I’ve lost count of how many times â€“ over the course of my 25-year career in the mathematical optimization software industry â€“ Iâ€™ve been asked this question: â€śCan you tell me what mathematical optimization is?â€ť

Itâ€™s a question that â€“ no matter how many times I hear it â€“ still surprises and puzzles me.

I always wonder how itâ€™s possible that so few people know about this AI technology given that mathematical optimization:

• Is so well established, with a history stretching back more than 70 years.
• Is so widely used, especially by leading global companies. A recent survey revealed that 85% of Fortune 500 companies utilize mathematical optimization in their operations.
• Has delivered such significant business value, generating billions of dollars in cost savings and revenue growth for organizations around the world.
• Has transformed entire industries â€“ including energy, telecommunications, aviation, logistics, and finance â€“ by empowering companies to tackle their toughest business problems and make optimal decisions that maximize their operational efficiency.

And all this begs the question: If mathematical optimization is such a proven, powerful, and pervasive problem-solving technology, why doesnâ€™t anybody know about it?

I think this is largely due to two factors:

• Mathematical optimization is used to solve business problems that are huge in scale and high in complexity like supply chain planning, energy distribution, and shipment routing. These business problems (and the mathematical optimization applications that are built to address them) are not visible or tangible to most people.
• Our brains are simply not capable of imagining how one might go about solving mathematical optimization problems â€“ as this requires the ability to rapidly comb through trillions or even more possible solutions to find the right one.

But the truth is that (with the right technologies) these problems are solvable and (with the right guidance) these problems are easy to spot â€“ and you may be surprised to discover that your company has business problems that should be addressed with mathematical optimization.

So, how can you determine if your company should be using mathematical optimization? Ask yourself these four questions to find out.

### 1) Do you have a business problem that involves a complex, interconnected set of decisions?

Mathematical optimization is a problem-solving technology â€“ it automatically generates solutions to your business problems, which you can use to help you make the best possible business decisions.

But not every business problem is a mathematical optimization problem. And just like you can identify a leopard when you see its spots, you can readily recognize a mathematical optimization problem by a few defining features.

One essential characteristic of a mathematical optimization problem is that it involves a set of decisions that interact in complex ways. The complexity of this interaction arises from the fact that many decisions have implications that propagate far and wide, impacting various areas of your operations and influencing other decisions.

Are you facing a business problem where itâ€™s impossible for you to keep track of all the interactions between decisions in your head and think through all the potential outcomes of each decision? If so, you may have a mathematical optimization problem on your hands.

### 2) Are you able to quantify and compare the outcomes of your business decisions?

If your business problem is a mathematical optimization problem, it will also have another essential characteristic: You will be able to capture and compare the outcomes of your business decisions in a quantitative manner.

In other words, you must be able state â€“ in mathematical terms â€“ what makes one solution to your business problem better than the others.

Whatever your desired business outcomes or objectives are â€“ you may, for example, work for a bank trying to improve risk-adjusted investment returns and regulatory compliance or an airline aiming to minimize flight delays and operating costs â€“ mathematical optimization enables you to automatically consider and compare all the possible solutions to your business problem, and find the solution that best fulfills (and balances the tradeoffs between) your business objectives.

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### 3) Would more efficient use of resources unlock new opportunities for your company?

Resources â€“ such as workers, machines, inventory, energy, and money â€“ are the fuel that makes every company run, and whether or not a company can reach its business goals largely depends on how efficiently it uses its resources.

If your company has resource constraints, mathematical optimization can empower you to make the best possible decisions on how to deploy your scarce resources â€“ so that you can maximize your operational efficiency and unlock new opportunities for business growth.

There are countless examples of companies â€“ including Microsoft, Walmart, Uber, FedEx, Air France, and the National Football League â€“ that have utilized mathematical optimization to make better use of their resources and thereby realized tremendous operational and financial benefits.

### 4) Does your company operate in a constantly changing business environment?

Mathematical optimization is especially effective for businesses that have to deal with constant changes in their business environment.

Unlike machine learning (which relies on historical data to make predictions), mathematical optimization uses all available information on current business conditions â€“ including historical and real-time data â€“ to deliver optimal solutions and drive optimal decision making.

Mathematical optimization gives companies the capability to react and respond in the most efficient and profitable manner possible to changes in their business situation.

If your company â€“ like many organizations today trying to cope with the unprecedented disruption caused by the coronavirus pandemic â€“ has to navigate a constantly changing business landscape, then mathematical optimization could be an invaluable tool for you.

Of course, thereâ€™s no silver bullet technological solution for all the challenges in the business world today, but, as Gartner says, â€śAI offers an important arsenal of weaponsâ€ť that can improve decision making and business outcomes. Mathematical optimization is one of these weapons.

If you answered â€śYesâ€ť to the four questions I discussed, then you should take the opportunity to learn more about mathematical optimization and discover how it can enable you to solve complex business problems that you thought were unsolvable and achieve business results that you didnâ€™t know were possible.

AUTHOR

### Dr. Edward Rothberg

Chief Scientist and Chairman of the Board

AUTHOR

### Dr. Edward Rothberg

Chief Scientist and Chairman of the Board

Dr. Rothberg has served in senior leadership positions in optimization software companies for more than twenty years. Prior to his role as Gurobi Chief Scientist and Chairman of the Board, Dr. Rothberg held the Gurobi CEO position from 2015 - 2022 and the COO position from the co-founding of Gurobi in 2008 to 2015. Prior to co-founding Gurobi, he led the ILOG CPLEX team. Dr. Edward Rothberg has a BS in Mathematical and Computational Science from Stanford University, and an MS and PhD in Computer Science, also from Stanford University. Dr. Rothberg has published numerous papers in the fields of linear algebra, parallel computing, and mathematical programming. He is one of the world's leading experts in sparse Cholesky factorization and computational linear, integer, and quadratic programming. He is particularly well known for his work in parallel sparse matrix factorization, and in heuristics for mixed integer programming.

Dr. Rothberg has served in senior leadership positions in optimization software companies for more than twenty years. Prior to his role as Gurobi Chief Scientist and Chairman of the Board, Dr. Rothberg held the Gurobi CEO position from 2015 - 2022 and the COO position from the co-founding of Gurobi in 2008 to 2015. Prior to co-founding Gurobi, he led the ILOG CPLEX team. Dr. Edward Rothberg has a BS in Mathematical and Computational Science from Stanford University, and an MS and PhD in Computer Science, also from Stanford University. Dr. Rothberg has published numerous papers in the fields of linear algebra, parallel computing, and mathematical programming. He is one of the world's leading experts in sparse Cholesky factorization and computational linear, integer, and quadratic programming. He is particularly well known for his work in parallel sparse matrix factorization, and in heuristics for mixed integer programming.

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