Mathematical Optimization: Past, Present, and Future (Part 3)

Author: Robert Bixby, PhD
Date: 5/5/2020

Thinking back to the beginning of my career in the mathematical optimization software industry nearly 40 years ago, I can honestly say that – at that time – I could not have envisioned that mathematical optimization technologies would become what they are today.

Back then, I didn’t foresee that mathematical optimization technologies such as linear programming (LP) and mixed-integer programming (MIP) would ultimately develop into powerful tools that – out of the box, without any sort of customization of code – could be used by companies across a wide range of industries to rapidly and robustly solve their real-world problems. But that is exactly what happened.

As a result of the pivotal technological breakthroughs made by Gurobi Co-Founders Zonghao Gu, Ed Rothberg, and myself as well as others, “black-box” mathematical optimization solvers can now be embedded in a vast array of applications that are used by thousands and thousands of leading businesses today to tackle their complex problems and make optimal decisions.

In the first and second blogs in this series, I chronicled the history of mathematical optimization technologies over the past 70 years, giving readers an overview of how these technologies evolved since they were first introduced in the late 1940s and early 1950s.

In this blog, I would like to focus on the importance of mathematical optimization technologies in our world today, and also share some thoughts on how I think these technologies will develop in the years to come.

A Technology for Today and Tomorrow

In today’s business world, the impact and applicability of mathematical optimization technologies across different industries continues to increase – with more and more companies using mathematical optimization tools every day.

The question is: Why is mathematical optimization – a technology that was first introduced more than 70 years ago – still so relevant and important today?

Here are some of the key reasons why I think mathematical optimization still remains such a significant technology today:

• Greater data availability and quality: Over the past few decades, the availability of data keeps increasing, and the quality of data keeps improving. Companies today have access to huge amounts of high-quality data, and they are looking to use this data to make better decisions – and that’s what mathematical optimization is all about. Mathematical optimization empowers companies to utilize their data to solve their challenging, real-world problems and make better decisions. There is no other technology that can do this with the same robustness as mathematical optimization and with a guarantee of the quality of the solutions that are generated.
• The emergence of advanced analytics technologies: In the past, mathematical optimization applications (and operations research projects in general) were often marginalized and relegated to the IT departments of companies. But over the last ten years, with the explosion of advanced analytics technologies such as AI and machine learning in the business world, a major change has occurred. Now, in many major companies, there are C-level executives (up to and including the CEOs) who appreciate the value of advanced analytics tools including mathematical optimization, and who understand the applicability of these technologies throughout their organizations. Now – at the highest levels of these companies – there is an awareness of the importance of being able to understand data and use it to make the best possible business decisions (which is precisely what mathematical optimization does). In fact, many major companies today have chief analytics officers who are responsible for leading the effort to employ advanced analytics technologies throughout their organizations. With the rise of advanced analytics technologies, mathematical optimization has taken on a central and critical role in many companies – and its significance and value will only increase in the coming years.
• The shift from planning to real-time execution: Over the past few decades, we have seen a shift in the way companies are utilizing mathematical optimization. Traditionally, mathematical optimization was used primarily as a decision support tool to address long-term planning problems, but now it is increasingly being used to solve real-time execution problems and make real-time (and often automated) decisions – and has thus become an integral part of day-to-day operations for so many companies. There are three key factors driving this shift in the use of mathematical optimization from planning to real-time execution:
  1. The improvements in the speed and power of mathematical optimization solvers – which are now capable of tackling even the toughest business problems, sometimes in a matter of milliseconds.
  2. The availability of user-friendly interfaces for mathematical optimization applications – which enable even the non-expert businessperson to be able to make use of these very sophisticated analytics tools.
  3. The robustness of mathematical optimization solvers – which can be embedded in a wide range of applications that are put in the hands of non-expert businesspeople, who can (without direct knowledge of the underlying mathematical model) make modifications to the model through a high-level interface.

These software developments and ease-of-use and performance improvements have made it possible for businesses to use mathematical optimization for real-time execution. Mathematical optimization has turned into an indispensable element of daily operations for countless companies across so many different industries, used in mission-critical applications to drive automated, optimal real-time decision making.

• The robustness of mathematical optimization in the face of changing business conditions: In today’s business landscape, change is the only constant – and companies need technological tools that enable them to act, react, and respond to changing conditions in the most efficient and profitable manner possible. Without a doubt, mathematical optimization is one of those tools. Unlike machine learning or heuristics applications (which often need to be tweaked or rebuilt whenever business conditions and data change), mathematical optimization applications are based on models that are dependent on business constraints but not the specific data. If the optimization model is built correctly (i.e. if it captures the key elements of a particular business problem including its decision variables, constraints, and objectives), then it will consistently be able to deliver optimal solutions to that business problem even as data changes on a daily basis. This robustness of mathematical optimization in the face of changing business conditions makes it a vital technology for the businesses of today.

Looking to the Future

For the reasons highlighted above (and for other reasons as well), mathematical optimization technologies are indispensable tools for companies today – and will continue to be in the future.

The applications of mathematical optimization in the business world are seemingly endless, the number of different industries that mathematical optimization has touched is growing every day, and the impact of mathematical optimization on our lives keeps expanding.

In the coming decades, I think that we will see mathematical optimization technologies will get even stronger and faster – and these tools will be able to handle business problems of ever-increasing size, breadth, and complexity.

Mathematical optimization technologies have had a long and interesting history that stretches back over 70 years, and they have a bright and promising future ahead.

I’m grateful to have had the opportunity to make a contribution to the development of mathematical optimization technologies, and I look forward to seeing (and playing a part in) how these technologies develop in the years to come.