Mathematical Optimization: What’s In A Name?

By Dr. Edward Rothberg, Chief Executive Officer and Co-founder, Gurobi Optimization

As the great William Shakespeare once wrote, “What’s in a name? That which we call a rose by any other name would smell as sweet.” Unfortunately, for these star-crossed lovers in Romeo and Juliet, names do matter. They matter to the Capulets and Montagues, and they matter to us in the real world.

As such, I find myself in a challenging spot. My company lives in a space that doesn’t know what to call itself. We call what we do “mathematical optimization,” but unless you already know what that means, your eyes have likely already glazed over.

To make matters more complex, our industry overlaps with many others. So, it’s reasonable to say we’re in the business of artificial intelligence (AI), prescriptive analytics, operations research and mathematical programming—and the list goes on. Although each of these terms has its merits, each one appears to miss the mark in an important way. We need simple, straightforward terminology but, as the bard would say, “Ay, there’s the rub.” If it’s too simple, it doesn’t communicate the transformative power of the technology. If we manage to pack in everything, it becomes an unapproachable technical word salad.

How did our industry get to this point, and how did we land on “mathematical optimization” in the first place? Here’s a bit of the history.

Operations Research And Mathematical Programming

The original name for our field was “operations research,” and “mathematical programming” was much of what we did. In today’s context, however, these terms are less clear: “Research” conjures up the scientific method and “programming” makes many people think of computer science.

When the field was founded in the 1940s, “programming” implied “setting a plan or course of action”—similar to how a theater program outlines the acts in a play. The term “mathematical programming” was meant to convey “using mathematics to develop a plan of action.”

Similarly, “operations research” was meant to describe “a rigorous approach to improving the operation of some organization.” I suspect that, nowadays, people are more inclined to view “research” as a precursor to “practice.”

Optimization

This term is widely used in the field, but it’s a very broad term and has been co-opted a number of times. Within our field, we use “optimization” to refer to “the process of finding values that optimize a mathematical function.” Outside our field, however, people hear “optimization” and they think of search engine optimization or code optimization. Although those are useful tools in their own right, they’re relegated to very narrow segments of business practices, and those segments are frequently not core to the company’s mission.

The Science Of Better

In the early 2000s, the professional society in this area (INFORMS) decided to focus significant attention on marketing the profession. This was a multi-pronged effort, but the main result was a term that was meant to be both appropriate for people in the field and also informative and intuitive to people outside the field.

The term they settled on was “The Science of Better.” Although many have debated the reasons why, unfortunately, the term didn’t succeed in its goal of drawing new people in.

Prescriptive Analytics

Analytics is, by definition, “using data to arrive at a conclusion.” Although it’s a commonly understood term, our industry is split on whether “analytics” is the appropriate umbrella for us to live under. Analytics is the journey to arrive at a conclusion—but mathematical optimization identifies how best to act on that conclusion. In other words, analytics focuses on the before, and mathematical optimization focuses on the after.

In the 2010s, Tom Davenport popularized the notion of an analytics maturity model, which showed organizations progressing through three levels of sophistication: descriptive, predictive and prescriptive analytics. Although “descriptive” and “predictive” have quite intuitive meanings, “prescriptive analytics,” which was meant to cover our area, doesn’t evoke similar intuition. “Prescriptive” implies that we’re imposing rules or courses of action on people when mathematical optimization actually aims to help people navigate complex decisions. It provides people with recommendations for the optimal way to proceed—not strict rules to follow.

Artificial Intelligence (AI)

Although AI has developed a lot in the past 20 years and will continue to do so, it essentially means “a computer performing tasks that would otherwise require human intelligence.” Is that what we do? Technically, yes, but “AI” also applies to self-driving cars, speech recognition and a number of other topics that are completely unrelated to what we do. Although it draws people in, it’s too broad to give a good sense of the sorts of problems we solve.

The Search Continues

At Gurobi, we currently use the term “mathematical optimization.” Our competitors use other terminology. I suspect that we all see the need to find a more approachable name. At a minimum, it should capture a few key points:

1. Complexity: This technology can help companies function more efficiently in complex, dynamic environments where activities can have significant interdependencies.

2. Data: This technology can pull (typically significant) value out of business data.

3. Decisions: This technology can help either support or automate the process of making better decisions.

In addition, the terminology needs to be easily understood by non-practitioners who may not have mathematicians on staff or understand what a mathematician can offer their business. The typical potential client doesn’t look at a problem and think, “I need mathematical optimization to solve this.” How can we give them the words they need to identify their needs and solutions accurately?

Again, I invoke the words of Shakespeare: “O for a muse of fire that would ascend the brightest heaven of invention.” Or, to put it another way, does anyone have any good ideas for a better name?