Equitable Data-Driven Resource Allocation to Fight the Opioid Epidemic: A Mixed-Integer Optimization Approach

The opioid epidemic is a crisis that has plagued the United States (US) for decades. One central issue of the epidemic is inequitable access to treatment for opioid use disorder (OUD), which puts certain populations at a higher risk of opioid overdose. We integrate a predictive dynamical model and a prescriptive optimization problem to compute high-quality opioid treatment facility and treatment budget allocations for each US state. Our predictive model is a differential equation-based epidemiological model that captures the dynamics of the opioid epidemic. We use neural ordinary differential equations to fit this model to opioid epidemic data for each state and obtain estimates for unknown parameters in the model. We then incorporate this epidemiological model into a corresponding mixed-integer optimization problem (MIP) that aims to minimize the number of opioid overdose deaths and the number of people with OUD. We develop strong relaxations based on McCormick envelopes to efficiently compute approximate solutions to our MIPs that have less than 1% optimality gaps. Our method provides socioeconomically equitable solutions, as it incentivizes investments in areas with higher social vulnerability (from the US Centers for Disease Control's Social Vulnerability Index) and opioid prescribing rates. On average, our approach decreases the number of people with OUD by 6.08 $\pm$ 0.863%, increases the number of people in treatment by 22.57 $\pm$ 3.633%, and decreases the number of opioid-related deaths by 0.55 $\pm$ 0.105% after 2 years compared to the baseline epidemiological model's predictions. We identify that treatment facilities should be moved or added to counties that have significantly less facilities than their population share and higher social vulnerability. Future iterations of our approach could be implemented as a decision-making tool to tackle opioid treatment inaccessibility.