests among 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 procedures. We fit the model to detailed data to quantify the overall effectiveness of the program in reducing hospitalizations and deaths, and also to understand the effects of several operational decisions. We conclude that self-testing is an extremely important intervention to consider for pandemic preparedness.