3 Reasons Why Mathematical Optimization Solver Speed Matters

Mathematical Optimization Speed

Author: Ed Klotz, PhD
Date: 10/26/2020


Users of mathematical optimization solvers have the need for speed. When it comes to choosing between the various open source and commercial solvers available on the market, speed is the most important factor for users.1 In fact, around 72% of users who switched from another solver to the Gurobi Optimizer, the world’s fastest solver, said that speed was the main reason behind their decision to switch..2

Not surprisingly, speed has also been an area of intense focus among mathematical optimization software developers ever since mathematical optimization technologies were first introduced over 70 years ago – and amazing progress has been made. For example, some mathematical optimization problems that can be solved in one second today would have taken 55 years to solve in 1991!

Although mathematical optimization technologies have made tremendous strides over the years – with dramatic improvements in terms of speed as well as accuracy and robustness –performance still remains a constant challenge. This is because – even though solvers keep getting faster and more powerful – the size and complexity of the problems in the business world continues to increase.

And so the quest to reach higher and higher peaks of performance continues, and solver speed remains a top priority among software developers (who continually strive to raise the bar and set new standards) and users (who are constantly looking to solve harder problems, faster).

But – one may wonder – why does mathematical optimization solver speed really matter? While winning benchmarks is nice, what is the value proposition for the users of the software?

In this blog, I will discuss three key reasons why solver speed is such a critical capability for businesses today.


#1: Real-Time Decision Making

The business world today is characterized by complexity and constant change. To survive and thrive, companies in many different industries must be able to make real-time, data-driven decisions on how to most efficiently utilize their resources – and mathematical optimization is an AI technology that empowers them to do exactly that.

One industry where mathematical optimization is used extensively in real-time applications is electric power. To manage the flow of energy across their electrical grids and keep supply and demand in balance, transmission and distribution system operators must have the capability to generate plans every 20 or 30 minutes and make real-time decisions on which sources of power to use to satisfy demand in the most efficient and profitable way. In this situation, having a solver that functions with the utmost speed is vital – as this enables electric power providers to rapidly generate plans as supply and demand dynamics shift, and make real-time decisions on how to best deploy their assets.

There are many other industries – including logistics and manufacturing – where mathematical optimization is widely used in real-time applications, and many companies in these industries rely on mathematical optimization solvers to consistently deliver fast and accurate solutions that enable optimal, real-time decision making.

When using mathematical optimization to facilitate (or even automate) real-time decision making, the speed of the solver really matters – as companies can’t afford to wait for their applications to generate solutions to their pressing, day-to-day business problems.


#2: Disruption Management

Another reason why having a high-speed solver is so pivotal is that it enables companies to more effectively handle disruptions.

Many business today – especially since the onset of the COVID-19 pandemic earlier this year – have to cope with severe disruption. In particular, the disruption caused by the pandemic has had a major impact on companies within global supply chains, who find themselves having to scramble to react quickly to volatile supply and demand dynamics across their end-to-end networks.

But even in “normal” times, companies in various industries such as manufacturing and aviation have to deal with disruptions – caused by unexpected events such as extreme weather, natural disasters, and machine breakdowns – on a daily basis.

When facing disruption, companies must strive to get their operations back on track as soon as possible – and every second counts as the sooner things can be restored to normal, the less costs will be incurred.

As a prescriptive analytics technology, mathematical optimization automatically delivers solutions – based on the latest available data – that prescribe the best course of action to handle a disruptive event. Armed with these solutions, companies can quickly make real-time decisions on how to respond to disruptions and redeploy their resources. In these time-sensitive situations, the faster the solver, the better – as the longer it takes to get operations running smoothly again, the higher operating costs will be.


#3: Robust Scenario Analysis

Another area where the speed of the solver is critical is in conducting scenario analysis.

Mathematical optimization technologies enable users to generate numerous what-if scenarios, evaluate and compare their potential impact on business operations and objectives, and determine the best courses of action.

Simply put, a faster solver gives users the capability to run more scenarios in a shorter amount of time – and this has tremendous business value.

One good example of this is the National Football League (NFL), which utilizes mathematical optimization to automatically create and analyze more than 50,000 possible scheduling scenarios. By using the fastest solver on the market today (the Gurobi Optimizer), the NFL – which has a finite period of time to examine various possible schedules and select the best one – can generate a huge pool of high-quality candidate schedules to choose from.

A high-speed solver enables companies to conduct rapid, robust what-if analysis – so that they can explore and evaluate numerous different scenarios and make the best strategic decisions.


Full Speed Ahead

For the three reasons I highlighted in this blog post (and for other reasons as well), mathematical optimization solver speed really matters.

I predict that in the coming years speed will continue to be a key consideration for buyers looking for mathematical optimization solvers, a critical capability for users who depend on these solvers to address their business problems, and a chief focus of developers striving to boost solver performance.

Indeed, in the future, as the problems in the business world become progressively more complex, the need for faster and better mathematical optimization solver performance will persist – and companies like Gurobi will continue to innovate and improve their technology to meet the challenges of the day.

Looking ahead, I also expect the performance gap between commercial and open source solvers to widen, rather than diminish.

Gains from improvements in computer chip speed appear to have reached the point of diminishing returns. Increased parallel computing capabilities still appear to have great potential for additional improvement, but those gains will not be attained just by plugging in an existing implementation; careful reimplementations of the algorithms will probably be needed to exploit the full power of massive parallelism. Quantum computers and other new architectures are still early in development regarding optimization software.  But, if successful, they too are likely to require reimplementations of the existing algorithms or different model formulations. Here is an example that illustrates this.

Gains – in terms of solver speed, accuracy, robustness, and integration with the hardware – will come from teams of software developers that are focused on mathematical optimization and have the resources to explore new ideas and reach new peaks of performance.


  1. Gurobi Customer Survey, 2020
  2. Gurobi Customer Survey, 2020