When Leila Hajibabai and her team at North Carolina State University built an optimization model to distribute vaccines fairly and efficiently, they ran into a wall: the math was so complex it would take impractical amounts of computing power to use. Their model had roughly 1.6 billion variables — decisions about where to send how many vaccine doses — and even powerful computers struggled to solve it quickly.
That posed a real problem. During the COVID-19 pandemic, health officials needed to make fast decisions about getting vaccines to the people who needed them most. A slow model, however smart, wouldn't help anyone on the ground.
So Hajibabai and her collaborator Ali Hajbabaie got creative. They combined machine learning — the kind of technology that learns from past examples — with a decades-old math technique called column generation. Column generation works by breaking enormous problems into smaller, manageable chunks. Machine learning then helps the system guess which chunks matter most, so the computer doesn't waste time checking every single possibility.
The result? Their new approach, called ML-CG, runs 79.1% faster than the old method while still reaching answers that are within 6% of perfect. "It substantially improves computational efficiency compared to the benchmark techniques," Hajibabai said.
To test it, the researchers used real data from Pennsylvania's COVID-19 vaccine shipments and demand, provided by the Centers for Disease Control and Prevention and state health departments. The model had originally been published in 2025, designed to minimize costs while maximizing coverage to specific census blocks.
The team published their findings in the journal Sustainability Analytics and Modeling. But they say the technique could apply far beyond vaccines. The same approach could help allocate food supplies after a disaster, route emergency crews after a storm, or distribute any scarce resource where getting the math right matters.
"These problems exist everywhere," Hajbabaie said. "Anywhere you need to figure out how to get limited resources to a lot of people — that's what this helps with."
For communities facing future pandemics, natural disasters, or supply chain crunches, faster optimization tools could mean the difference between supplies arriving in time or arriving too late. By making these models practical to run, NC State researchers have opened a door that once seemed locked shut.