Vaccination and Testing Process Optimization

Vaccine and Test Kit Distribution

Problem definition: Speeding up testing and vaccination is essential to controlling the coronavirus disease 2019 (COVID-19) pandemic that has became a global health crisis. In this paper, we develop mathematical frameworks for optimizing locations of distribution centers and plans for distributing resources such as test kits and vaccines under spatiotemporal uncertainties of infection and demand trends. We aim to balance between operational cost (including costs of deploying facilities, shipping and storage) and quality of service (reflected by delivery speed and demand coverage), while ensuring equity and fairness of resource distribution based on historical infection data and demographics of estimated demand.

Methodology and results: Using weighted multiple objectives, we formulate a stochastic integer program and also seek robust solutions against the distributional ambiguity of demand. For the latter, we propose a distributionally robust optimization model using a moment ambiguity set, and derive monolithic reformulations depending on specific forms of this set. We compare different approaches by solving instances generated using real COVID-19 infection data for distributing vaccines and test kits over the United States and the state of Michigan, respectively. We demonstrate results over distinct phases of the pandemic to estimate cost and speed of resource distribution depending on the scales and coverage.

Managerial implications: Our results indicate the importance of incorporating demand uncertainty in resource distribution as the stochastic and robust approaches always outperform the deterministic one. If we prioritize the worst-case performance in terms of unmet demand (i.e., untested or unvaccinated people who qualify), then the distributionally robust approach is preferred despite of its higher overall cost. Nevertheless, the stochastic programming approach can provide an intermediate plan under budgetary restrictions without significant compromises in demand coverage.

IOE510 Projects on COVID Testing

To design an optimal screening policy and testing facility locations to conduct COVID testing more effectively, given random virus spread, limited amounts of test kits, imperfect screening, etc.