Mathematical Optimization: Powerful Prescriptive Analytics Technology That Is Part of Your Data Science Toolbox


In this special guest article, Dr Gregory Glockner, vice president and technical researcher at Gurobi, explains how you can get started with mathematical optimization and provides some examples of how this prescriptive analytics technology can be combined with machine learning to deliver business benefits across various industries. Prior to joining Gurobi in 2009, Dr. Glockner was a partner and COO of Dwaffler, a provider of business intelligence tools. Dr Glockner holds a BS magna cum laude from Yale University in Applied Mathematics and Music, as well as an MA and PhD. in Operations Research from the Georgia Institute of Technology. He has trained optimization software users in Brazil, Hong Kong, Japan, Singapore, South Korea, as well as the United States and Canada. He is an expert in optimization modeling and software development.

We are in the midst of a “golden age” of data analytics, where high-quality data abounds and powerful and advanced analysis tools are readily available.

Businesses across industries are looking to leverage these analytical tools to generate solutions to their critical problems, guide their forecasts and decisions, and gain a competitive advantage. But with so many analytics tools on the market, many companies struggle to determine which ones they really need.

Generally speaking, “analysis” consists of three different types of tools:

  • Descriptive analysis: Using data aggregation, data mining, and business intelligence tools, you can gain insight into what happened in the past or what is happening now in your business environment .
  • Predictive analytics: Using statistical models and machine learning tools, you can predict and predict what will happen in the future.
  • Prescriptive analysis: Using heuristics or mathematical optimization tools, you can make (and often automate) complex decisions about what actions to take to achieve your business goals.

The three types of analysis tools are widely used by organizations today. For example, as governments and the health sector rush to immunize the world’s population against COVID-19, descriptive analysis tools can provide us with an accurate, real-time snapshot of current immunization and vaccine rates. infection; predictive analytics tools can predict what would happen to infection rates if we administered more vaccines in specific locations at certain times; and prescriptive analysis tools can help us decide exactly where and when to distribute vaccines.

If you as a data scientist or IT professional want to extract maximum value from your data (using it to generate insights, predictions, decisions, and the best possible business outcomes), you need to use all three types of analysis tools, ideally in an integrated manner.

You are probably very familiar with descriptive and predictive analysis tools, but you may not be very familiar with prescriptive analysis in general and mathematical optimization (the main prescriptive analysis tool) in particular.

In this article, I will briefly explain how you can get started with mathematical optimization and give some examples of how this prescriptive analytics technology can be combined with machine learning to deliver business advantages in various industries.

Learn how to take advantage of large-scale mathematical optimization

Chances are, like most data scientists and IT pros, you already have some experience with mathematical optimization, probably in Excel.

Like a Swiss Army Knife, Excel gives users access to a number of different tools, including forecasting and scenario analysis functionality and a basic mathematical optimization solver.

Although Excel gives you the opportunity to familiarize yourself with these analysis tools and perform simple tasks, the capabilities of this software are quite limited because it cannot handle large multidimensional data sets or problems with significant complexity.

If you want to use mathematical optimization or other sophisticated large-scale analysis tools, you need a more specialized and robust tool for the job.

When it comes to mathematical optimization, there is a wide range of commercial mathematical optimization calculation and modeling tools on the market, many of which interface with many popular programming languages ​​that data scientists are used to. , such as Python, MATLAB, and R.

You can use any programming language you want to build mathematical optimization models and applications, just like you do with machine learning.

Of course, it will take time and effort to learn how to write code for mathematical optimization, but in the end it will pay off, as you will be able to use this powerful prescriptive analysis technology – alone or in combination with it. machine learning. – to automatically generate solutions to your most critical and difficult business problems and make optimal decisions.

Make an impact in all sectors

Mathematical optimization and machine learning have proven to be a dynamic duo, and companies from many different industries have used these two analytical technologies together to solve a wide range of real business problems and achieve increased productivity and profitability. .

Here are just a few examples of how this combination of mathematical optimization and machine learning delivers major business value across various verticals:

  • Retail: Major retailers use machine learning to forecast demand for specific products, in certain locations, at specific times. Then, they feed those predictions into a mathematical optimization application, which uses them as input to generate optimal production, pricing, inventory and distribution plans, make business decisions that maximize profits and customer satisfaction. , and minimize operating costs.
  • Financial services: Banks and other financial services companies rely on machine learning and mathematical optimization to determine the right allocation of their investment portfolios. With machine learning, they predict the performance of particular assets and then channel those predictions into their mathematical optimization application. The mathematical optimization application automatically determines the optimal portfolio allocation (based on these forecasts as well as the latest market movements and individual investment goals and preferences), thereby maximizing risk-adjusted returns and reducing risk .
  • Online advertising: Internet search engine giants take advantage of machine learning to predict which products and services will be of interest to individuals (based on their previous search history and other factors), then use mathematical optimization to determine the online ads to show individual users at specific times and how much to charge advertisers (to maximize revenue).
  • Electric power: As the electric power sector shifts from reliance on fossil fuels to renewable resources such as solar and wind power, governments and industry players must make high-stakes decisions on strategic investments in network infrastructure and resources. These organizations use machine learning to predict future electricity demand and capacity requirements, then feed those forecasts into mathematical optimization applications, which generate optimal long-term investment plans. Interestingly, organizations in other industries, including telecommunications and cloud computing, use mathematical optimization and machine learning in the same way to accurately assess long-term demand and capacity needs, then make optimal strategic investment decisions.

Adding Math Optimization to Your Data Science Toolkit

There has been a continuous increase in the number of data scientists using mathematical optimization, as well as the number of different use cases of this prescriptive analytics technology (alone and in combination with machine learning), in various sectors.

If you want to add math optimization to your toolbox, you can start by exploring and experimenting with math optimization in Excel. Then, when you are ready to take advantage of the full power of this technology, you can move on to industrial grade mathematical optimization tools that will allow you to solve huge problems in terms of complexity, scale and importance.

If you want to unleash the true value of your data (using it not only to gain insights and predictions, but also to make optimal decisions), you need mathematical optimization – as well as machine learning and other analytics technologies – in your toolset. .

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