Modeling A Mixed-Integer Optimization Approach to Allocating Housing Resources for the Homeless

Abstract

As of January 2022, the number of homeless individuals in the US was estimated to be over 580,000. Although funding has increased over the years to tackle this problem, there have been minimal advances in providing concrete solutions that alleviate the most central factors, most notably housing prices and lack of homeless assistance resources. We seek to address the resource allocation problem by modeling the unique dynamics of homeless populations across the United States using ordinary differential equations and integrating them into a mixed-integer optimization problem to determine optimal allocations of resources. This modeling framework is an extension of work that is central to epidemiology, and more recently, the opioid crisis. In this thesis, we formulate a preliminary ODE model that serves to capture how homeless individuals move between states of being unsheltered and different types of homeless housing resources. We are primarily concerned with the number of beds available to unsheltered individuals and the funding that is allocated to communities - we use a mixed-integer optimization problem that seeks to minimize the number of unsheltered individuals by allocating beds and funds in an efficient and fair manner, while taking into account the unique dynamics of homeless communities around the country. Our work shows decreases in unsheltered individual populations across all states, and an average increase in individuals using certain housing assistance programs. This thesis provides a basis for future modeling methods concerning homeless populations and how resources can be better allocated for unsheltered individuals.