Author: Edward Rothberg, PhD
Date: 2/26/2020

I have devoted the past 23 years of my professional life to the development of mathematical optimization technologies and, during that time, have witnessed how mathematical optimization has literally transformed numerous industries and touched countless areas and aspects of our everyday lives.

Indeed, mathematical optimization is everywhere in our modern world, and has a profound and positive impact on so many things – from the energy we use to the water we drink to the cars, trains, and airplanes we ride in and the products and services that we rely on.

Leading companies around the world and across a wide range of industries utilize mathematical optimization to solve their complex, real-world problems and make optimal business decisions that maximize their operational efficiency. For us as consumers, this – generally speaking – means that these companies can more consistently deliver better products and services, at a lower cost.

So – given that mathematical optimization is such an essential element of today’s world – why is it that so few people seem to truly grasp the power of mathematical optimization and its presence in so many parts of our daily lives?

I think the answer to this question lies in the fact that mathematical optimization applications are usually used to address highly complex, large-scale business problems – and are thus not as tangible or visible to most people as other AI technologies such as machine learning (which has many consumer-facing applications such as speech recognition and autonomous driving).

So I started wondering how I could illustrate the importance of mathematical optimization in our everyday lives – and realized that a good way to do this would be to imagine a world without mathematical optimization.

Indeed, as the old saying goes, “you don’t know what you’ve got till it’s gone” – and it is my hope that, by imagining a world without mathematical optimization, you can gain an appreciation of its true value in our world today.

In this series of blogs, I will highlight the impact of mathematical optimization on today’s business landscape and explain how various industries (and our lives) would be fundamentally changed if we didn’t have mathematical optimization technologies.



We have all experienced airline flight delays (which can be caused by a variety of factors including weather conditions, aircraft technical issues, and airport congestion), and everyone hates to wait for however long it takes (it’s usually a matter of minutes or hours) for their flight to finally take off.

In a world without mathematical optimization, however, a bad storm could cause your flight to be delayed for days or even weeks. Why would this be the case?

Without mathematical optimization, such a situation would wreak havoc on airline schedules, which involve a lot of moving pieces including aircraft, passengers, pilots, cabin crew, maintenance personnel, airport staff, luggage, and freight. If there’s a disruption that causes any one of these pieces not to be in the right place at the right time, that creates a hole in the schedule – which will have a disastrous, domino effect that reverberates throughout the entire operational network, throwing everything out of whack and triggering widespread delays. Using manual tools and techniques, it would take airlines days or weeks to plug all the holes in their schedules and get flight operations back on track.

With advanced planning and scheduling systems powered by mathematical optimization, however, airlines can automatically generate robust, resilient schedules that take into account various factors including demand forecasts, capacity requirements, and the likeliness of disruptions. When disruptions occur, airlines can use such systems to dynamically revise and reoptimize their schedules – so that they can make the best decisions on how to redeploy their resources to minimize delays and get flight operations running smoothly again as soon as possible.

So, the next time you are stuck at the airport for a few minutes or hours due to a flight delay, just think about how much worse your situation would be in a world without mathematical optimization.

This is, however, only one example of how mathematical optimization is utilized by companies in the aviation industry – there are numerous other applications. Indeed, mathematical optimization is used by companies across the aviation ecosystem – including airlines, airports, ground handlers, cargo carriers, and MRO providers – to improve their operational efficiency and on-time performance, and reduce costs.

Needless to say, global aviation operations as we know them today – which run with such great speed and precision and on such a global scale – would not be possible without mathematical optimization.



Let’s say you are thinking of building a house or constructing an addition to your house – you probably need to go out and purchase a fair amount of lumber. In today’s world, you can assume and expect that the wood you need will be available when you are ready to commence construction – in the right quantity and at a reasonable price.

In a world without mathematical optimization, however, you may have to put your construction plans on hold as there may be a shortage of lumber available on the market or a spike in prices for the commodity. Why would this happen?

In order to ensure that they are able to consistently meet consumer demand by delivering the right products to the market at the right times and at the right prices, lumber companies use mathematical optimization to create long-term planting and harvesting plans. Armed with these strategic plans – which cover a 20 to 30-year time horizon and take into account numerous factors including the amount of available land, the ages of trees on certain plots of land, inventory levels, demand levels, and expected prices – lumber producers can make optimal decisions on where, what, and when to plant and harvest. With mathematical optimization, these companies can attain the long-term visibility they need to prevent shortages, mitigate price fluctuations, and keep lumber supply and demand in balance over the long haul.

So, as you stand there admiring your newly-constructed dream house, remember that you may have not been able to build that house – at that time or at that cost – without mathematical optimization.

It’s important to note that this is just one example of how lumber producers and other companies in the forestry industry and related industries such as paper and pulp manufacturing use mathematical optimization.

Indeed, the breadth of mathematical optimization applications in today’s business world is enormous and ever-expanding. In this blog, we have just scratched the surface as aviation and forestry are merely two of over 40 industries that have been transformed by mathematical optimization.

In the next blogs in this series, we will take a look at other industries where mathematical optimization has had a profound impact, and see how these industries and our everyday lives would be dramatically different without mathematical optimization technologies.

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