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Mathematical Optimization: A Powerful Prescriptive Analytics Technology That Belongs In Your Data Science Toolbox

In this special guest feature, Dr. Gregory Glockner, Vice President and Technical Fellow at Gurobi, explains how you can get started using 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 partner and Chief Operating Officer for Dwaffler, a provider of decision analysis tools. Dr. Glockner has a B.S. magna cum laude from Yale University in Applied Mathematics and Music, and an M.S. and Ph.D. in Operations Research from the Georgia Institute of Technology. He has trained users of optimization software in Brazil, Hong Kong, Japan, Singapore, South Korea, and throughout the USA 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, advanced analytics tools are readily available.

Enterprises across industries are looking to leverage these analytics tools to generate solutions to their mission-critical problems, guide their predictions and decisions, and gain a competitive advantage. But with so many analytics tools on the market, many companies have difficulties determining which ones they truly need.

Broadly speaking, “analytics” consists of three different types of tools:

  • Descriptive analytics: Using data aggregation, data mining, and business intelligence tools, you can get insights on what has happened in the past or what is happening currently in your business environment.
  • Predictive analytics: Using statistical models and machine learning tools, you can forecast and predict what will happen in the future.
  • Prescriptive analytics: Using heuristics or mathematical optimization tools, you can make (and often automate) complex decisions about which courses of action to take to achieve your business objectives.

All three types of analytics tools are widely used by organizations today. For example, as governments and the healthcare industry rush to vaccinate the global population against COVID-19, descriptive analytics tools can provide us with an accurate, real-time overview of current vaccination and infection rates; predictive analytics tools can forecast what would happen to infection rates if we administer more vaccines in specific locations at certain times; and prescriptive analytics 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 (by utilizing it to drive insights, predictions, decisions, and the best possible business outcomes), you should use all three types of analytics tools, ideally in an integrated manner.

You probably have a very firm grasp of descriptive and predictive analytics tools, but perhaps are not that familiar with prescriptive analytics in general and mathematical optimization (the primary prescriptive analytics tool) in particular.

In this article, I’ll briefly explain how you can get started using mathematical optimization and provide some examples of how this prescriptive analytics technology can be combined with machine learning to deliver business benefits across various industries.

Learning to Leverage Mathematical Optimization at Scale

Chances are that you, like most data scientists and IT professionals, already have some experience using mathematical optimization – most likely in Excel.

Like a Swiss Army Knife, Excel provides 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 get your get your feet wet with these analytics tools and perform simple tasks, this software’s capabilities are quite limited as it can’t handle large, multi-dimensional data sets or problems of significant complexity.

If you want use mathematical optimization or other sophisticated analytics tools at scale, you need a more specialized and robust tool for the job.

When it comes to mathematical optimization, there’s a wide array of commercial mathematical optimization computational and modeling tools on the market, many of which interface with many of the popular programming languages that data scientists are accustomed to such as Python, MATLAB, and R.

You can use your programming language of choice to build mathematical optimization models and applications – just like you do with machine learning.  

Of course, it will take some time and effort to learn to write code for mathematical optimization, but in the end it will pay off, as you will be able to utilize this potent prescriptive analytics technology – on its own or in combination with machine learning – to automatically generate solutions to your most critical and challenging business problems and make optimal decisions.

Making an Impact Across Industries

Mathematical optimization and machine learning have proved to be a dynamic duo, and companies across many different industries have used these two analytics technologies together to address a wide range of real-world business problems and achieve greater productivity and profitability.

Here are just a few examples of how this combination of mathematical optimization and machine learning is delivering major busines value in various industry verticals:

  • Retail: Leading retailers utilize machine learning to forecast demand for specific products, in certain locations, at given 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 firms rely on machine learning and mathematical optimization to determine the right allocation of their investment portfolios. With machine learning, they forecast 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 those predictions as well as the latest market movements and individual investment objectives and preferences), thereby maximizing risk-adjusted returns and reducing risk.
  • Online advertising: Internet search engine giants leverage machine learning to predict which products and services individuals will be interested in (based on their prior search history and other factors), and then utilize mathematical optimization to figure out which online advertisements to show individual users at specific times and how much to charge advertisers (in order to maximize revenues).
  • Electric power: As the electric power sector shifts from being dependent on fossil fuels to renewable resources such solar and wind, governments and industry players need to make high-stakes decisions on strategic investments in network infrastructure and resources. These organizations use machine learning to predict future electric power demand and capacity needs, and 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 a similar fashion to accurately assess long-term demand and capacity requirements and then make optimal strategic investment decisions.

Adding Mathematical Optimization to Your Data Science Toolbox

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 (on its own and in combination with machine learning), across various industries.

If you are interested in adding mathematical optimization to your toolbox, you can get started by exploring and experimenting with mathematical optimization in Excel. Then – when you are ready to experience the full power of this technology – you can move on to industrial-strength mathematical optimization tools that will enable you to tackle problems that are huge in terms of complexity, scale, and significance.

If you want to unlock the true value of your data (by using it to not only derive insights and predictions, but also to drive optimal decision making), then you need mathematical optimization – along with machine learning and other analytics technologies – in your toolset. 

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