How an algorithm can cut the cost of going green

Operations in the industrial sector—including steelmaking, plastic production, and oil refining—are responsible for roughly 30% of global carbon dioxide emissions. Decarbonizing this sector means retiring assets before the end of their useful life to adopt low-carbon technologies that aren’t fully mature yet. This is not only a difficult challenge but a very expensive one.

For an industrial plant to make this green transition, they must operate with flexibility to adapt to the intermittent renewable energy sources. This means cranking up production when wind and solar power are cheap and abundant, and scaling back or drawing from stored energy when grid prices skyrocket.

For the engineers tasked with planning these multi-million-dollar overhauls, mapping out this transition is a logistical nightmare. They must simultaneously predict long-term equipment investments over 15 years while calculating the factory’s flexible, hour-by-hour operational responses to volatile electricity prices.

Now, researchers from Carnegie Mellon University’s Department of Chemical Engineering have developed a mathematical blueprint to solve this puzzle, proving that smarter algorithms can help plan the industrial transition to clean energy better while slashing corporate costs.

The peer-reviewed study, published in Computers & Chemical Engineering, introduces a novel computational algorithm that allows industries to confidently navigate the economics of deep decarbonization.

Originally, the math required tracking both the investment timeline across a 30-year period and hourly operating decisions, which considered the fluctuating electricity prices for each year. This was too massive for standard computers to solve as a single, gigantic problem. To bypass this, planners relied on time-series aggregation, a mathematical shortcut that clumps similar days together into a few representative averages.

The researchers discovered a critical flaw in that method: the final answers are incredibly sensitive to how these shortcuts are set up. A tiny tweak to the settings used while running the algorithm could completely alter what equipment the computer recommended buying, potentially costing companies millions in mistaken investments.

We wanted to eliminate the guesswork from industrial transition planning.

Ana Torres, Associate Professor, Chemical Engineering

To eliminate this, the research team developed a hybrid solution strategy. They modified a classic mathematical technique known as Benders decomposition, which breaks the massive problem into two interconnected pieces: a master program that handles annual investment decisions and smaller subprograms that calculate hourly operational flexibility.

By incorporating a specialized data-clustering technique, their algorithm does something previous methods could not: it provides mathematically rigorous “bounds” or safety nets. This ensures that even when the computer uses a shortcut, the answer is guaranteed to be within a specified range.

“We wanted to eliminate the guesswork from industrial transition planning,” said Ana Torres, associate professor of chemical engineering. “By creating a framework that provides mathematical guarantees, we can accurately capture the immense economic value of hourly operational flexibility without crashing the computer.”

To prove the power of their new algorithm, the researchers applied it to a complex real-world scenario: the decarbonization of an oil refinery through electrification and carbon capture.

The results were definitive. When the computer was forced to accurately look at hour-by-hour operational flexibility under fluctuating energy prices, it completely changed its investment advice. Rather than delaying the green transition, the smarter model championed the immediate, earlier adoption of electricity-based technologies.

Specifically, the optimal solution proved that refineries could drastically reduce their long-term transition costs by investing early in a coordinated suite of equipment:

• E-boilers: High-powered electric boilers capable of partially replacing fossil fuels for massive industrial process heating.
• Proton exchange membrane (PEM) electrolyzers: Advanced technologies that use electricity to split water into clean hydrogen used for refinery’s reactions.
• Hydrogen storage: On-site tanks to store that hydrogen, allowing the plant to run cleanly even when electricity prices spike.

By replacing unreliable mathematical shortcuts, this research provides global industrial giants with a precise, safer playbook to phase out fossil fuels.

“By providing a more efficient pathway to industrial decarbonization, our work marks a step forward for global sustainability,” said Sampriti Chattopadhyay, a Ph.D. candidate and lead author of the paper.

Additional collaborators included CMU’s Ignacio Grossmann, professor of chemical engineering, and Rahul Gandhi of Shell Technology Center in Houston.