Putting together a baseball schedule is an exercise in the immeasurable. In theory, each schedule presents more possibilities than there are atoms in the universe.

The daunting act of schedule-making has historically been accomplished by a determined individual equipped with a plentiful supply of erasers and an even more plentiful supply of patience. Dave Rosenfield, the legendary Norfolk Tides executive responsible for more than four decades' worth of International League schedules, believes the secret ingredient is "brute force."

This old-school approach -- admirable and, until recently, absolutely necessary -- isn't the only one used in Minor League Baseball. In 2016, the New York-Penn, South Atlantic and Southern leagues are utilizing computer-generated schedules created by students and faculty in the applied math and statistics department of Johns Hopkins University's Whiting School of Engineering. The International League will follow suit in 2017 (thus concluding Rosenfield's epic run), and the Florida State League is considering the option.

Brute force is on the way out. The applied mathematics concept of combinatorial optimization -- finding an optimal object from a finite set of solutions -- is on the way in.

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Although the specifics vary according to the needs of each circuit, Minor League schedule-making is a universally complicated process. Factors that need to be taken into consideration include the 500-mile rule (teams may not travel by bus for more than 500 miles in a single trip), imbalanced divisional schedules, mandatory off days, minimum and maximum lengths for homestands and road trips and myriad requests from each team regarding days on which they need (or at least strongly want) to be home or away.

"The biggest challenge, as someone who has operated a team, is to put your self-interest aside and look at it as an aggregate," said Rick Murphy, executive vice president of the Tri-City ValleyCats and chairman of the New York-Penn League scheduling committee. "General managers and club operators are hired and evaluated based on the performance of the franchise, so it can be difficult to take a step back. From that standpoint, it inevitably becomes a challenge."

It's a challenge that has long interested Anton Dahbura, who spearheaded Johns Hopkins' baseball scheduling initiative via his role as executive director of the university's Information Security Institute.

"This goes back to the early 1990s, when I was talking to the traveling secretary for the Detroit Tigers, Bill Brown, at a Red Sox game," said Dahbura, a Johns Hopkins alumnus. "Out of nowhere, I commented to him that, 'Gee, it must be an interesting math problem to do a baseball schedule. He looked at me and said, 'Yeah, it must be.'"

Brown put Dahbura in touch with Major League Baseball.

"I worked on some alternative formats for [MLB]," Dahbura said. "They were interested in the potential of computer-generated schedules but recognized that it was going to be a long process for the technology to develop.

"In the '90s, it was maybe one step removed from human schedule-making, nowhere close to where we are today. There are a lot of tricks in modeling these problems mathematically. We have to be on the forefront of technology, and even five years ago we wouldn't be having this conversation. The technology, hardware, speed and sophistication of the software weren't there yet."

In 2010, Dahbura was part of an ownership group that bought the South Atlantic League's Hagerstown Suns. Two years later, he assumed his current role at Johns Hopkins. This combination of industry connections and university resources allowed him to approach league scheduling with a renewed vigor. He gave a seminar on the topic to individuals within the applied math department, which captured the attention of associate research professor Donniell Fishkind. Fishkind soon began recruiting high-performing students from his Introduction to Optimization course to work with him and Dahbura on an independent Minor League Baseball scheduling project, for which the students earn research credits.  

"There is typically a group of about 12 students working on different schedules -- undergrad and Masters, mostly applied math," Dahbura said. "The schedules are a byproduct of research in schedule optimization. We're using at this point different parameters, league preferences, team requests, all these constraints, and try our best to put together a schedule. ... Each league has its own personality, and I think the reason we've been successful is that we've learned the language of these leagues. We've grasped their preferences."

Dahbura calls the students' work a "translational opportunity" in that it could be directly applicable to a post-graduation commercial enterprise.

"Our students are stellar. Once we give them the basics, every single project results in something that improves the overall process," he said. "They are able to get a taste of the real world, dealing with deadlines, and they have a great story to tell to a potential employer."

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Noah Presler, an undergrad studying computer science, entrepreneurship and management, became part of the Minor League optimization team via Fishkind's Introduction to Optimization class. He said one of the things that attracted him to the project was its "real-life applications, since we interface with clients and build real products with an influence in the market."

After familiarizing himself with baseball industry terminology (which he said felt like "studying for the SATs again"), Presler began work on creating an algorithm that would determine optimal divisional alignment for a given league to minimize travel distance and maximize local rivalries. Presler transitioned from this project, still in the testing phase, to the 2017 South Atlantic League schedule.

"We start with a template, as that's the way we process the information that the league gives us -- what slots you can play in, the length of the season and reserved dates home or away," Presler said. "After that, we go through the constraints -- you can't have a homestand of a certain length, you have to play a team a certain number of times, you can't travel more than 500 miles. Once we have that, we take all of it and turn it into a giant math equation.

"This equation is on the order of magnitude of tens of thousands of math equations," he added. "We write algorithms to solve it, and the time it takes [for the computer] to solve it can be as long as five days. Then we put new constraints on it to make it more optimal. ... [This method] is definitely more flexible than doing it by hand. We can provide [the league] with many schedules, with different highlights and focuses. That's a huge advantage."

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This flexibility is important to the Short Season New York-Penn League, which in 2015 became the first in the Minors to use a Johns Hopkins-designed schedule.   

"We had a number of conversations with Tony [Dahbura] about the geographical challenges in the league," said Murphy, who is in his sixth year as chairman of the scheduling committee. "It was at one point a commuter league, and now we have a team in West Virginia. There are challenges we face with 14 teams in three divisions while needing to ensure that road trips are no greater than 500 miles. And the format we're working under, we play every team in the league every year, which also restricts flexibility. So you add that in, and then you have the operating preferences of each team in terms of what's going on in their market and what days are better than others."

He continued, "With Johns Hopkins, the computer allows us to look at multiple outcomes. Working manually, it would be taxing and unrealistic for a short-season league to explore alternate formats and models."

This exploration has extended beyond possibilities for the 2015 season as the league looked at potential long-term changes it could make to its current model.

"Hypothetically, let's just say the [league] wanted a schedule that was entirely four-game homestands and four-game road trips. What's the impact of that?" Murphy asked. "Or you could create a model where each team would only play the 10 teams it's closest to. ... The committee can see these various models and present them to [league president] Ben [Hayes] and our members, to see if they want to change or adopt the criteria."   

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In the meantime, Dahbura, Fishkind and their rotating cast of motivated students will continue to refine and improve their scheduling approach.

"One of our longer-range goals is to tie the schedule to a team's ability to generate revenue," Dahbura said. "We're making strides toward that goal and, as an intermediate step, we've done a pilot program giving teams the ability to look across the entirety of the schedule and place different weights on dates to be home or away. The computer incorporates that into the calculation."

In other words, the journey toward the optimal is far from over.  

"We're looking for needles in the haystack, the very small number of schedules that meet the needs and wishes of the league," Dahbura said. "This is a long-range research effort, taking scheduling to a whole new level, and it's hard to say what the future will bring."