Virtually no industry is immune to global disruption, as we all discovered during the pandemic. The question is: How can businesses today navigate these uncharted waters and find new pathways to profitability amid a sea of uncertainty?

Many companiesÂ utilize AI toolsÂ such asÂ machine learningÂ and heuristics to help them manage their operations and make data-driven plans, predictions and decisions. But the problem is that many of these tools depend on historical data, and given the unprecedented nature of todayâ€™s economic challenges, past performance is not a reliable indicator of future business outcomes.

To deal with todayâ€™s disruption and chart a course to profitability amid such immense uncertainty, companies must have AI tools that take into account their current business situations, challenges and constraints â€” and mathematical optimization is such a technology.

With mathematical optimization, you can:

• Use those models (along with up-to-date data and a mathematical optimization solver) to help you tackle your real-world business problems and make the best possible decisions.

By relying on models of your real-world business environment and running on the latest available data, mathematical optimization technologies help you explore and understand your business situation today, so you can react effectively to changing conditions and disruptions.

### What Is a Mathematical Optimization Model?

Technically speaking, a mathematical optimization model is a mathematical representation of your real-world business problem that is made up of three key features:

• Decision Variables: The decisions that you have to make.
• Business Objectives: The various (and often conflicting) business goals you are aiming to achieve.

To give you an example that was widespread during the Covid-19 pandemic, a hospital network whose business problem is equipment and facility capacity planning could create a model that captures that business problem’s:

• Decision variables such as which medical equipment, including testing kits, PPE and ventilators, to distribute to which hospitals and which ICU wards, beds and operating theaters to allocate to which patients.
• Constraints such as conventional, contingency and crisis capacityÂ levels for PPE across the hospital network and regulations regarding which wards and beds need to be reserved for patients with various conditions.
• Business objectives such as maximizing resource utilization and service-level performance while minimizing operating costs.

This hospital networkâ€™s model would probably have millions or more decision variables and constraints, and these inputs could be adjusted at any time to accommodate changing conditions in the operating environment and shifts in supply and demand dynamics.

There are countless other challenging and critical business problems today, from food production to shipment routing to electric power generation and transmission toÂ classroom seating assignmentsÂ (while respecting social distancing), thatÂ can be capturedÂ in mathematical optimization models.

A mathematical optimization model is a dynamic digital representation of your current business situation, encompassing all the complexity and volatility that you are facing today.

The act of defining your business problem as a mathematical optimization model can enable you to attain a greater awareness of your business conditions and challenges, but how can that model actually be used to help you deal with disruption? To do this, you need to feed your model up-to-date data and integrate it with a mathematical optimization solver that:

• Automatically processes the data and reads the model.
• Combs through and considers an astronomical number of possible solutions to your business problems.
• Finds the optimal solutions that you can use as the basis to make your business decisions.

With up-to-date data and a solver, a mathematical optimization model becomes much more than merely a representation of your business problem; it becomes an integral part of the solution to that problem.

Combining these three elements (your model, your data and a solver) in a mathematical optimization application gives you the power to:

• Visualize: Get a 360-degree, birdâ€™s-eye view over your operations and gain a deep understanding of the dynamics and disruptions present in your business landscape.
• Analyze: Explore various scenarios and gauge their potential impact on your business so you can identify risks and opportunities.
• Decide: Rapidly generate optimal solutions to your business problems and use those solutions to determine courses of action.

By fusing your model with a mathematical optimization solver and fueling it with up-to-date data, you get visibility and control over your operational network. No matter how profoundly the business world changes, your mathematical optimization application has the flexibility and robustness to consistently deliver optimal solutions.

### A Technology for Today

The unprecedented economic disruption triggered by Covid-19 set off a seismic shift in our business dynamics and data. Companies must continue to leverage AI tools to enable data-driven decision making, but they cannot solely rely on those tools (like machine learning) that use data from the past to make predictions about the future.

The most valuable AI tools for companies today are those â€” like mathematical optimization â€” that run on up-to-date data, encompass the present-day reality, and empower decision-makers to respond to disruption in the most efficient and effective manner possible.

To get started, imagine what it would mean to your organization to be able to model and understand your business situation today. Then,Â identify which business problems you haveÂ that could be addressed with mathematical optimization. From there, you can start to figure out how your organization can use mathematical optimization to deal with disruption and drive improved decision-making and business outcomes.

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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