Supply chains consist of imperfect humans struggling to make perfect decisions. In the end, though, it all comes down to a game of numbers.

That, at least, is the theory behind mathematical optimization, and the way it’s being applied to supply chain management today.

By itself, the word “optimize” doesn’t mean anything specific. “A lot of people overuse the term, just to say ‘I made something better,’” says Jerry Yurchisin, senior data science strategist with Gurobi, provider of a prescriptive analytics software platform built on decision intelligence technology.

Add the word “mathematical,” and you’re talking about a rigorous process that can be applied to any number of business challenges. Three key factors are part of the mix: the stated objective, the variables at play, and the constraints that narrow the possibilities to define the ultimate “perfect” decision.

“What makes it mathematical,” Yurchisin explains, “is what comes out of it when you develop a problem, go from beginning to end, then get what’s guaranteed to be the one global optimal solution — there is nothing better.”

“If the problem is measurable, then it’s solvable,” writes Gurobi chief executive officer Duke Perrucci in the Harvard Business Review.

The word “perfect,” of course, can be misleading. What it means in this context is striking the optimal balance among often-competing priorities — such as the need to expand one’s base of suppliers versus the additional cost of doing so.

Mathematical optimization drives the analyses of multiple “what-if” scenarios, allowing the business to examine them in a virtual environment, then compare the potential outcomes of each before committing to the best one under the given circumstances.

Using the approach known as multi-objective optimization, Yurchisin says, businesses can balance two or more goals, crafting a model that’s flexible enough to be updated quickly. That’s an especially valuable tool for dealing with today’s ever-changing tariff schemes. “Businesses can even lock in decisions they’ve already made, then re-optimize the rest of the model under new trade conditions,” he says.

Under the hood, so to speak, the model is translating human inputs into numbers and mathematical formulas. “Let the algorithms churn through all the options and say ‘this is the one that wins,’” Yurchisin says.

That, of course, is a particular strength of modern-day artificial intelligence, which delivers the ability to input and analyze vast amounts of data, far beyond the capability of humans to do so. What makes mathematical optimization especially valuable, Yurchisin says, is its prescriptive — as opposed to merely descriptive — nature. For a retailer, that might take the form of guidance as to where and how much to produce items, how to transport them, and where to position them in a manner that best reflects actual consumer demand.

In a sense, mathematical optimization is the latest refinement of the concept of an “expert system,” a term from the early days of AI development that described efforts to mimic the knowledge base acquired by human managers through years of experience.

Others cite the use of a “digital twin” — a virtual representation of an entire supply chain — to create and review various what-if scenarios. “I like to think of this as a mathematical twin,” Yurchisin says. “You’re describing your system in words, then taking that and representing it with math.”

Mathematical optimization isn’t exactly plug-and-play. It requires a level of skill on the part of human users, in the form of operations research analysts to oversee the process. Yurchisin says the demand for that type of expert is increasingly rapidly, as businesses and supply chains begin to embrace AI as a decision-making tool.

Yurchisin predicts that the granularity of mathematical optimization — its ability to delve into the minutest details of global supply chains — will continue to improve. “A mathematical model is just an abstraction of some real thing,” he says, “but you can always add detail that makes it more realistic.”

Increasingly, he says, mathematical optimization will fulfill the goal of an “autonomous” supply chain — one that functions with a minimal amount of human intervention. That’s essential, he believes, to surviving in a world where markets are in a state of constant change.

“Rapid-fire, essentially live decision-making only happens when you have a reliable and fast solver behind the scene,” he says.