October 3, 2025 The World is Getting More Complex—Optimization Helps

Mathematical optimization helps businesses simplify increasingly complex problem-solving needs and discern the best possible solutions.

By Dr. Kostja Siefen, Senior Director of Technical Account Management, Gurobi Optimization

The world isn’t getting any simpler. This statement may seem like an oversimplification in itself, but it’s largely true. It’s actually been mathematically proven on a molecular level—as the countless particles that make up the cosmos strive to reach an equilibrium, their entropy, and therefore complexity, steadily increases. So yes, at least according to the theorizing of nineteenth-century researcher Ludwig Boltzmann, the world is actually becoming more complex.

In a less scientific sense, this complexity is also reflected across many facets of our lives. Everything from societal shifts to business, political, and economic changes seem to be nearly inescapable. This is especially true for contemporary businesses, which operate in a realm regularly upended by rapid market changes, evolving economic and political regulations, changing consumer demands, and the long-tail effects of the pandemic. Simply put, business decisions must now consider more rules, factors, dependencies, and alternatives than ever before.

This all-encompassing complexity is industry agnostic. Whether you’re managing the balance between supply and demand in an energy grid or deciding how much of a product line to ship to local warehouses, factors that impact your decision-making process, much like Boltzmann’s particles, are ever increasing. And as these factors and challenges grow, the number of potential solutions do the same.

The question today’s businesses need to solve is not “How can we make things less complex?” The real question they need to solve is, amid a constantly shifting field of challenges and potential solutions, “How can we master this growing complexity and still find a best path forward?”  

The Complexity of Modern Problem-Solving

Answering this question starts with examining just how complex contemporary problem-solving has become. As each new factor or choice—be it economic, regulatory, consumer-related, or otherwise—is added to a given problem, it creates both new challenges and new potential solutions. This is reminiscent of the mathematical concept of combinatorial explosion, in which the number of potential outcomes to a problem grows exponentially with each increase in the number of variables involved.

For example, imagine you’re tasked with scheduling production at a manufacturing plant. If your plant was only responsible for building one specific product, including all of its parts and components, the combinatorial complexity of your production could be relatively low. Unfortunately, this is not likely to be the case for any modern manufacturer. Instead, each of your production plants is likely to produce a variety of different products, each made up of parts from a number of different suppliers.

If that wasn’t enough to keep track of, your operations are likely subject to the changing whims of customer demand, supply chain reliability, and economic, political, and environmental regulations. Each change in these factors—fluctuating energy prices, a new tariff, a gap in your supplier’s production, a new regional emissions regulation—will impact your capacity to schedule manufacturing that is efficient, compliant, reliable, and cost-effective.

Using Optimization to Overcome Complexity

While these shifting factors aren’t going to make your problem any less complex, they can actually make it easier for you to solve. Solving complicated decision-making situations, even those with a near combinatorial explosion of variables and factors involved, is the explicit purpose of today’s cutting-edge mathematical optimization solvers.

Mathematical optimization—or optimization, as we’ll refer to it in this article—is the practice of using algorithms to assess the many variables and constraints of a multifaceted problem and provide the best possible solution in the shortest amount of time. In short, it’s using math to find the mathematically proven best answer to a complex decision situation. It does so by translating three core components—the goals you want to achieve, the variables that you can control, and the constraints that you must adhere to—into mathematical representations that can be processed by an optimization solver.

By leveraging highly efficient mathematical algorithms, optimization solvers can assess the countless possibilities that arise from the manipulation of different variables and identify which solution is the best possible route forward. This enables teams to take all of the work that might go into the time-consuming manual assessment of outcomes and reduce it to the time it takes to build and solve a suitable mathematical model.

The Impact of Optimization

What might this look like in practice? Let’s return to our manufacturing example. When scheduling production, your ultimate objective is to ensure the right number of the right products are created in the right timeframe. The controllable variables include things like your production rate, timing, batch size, equipment utilization, and resource allocation. Your constraints will vary depending on shifting factors, but are likely to include demand forecasts, production capacity, supply chain limitations, and sustainability goals.

If these factors were put into an optimization solver, it’d provide you with the best possible production schedule to meet demand forecasts in a timely and reliable manner. But what if a primary supplier suddenly experiences a product shortage and delays your next delivery? Or maybe a new regulatory standard adds a time-consuming emissions assessment to your quality assurance process? The combined impact of these changes has the potential to upset your existing schedule, limit your productivity, and overcomplicate your decision-making process.

With optimization, these problems can be solved in the short time it takes to adjust your forecast. All you need to do is reconfigure the same optimization model for a new scenario that considers any short-term changes. Optimization is dynamic, and any new model components do not require any changes in the solver’s algorithmic framework. There’s no need to start from square one and agonize over which is the best path forward—a solver will automatically handle these changes to model or data.

More Complex, but Less Complicated

Mathematical optimization is a resilient technology against the growing complexity of the world. And, like complexity itself, it’s not exclusive to a specific industry or problem type. Whether used to optimize production schedules, inform tax-smart investment solutions, deliver optimal grocery shopping experiences, or create the best possible NFL schedule, optimization has a wide range of applications for streamlining complex decisions.

By leveraging today’s increasingly powerful and accessible optimization tools, we can all make our decisions a little less difficult—even as the universe itself continues to become more and more complex.

About the Author:
Dr. Kostja Siefen leads the global Technical Account Management team at Gurobi Optimization. Kostja holds a Ph.D. in Operations Research from the University of Paderborn (Germany). He joined Gurobi in 2015 after many years of experience in the development and design of decision support systems using mathematical optimization. Before joining Gurobi he worked at Daimler Research & Development and as a lecturer at the University of Paderborn.

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