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 MATHEMATICS IN INDUSTRY 2012

The Role of Mathematical Sciences in Industry

Trends and Case Studies

In this section of the report, we give a broad but not exhaustive survey of the business applications of mathematics. We hope that the 18 case studies presented below will provide some answers to students who want to know what mathematics is used for “in the real world.” Most of the case studies are applications we heard about on our site visits, supplemented by published articles.

2.1 Business Analytics

The software industry is making a big bet that the data-driven decision making … is the wave of the future. The drive to help companies find meaningful patterns in the data that engulfs them has created a fast-growing industry in what is known as “business intelligence” or “analytics” software and services. Major technology companies—IBM, Oracle, SAP, and Microsoft—have collectively spent more than $25 billion buying up specialist companies in the field.
 [Lohr, 2011-a]
“Business analytics” has become a new catchall phrase that includes well-established fields of applied mathematics such as operations research and management science. At the same time, however, the term also has a flavor of something new: the application of the immense databases that are becoming more and more readily available to business executives.
Mathematical approaches to logistics, warehousing, and facility location have been practiced at least since the 1950s. Early results in optimization by George Dantzig, William Karush, Harold Kuhn, and Albert Tucker were encouraged and utilized by the US Air Force and the US Office of Naval Research for their logistics programs. These optimization techniques, such as linear programming and its variations, are still highly relevant to industry today.
The new opportunity, both for businesses and for students hoping to enter industry, lies in the development of algorithms and techniques to handle large amounts of structured and unstructured data at low cost. Corporations are adopting business intelligence (i.e., data) and analytics (i.e., quantitative methods) across the enterprise, including such areas as marketing, human resources, finance, supply chain management, facility location, risk management, and product and process design.
Case Study 1: Predictive Analytics
In 2009 and 2010, IBM helped the New York State Division of Taxation and Finance (DTF) install a new predictive analytics system, modeled in part on IBM’s successful chess-playing program Deep Blue and its Jeopardy!-playing engine, Watson. The Tax Collection Optimization Solution (TACOS) collects a variety of data, including actions by the tax bureau (e.g., phone calls, visits, warrants, levies, and seizure of assets) and taxpayer responses to the actions (e.g., payments, filing protests, and declaration of bankruptcy). The actions may be subject to certain constraints, such as limitations on the manpower or departmental budget for a calling center. The model also includes dependencies between the actions. TACOS predicts the outcome of various collection strategies, such as the timing of phone calls and visits. The mathematical technique used is called a Markov decision process, which associates to each taxpayer a current state and predicts the likely reward for a given action, given the taxpayer’s state. The output is a plan or strategy that maximizes the department’s expected return not just from an individual taxpayer, but from the entire taxpaying population.
In 2009 and 2010, TACOS enabled the DTF to increase its revenue by $83 million (an 8% increase) with no increase in expenses. The results included a 22% increase in the dollars collected per warrant (or tax lien), an 11% increase in dollars collected per levy (or garnishment), and a 9.3% reduction in the time it took cases to be assigned to a field office, [Apte, 2011]. Similar methods, though different in detail, could clearly be applied by other businesses in areas like collections and accounts receivable.
Case Study 2: Image Analysis and Data Mining
SAIC is a company that develops intelligence, surveillance, and reconnaissance (ISR) systems for military applications. These automated systems have been heavily exploited during the war in Afghanistan: in 2009, unmanned aerial vehicles (UAV) captured 24 years of full-motion video, and in 2011 they were expected to capture thirty times that amount.
This poses an obvious problem: How can the information in the videos be organized in a useful way? Clearly the army cannot deploy thousands of soldiers in front of computer screens to watch all of those years of video. Even if they could, humans are fallible and easily fatigued. In hours of surveillance video it is easy to miss the one moment when something isn’t right—say, a car that has previously been associated with bomb deliveries drives up to a particular house.
SAIC developed a “metadata” system called AIMES that is designed to alert humans to the possible needles in the haystack of data. First, AIMES processes the video to compensate for the motion of the UAV—itself an interesting mathematical challenge. Then it searches for objects in the field of vision and stores them in a searchable database. It also “fuses” other kinds of data with the video data—for example, if the operators of the UAV say, “Zoom in on that truck!” the program knows that the object in the field of view is a truck and it may be of interest. Finally, AIMES is portable enough to be deployed in the field; it requires only a server and two or three monitors. See [“SAIC AIMES’ 2010].
While stateside industry may not have quite as many concerns about terrorists or roadside bombs, audio and video surveillance are very important for the security of factories or other buildings. Cameras and microphones can be used for other purposes as well; for example, a microphone might be able to tell when a machine isn’t working right before human operators can.  Surveillance devices can also help first responders locate victims of a fire or an accident. See [“SAIC Superhero Hearing” 2010].
Case Study 3: Operations Research
In 2002, Virginia Concrete, the seventh-largest concrete company in the nation, began using optimization software to schedule deliveries for its drivers. The company owns 120 trucks, which had been assigned to 10 concrete plants. A significant constraint is that a cement truck has roughly two hours to deliver its load before it starts hardening inside the truck. Also, the construction business is very unpredictable; typically, 95 percent of a company’s orders will be changed in the course of a day.
Virginia Concrete brought in mathematicians from George Mason University and Decisive Analytics Corporation to develop tools to automate truck dispatching. Among other changes, the mathematicians found that the company could improve delivery times significantly by moving away from the model in which individual trucks were assigned to a “home” plant. Instead, they recommended that trucks should be able to go to whichever plant is closest. Also, in overnight planning it turned out to be useful to include “phantom” trucks, representing orders that were likely to be canceled. If the order was not canceled, it could be reassigned to a real truck.
For testing purposes the company used the software to make all of the scheduling decisions; however, since system’s installation, dispatchers have been allowed to override the computer. The system has enabled Virginia Concrete to increase the amount of concrete delivered per driver by 26%. [Cipra 2004].

2.2 Mathematical Finance

…there is likely to be less emphasis on exotic derivatives and more trading will take place on exchanges.
In the future, models will have to have realistic dynamics, consistent with observation. Control of execution costs will also be critical, and for that, a good understanding of market microstructure and trade data will be essential. [From interviews.]
Quantitative methods in finance got a black eye from the credit crisis of 2007 and 2008, which in many circles was interpreted as a failure of quantitative models to account for dependencies in market data. Risk models assumed that real estate defaults in, say, Miami and Las Vegas were independent of one another; or at least that the correlations were small. But in a panic situation, all of the correlations went to one.
However, in the fallout of the crisis and subsequent recession, financial managers learned some very worthwhile lessons. They have learned that mathematical models are not just plug-and-play; you have to seriously examine the assumptions behind them. The failure of certain simplistic models does not mean all mathematical models are bad; it means that the models have to become more realistic. Above all, it is important for students to realize that the financial industry is not fleeing from quantitative analysis. Mathematicians and applied mathematicians are still in great demand; their skills will become even more valued as quantitative models become more sophisticated and as managers try to understand their limitations. It may be the case, though, that students’ mathematical skills should be backed up by a greater knowledge of the financial industry than was needed in the past.
Case Study 4: Algorithmic Trading
In 2009, Christian Hauff and Robert Almgren left Bank of America, the world’s top firm in algorithmic trading of stocks and derivatives, to form a new company called Quantitative Brokers. They saw an opportunity to apply the same principles of high-frequency trading to a class of assets that had not yet become highly automated: interest-rate futures.
Automated trading has become commonplace in the options market, in part because the tools of mathematical finance require it. Large banks want to hold their assets in a risk-neutral way, which allows them to make money (or at least avoid losing money) no matter which direction the market moves. In the early 1970s, Fischer Black and Myron Scholes discovered how to do this with a strategy called dynamic hedging, which requires constant small trades.
The main emphasis of Black and Scholes’ work was the pricing of options. It took another two decades for financial engineers to start taking into account the process of execution of a trade. There are many reasons for not executing a trade all at once. You may want to wait until trading partners, who are willing to give you a good price, arrive, or until the market moves toward your target price. If your trade represents a significant fraction of the market for an asset in a given day, you may want to move slowly to avoid unduly influencing the market price.
Trade execution is Quantitative Brokers’ main business. The company uses computer algorithms to plan a strategy for a path that leads from a client’s position at the beginning of the day to the desired position (say, buying X lots of Eurodollar futures at a price less than Y) at the end of the day. Each client has a certain degree of risk aversion, so the client’s utility function will be a linear combination of expected profit and expected risk. Quantitative Brokers’ STROBE algorithm finds the trajectory that optimizes the client’s utility function, and it generates an envelope around the optimum that summarizes the range of acceptable deviations. Mathematical tools include differential equations and the calculus of variations.
See [“Anatomy of an Algo” 2011.)
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