Applied and Industrial Mathematics

Now in its eighth year, VMI’s Applied and Industrial Mathematics (AIM) program has the goal of letting cadets practice their applied mathematics skills by helping a real-world business or organization.

This summer, five cadets got a chance to put their data analysis skills to use through that program. Two of them, Seth Gibson ’22 and Emily Gothard ’21, did their work for the Frontier Culture Museum in Staunton, Virginia, a state-supported entity that must raise 30 percent of its operating budget each year, primarily through sales of admission tickets, season passes, and merchandise in its gift shop.

Gothard explained that the first thing she and Gibson did was try to find which gift shop items were the biggest sellers so Frontier Culture Museum staff could allocate more funds towards purchasing those items.

“We looked at all of their vendors to see how much they’d spent … so we could categorize their budget sheet,” said Gothard. “We did that in order to create the budget, and then we broke it into 17 categories.”

It didn’t take the cadets long to figure out which items turned over quickly and which ones sat on the shelf. “They spent a lot of money on books, but they aren’t big sellers,” said Gibson. In the end, the cadets found that small items appealing to children, such as fudge, pencils, and stuffed animals, were the shop’s biggest sellers.

“We’ve had some surprises as to what kinds of things are selling and what kinds of things aren’t selling,” confirmed Megan Newman, executive director of the Frontier Culture Museum and a former VMI employee. Already, she noted, the work of Gibson and Gothard has led her to see that an expansion of the gift shop isn’t a wise fiscal move.

Newman said she’s very hopeful that the relationship between VMI and the Frontier Culture Museum will continue to grow. “We have project potential for cadets galore, whether it’s through AIM or [the Summer Undergraduate Research Institute],” said Newman.

While Gibson and Gothard were working in Staunton, David Carter ’19 undertook an AIM project on post. His project was to analyze data on alumni donors and giving patterns for the VMI Alumni Association.

“I’m looking at ways [the Alumni Association] can be more cost-effective and save money while at the same time have the same level of alumni interaction and involvement,” said Carter in mid-July.

To further that goal, Carter created ZIP Code maps of where alumni are living and where chapters of the VMI Alumni Association are present. That process revealed gaps, as there are some sections of the country where alumni are living but no chapters are present to organize events. Salt Lake City, Utah, is one example of such a chapter gap.

“The next goal is to create a list of all of the areas where there are alumni and no chapters, and then rank them based on what would probably be the best place to start building chapters,” said Carter, who will graduate in December and commission into the U.S. Navy.

Carter’s project will continue through the fall semester, but he’s hopeful that the work he’s begun will be kept going long after he’s graduated.

“Ideally, I’d like to create a standing program for the Alumni Association, so whenever they get new data, they could plug it in as an Excel document and it would just calculate a new list for them,” he stated.

Calling the impact of Carter’s work “tremendous,” Thom Brashears ’95, chief operating officer of the VMI Alumni Association, said that Carter had unearthed valuable information that would help the association do its job better.

“A lot of the things he’s finding we kind of expected, but there have been a few surprises,” noted Brashears. “If we want to improve, if we want to have a better strategic vision, we’ve got to be able to point to facts rather than just guess all of the time. This was a way to do that.”

Since its inception, AIM has been organized by Lt. Col. John David, associate professor of applied mathematics, who had run similar programs at three other colleges and universities before coming to VMI. Right away, he knew he wanted to make cadets aware that applied mathematics wasn’t just a buzz word.

“That was my goal when I became a tenure-track professor at VMI … I saw a huge need for getting cadets integrated with businesses,” David commented. “There’s a lot of great projects you can do that are very academically interesting. I want them to be able to solve concrete problems.”

In addition to Gibson, Gothard, and Carter, other cadets working on AIM projects this summer were Johnny Vesterman ’21 and Kaleb Tucker ’20. Vesterman worked with David and Col. Atin Basuchoudhary, professor of economics and business, to develop statistical applications for predicting civil conflict, while Tucker worked with Laser Tag Source, a company that rents laser tag equipment, to help them learn more about their client base.

 – By Mary Price

Cadet Robert “Chap” Michie ’15 spent his summer pouring over spreadsheets in an internship that was a far cry from his previous summer job as a bag boy at a golf course.

Michie, an applied mathematics major from Richmond, is analyzing the city of Lexington’s energy usage over the past six years, to help City Manager Jon Ellestad identify buildings that are “energy hogs.” By mid-July, he had taken six years’ worth of energy usage data on paper and put that information into spreadsheet form. By the end of the summer, he planned to have a visual model of the energy usage for each of the city’s 27 billable accounts.

“The hope is that [the city of Lexington] can take this information … and make the buildings more efficient,” said Michie.

Michie said he chose the project in part because of his interest in sustainability, which he defined as “the effort to meet the social, economic and environmental needs of present and future generations.”

Michie’s project is one of four this summer under the auspices of a new program called REMACS – Research Experiences in Mathematics and Computer Science. REMACS is the brainchild of Maj. John David, who participated in a similar program while he was conducting post-doctoral research at the College of Wooster in Ohio. “The idea of REMACs is to show the cadets what you can do with applied mathematics,” said David, an assistant professor in VMI’s Department of Mathematics and Computer Science. “They need to see math in a real-world setting.”

Part of the benefit of taking on a real-world math problem such as that provided by REMACS, said David, is for cadets to have the experience of reporting to a boss.

“You have a client, and the problem isn’t posed like it is in a textbook,” he commented.

Michie’s work is overseen by Maj. Geoff Cox, assistant professor of applied mathematics, and he’s also receiving assistance from Maj. Todd Pegg, energy manager with the VMI physical plant.

Pegg has been working to reduce VMI’s energy consumption ever since his arrival in 2007, and he’s been sharing with Michie the spreadsheets and 3-D modeling tools which have enabled him to track the Institute’s energy usage and identify areas for improvement. Pegg said his use of these tools has helped VMI to reduce its energy usage “substantially” over the past five years, even as the Institute has added new buildings at a rapid rate.

Pegg explained that utilities such as Dominion Virginia Power have a multitude of rate schedules, and having modeling data available on a spreadsheet allows a customer, such as VMI or the city of Lexington, to see how its bill might be affected by a change to a different rate.

Having a digital model available for such simulations “adds a level of micro-management to the city that VMI has, and the city currently lacks,” said Michie.

After graduation from VMI, Michie hopes to go to graduate school in economics or earn an MBA. “My really big goal is to work in the financial field and apply math skills to the world of economics and finance,” he said.

Cox, meanwhile, has enjoyed a chance to step away from the theory of math and plunge into its real-world applications. “A whole bunch of math just comes from the fact that things are proportional,” Cox said. “It’s nice to be able to take a real-life situation and be able to apply math to it.”

– By Mary Price

Some people love math.  They enjoy reading a complicated word problem, applying the numbers to it, and solving it.

Cadet Joe Bobay ’17 is one of those people.  The trick is finding problems that need solving.

That’s why VMI’s Applied and Industrial Mathematics program was a sure fit for Bobay.  The AIM programs pairs cadets with businesses that have a problem and gives the cadets five weeks to use their math skills to find a solution.

Laser Tag Source of Lynchburg rents laser tag equipment to companies in all 50 states. On the East Coast, the rentals are en route for only two days. West Coast rentals, though, are a whole different story, often tying up equipment for weeks rather than days.  But owner Mike Kirby thought the company was years away from opening a second location in the West – that is, until Bobay presented his findings.
The journey to that presentation turned out to be very different from the textbook problems Bobay has solved for his classes.

“Very often it’s a far more vague problem than students are used to; that’s a big thing that’s really good about this program – it’s not ‘do this integral,’” explained Maj. John David, assistant professor of applied mathematics and AIM coordinator.  “In a real job no one is ever going to ask you to compute this covariance matrix or calculate this integral; they’re going to ask you something that probably has a lot of math in it but they don’t know it has a lot of math.”

In the Laser Tag problem, Bobay found he had to consider time as well as geography.  Laser tag equipment is heavy and bulky, and the only way it can be shipped is by ground service.

“I just want to be able to present them with some data that says if you open a second location, this is how much you’ll be saving on shipping, this is how much of an increase you’ll have on product availability, then be able to tell them whether … it is cost-effective to open a new place or not.  Maybe they need to wait longer; maybe they need to not do it at all.”

Coming to that conclusion is a tremendous learning experience for Bobay.

“Their worry stops when they sign up.  Joe’s worry starts when the project begins,” said Maj. Ben Grannan, assistant professor of economics and business and Bobay’s academic adviser on the project.  

As lead pastor of Lynchburg Church of God, Kirby started Laser Tag Source almost by accident.  He had bought some laser tag equipment for a youth event; to make his money back afterward, he rented out the equipment, discovering a demand that inspired him to launch a website. Three years later he found himself on the cusp of a coast-to-coast business.

“Basically we could open another location today,” said Kirby, ready to explore Bobay’s suggestion. “Joe exceeded our exceptions, and I was very impressed with his work.  We were shocked to find out how much we could save by opening a second location.

Getting a solution to a problem is only part of the point for some participating companies. Many businesses, said David, appreciate being able to provide a learning opportunity in addition to paying less for an expensive service in the professional world.

“The program is like an academically oriented consulting firm,” David explained. Twenty-one cadets have participated as of June 2015, with some of those experiences leading to job offers.

“I would highly recommend this [AIM] program to any business owner who deals with large amounts of data – sales, marketing, shipping, etc.,” added Kirby. “I am more than pleased with this project.”

– Kelly Nye

In the world of academia, Shakespeare and math do not seem to have much in common. But in the real world this summer, the two seeming academic opposites walked hand in hand.

The Applied and Industrial Mathematics program at VMI made sure of that when cadet Ryan Poffenbarger ’16 was assigned the task of crunching numbers for the American Shakespeare Center in Staunton. Thanks to his research, the organization now has a better grasp on how to market its product.

“It’s going to help us target our marketing in a much better way rather than just making queries,” said Amy Wratchford, the managing director for the center. “We have all of this data we don’t have the time or expertise to dig into. They helped us make sense of all of our data.”

Through his analysis, Poffenbarger uncovered a number of trends at the center and the Blackfriars Playhouse, including the number of customers who attended multiple performances, the number who tended to return each year, and the number of seats that sold the most often. He presented this information to Wratchford in June.

“It was a lot of detective work,” Poffenbarger said. “They know the business part of the Shakespeare Center better than I do, so I was looking for things that would be related to making business decisions for them.”

“That’s the role of the analyst: look at the numbers, do the technical stuff, and help them make smart decisions,” said Maj. John David, assistant professor of applied mathematics and AIM coordinator. “They are ultimately going to make the decision about what to do. We just try to help them make fewer guesses.”

According to Maj. Geoff Cox, also an assistant professor of applied mathematics, who served as the cadet’s supervisor, the role of the data analyst is only to crunch the numbers, not make recommendations. 

“There is a lot of uncertainty,” Cox said. “You want to tell them, ‘This is what we found; here’s a possible interpretation.’ But there are many others.”

Poffenbarger’s project was one of three by cadets associated with AIM. Another was with an investment firm in Lexington, while the third was with a local manufacturer. The AIM program is a collaboration of the VMI Center for Undergraduate Research, the applied math department, and external clients.  AIM generates revenue from the client, which pays the cadet’s stipend, and VCUR supports the professor’s stipend via its Summer Undergraduate Research Institute.

Poffenbarger was the 17^th cadet to work with David over the last three years. He learned a great deal from the experience, and not just in math.

“The one thing I learned the most was programming,” said Poffenbarger, who noted that he often had to reformat the data sent to him from the Shakespeare Center. “I went from zero programming experience, aside from HTML, to writing what I thought were pretty complex solutions to a formatting problem.”

David became aware of the predicament at the Shakespeare Center while he was giving a presentation of his findings from an AIM project for the United Way. Wratchford happened to be in attendance, and she immediately began thinking of how the VMI program could help her outfit.

“She thought it was a really cool idea,” said David. “She was definitely excited about what quantitative thinking can do to make a place work better.”

And that is the purpose of AIM. So often, it is hard to visualize how higher math can be beneficial in real-world situations; AIM takes care of that.

“It’s about going out and getting real-world problems from government, business, [and] industry, [and] bringing them back to have our VMI cadets solve them,” said David.

“It’s a good contrast from the classroom,” added Cox.

Did VMI’s AIM program help? Wratchford seemed encouraged by the findings.

“We’ve been very pleased,” she said. “They [helped] us get our vision wrapped around our patron and donor database.”

And the AIM team proved that maybe Shakespeare and mathematics do belong together.

Cadet James Snyder ’13 didn’t have any trouble picking a topic for his Summer Undergraduate Research Institute project. After all, he’s an applied math major with a lifelong interest in sports – so why not delve into the use of statistics to predict the outcome of basketball games?

This summer, Snyder is working under the guidance of Maj. John David, assistant professor of applied mathematics, to take data from several seasons’ worth of NBA games and use that data to build a computer model which can predict the outcome of future games.

Snyder, a Georgia native and avid fan of the Atlanta Hawks, got interested in doing a sports-oriented summer research project when his friend Will Lucas ’14 did a similar project on baseball last summer. David, also a lifelong sports enthusiast, already had experience with predicting professional football games, and he’d overseen Lucas’ work, so he welcomed Snyder’s interest.

Snyder began by taking NBA statistics from six seasons. With 30 teams in the association, each playing 82 games per season, and 32 statistics available per team, Snyder found himself almost drowning in information.

“There are millions of data points,” Snyder commented. “We’re taking all that data and using it to make future predictions for the games.”

To check for accuracy, Snyder fed data from the 2004-2009 seasons into the computer and asked it to make predictions for the 2010 season.

So far, Snyder’s program has racked up an impressive accuracy rate of 72 to 73 percent – which puts him in a position to be competitive with or even outdo, popular websites that claim to be able to predict the outcomes of games.

“We’re on pace with those guys, and I’m pleased with that,” he said.

For Snyder, the summer project has been an ideal capstone to his time at VMI, which is rapidly coming to a close. “You get to do math and see the outcome of sports,” he said. “That’s fascinating to me. We’re doing some pretty complex math techniques, … and at the same time we get to play with basketball statistics.”

Snyder has already accepted a job with the Applied Physics Lab at Johns Hopkins University in Baltimore, Md., which has hired several VMI graduates over the past few years. There, he’ll be testing technology for submarines and other forms of undersea warfare. His work there will begin Aug. 12.

“I’m hoping to take some of the research I’ve done this summer and apply it on the military/government side of things,” said Snyder, who played center on the VMI football team during his cadetship.

And since he’ll be in the neighborhood, Snyder is planning to join David to give a presentation on math and sports at a meeting of three major mathematical organizations, to be held in Baltimore in January.

“The interest in using quantitative analysis in sports has really grown in the past 10 or 15 years,” said David, who enjoys informal games of pickup basketball with a group of professors and cadets.

He continued, “It’s a fascinatingly rich thing in math. It’s a rich area for machine learning and quantitative analysis and data mining. …It’s a wonderful training tool. I can trick [the cadets] into some of this stuff by using sports.”