Optimization models do an excellent job of ensuring products get where they are needed in the most efficient way possible, but those models require an impractical amount of computing power when dealing with large-scale problems – such as distributing vaccines to millions of people. Researchers have now demonstrated a way to drastically reduce the computing power needed to run these optimization models while still producing near-optimal results.

“We had developed an optimization model that ensures supplies of vaccines are distributed efficiently and equitably to the places they are most needed,” says Leila Hajibabai, corresponding author of a paper on the work. “However, the computational power needed to run that optimization model at a statewide level was not practical. Our goal with this work was to develop a methodology that allows us to use that model but requires far less computing power – making it a viable tool for practical use.” Hajibabai is an associate professor in North Carolina State University’s Edward P. Fitts Department of Industrial and Systems Engineering.

Specifically, the work by Hajibabai and her collaborators builds on a model they published in 2025 to minimize total distribution cost while maximizing vaccine allocation to specific census blocks. That work drew on a detailed dataset they created with data from the Centers for Disease Control and Prevention and health departments in Pennsylvania related to vaccine shipments and demand during the COVID-19 pandemic.

“But running that model involved approximately 1.6 billion potential binary and integer decision variables,” says Ali Hajbabaie, co-author of the paper and an associate professor of civil, construction and environmental engineering at NC State. “It required so much computational power that it would be impractical to use on large scales – particularly if you wanted to run the model with new information on any sort of regular basis.”

To resolve this challenge, the researchers took a novel approach: combining machine learning with a technique called column generation. Column generation is a longstanding method used to address optimization challenges involving large numbers of variables. In broad terms, it breaks large problems down into smaller problems.

“However, if a problem is big enough, column generation alone is not enough to sufficiently reduce the computational cost of running the optimization model,” says Hajibabai.

This is where machine learning comes in.

“Machine learning can learn from previously solved instances to predict promising decisions for one step of the optimization process, allowing the algorithm to focus its computational effort where it is most likely to improve the solution,” says Hajibabai. “That reduces the search space and the number of optimization calculations in later iterations.”

So, instead of having to evaluate an enormous number of potential decision variables, you might only have to determine the most promising subset using column generation – and machine learning would give you good estimates for many of the remaining decision variables, reducing the number that must be explicitly optimized.

Researchers found that using this machine learning-guided column generation (ML-CG) approach accelerated run-time for their vaccine optimization model by 79.1% compared to pure column generation – while still providing high-quality solutions. Across all of the techniques the researchers evaluated, ML-CG also delivered the best balance between computational speed and solution quality.

“It substantially improves computational efficiency compared to the benchmark techniques,” says Hajibabai. “And while it does not produce the exact same results, it can get within 6% of the optimal outcome – which is very good.”

“This work was done to address a challenge involving vaccine distribution optimization, but the method we’ve demonstrated here has utility for a wide range of resource allocation problems,” says Hajbabaie.

“For example, the same approach could help optimize disaster relief operations, humanitarian logistics, transportation systems, energy systems planning, and other large-scale, complex infrastructure and supply chain problems where decisions must be made quickly and efficiently,” says Hajibabai.

“We hope other researchers will build on both the dataset and the methodology, applying them to new problems and helping advance the next generation of computational methods for solving large-scale real-world challenges[LH1],” Hajibabai says.

The paper, “Machine Learning-Guided Column Generation for a Maximal Covering Location-Allocation Problem,” is published open access in the journal Sustainability Analytics and Modeling. First author of the paper is Kuangying Li, a former Ph.D. student at NC State. The paper was co-authored by Hiruni Niwunhella, a Ph.D. student at NC State. This work was done with support from the National Science Foundation under grant 2124825.