Operations research approach solves farmland conundrum in Bavaria and other real-world problems.

By Oliver Bastert

Sure it looks picturesque, but solving land consolidation challenges can mean economic life or death for rural Bavarian farmers.

Picture an area of farmland from a bird’s eye view subdivided into different colored plots by ownership, a crazy patchwork. It might be a pretty picture, but when each hue represents a different farmer’s land, it’s a nightmare to economical farming. But it’s also a significant challenge to consolidate the colored portions into larger plots that would make each farmer’s land cheaper and easier to harvest. 

Or, imagine a pharmaceutical company trying to test a new drug at 100 different sites, where the patient populations are dramatically different in terms of age, weight and lifestyle. How can anyone accurately identify trends in the resulting medical outcomes?

These practical complexities are real-life problems . . . with real-life solutions. Last year, a team of researchers from Germany’s Technische Universität München, including Peter Gritzmann and Andreas Brieden, received an Excellence in Practice Award from the Association of European Operational Research Societies (EURO) for solving a farmland conundrum in Bavaria with a cluster optimization approach to help farmers more effectively manage land and allocate resources. 

Cluster optimization

Cluster optimization, or grouping like objects together, has hundreds of potential real-world applications, and for more than a decade professors Gritzmann and Brieden have been researching methods to extend the technology to a variety of applications. A generalization of this particular approach has been applied, for example, to matching up available airplanes with cargo shipments, a logistical nightmare. Determining the most profitable insurance premiums is another challenge where these techniques can be applied.

Car insurance premiums are assigned based on various factors, sometimes 20 or more. An auto insurance company easily may have millions of customers. In the past, an insurer would impose a rather simplistic segmentation on the existing data, in effect putting people into established categories or boxes. In reality, this is not an effective way to look at customers because a human observer assessing a mountain of data may miss similarities in risk profiles. Also, individuals that appear to belong in the same category at first glance may in reality have completely different risk profiles. New drivers and elderly drivers, starkly different to a human observer, are actually similarly situated because they tend to have accidents more than middle-aged, experienced drivers. 

Before (top) and after (bottom) applying cluster optimization to farmland in Bavaria to make each farmer's land cheaper and easier to harvest.

The traditional segmentation methods may also result in too few comparable risks, imposing several challenges to the analytic process. Two 18-year-old sons of billionaires who drive brand new red Ferraris in Los Angeles appear similar at first glance. But one is a party animal with a history of reckless behavior, while the other is an art student who spends free time bird watching. It does not make sense that they should both pay the same premium, nor that the risk for the entire category should be spread between only these two people. The solution is to find the balance – the right number and selection of segments homogeneous to their risk profile, each populated with a sufficient number of people. Cluster optimization helps insurance companies reasonably spread risk across groups by determining a profitable premium rate. This is the crucial decision point that determines whether the insurance company makes money.

By the same token, solving land consolidation challenges can mean economic life or death for rural regions. One of the problems is that farmers will often have multiple lots that are distributed, not adjacent and connected, which wastes their resources and also prohibits them from using large machinery to farm the land. There is huge economic value in consolidating farmers’ lots into larger, connected plots. The Bavarian farmland problem may sound like a straightforward one to solve, almost like assembling a jigsaw puzzle – but it isn’t. Farmers can’t solve the challenge themselves, and they often have conflicts with neighboring farmers going back hundreds of years that make simple land exchanges difficult. 

Looking for answers, the Bavarian Ministry of Nutrition, Agriculture and Forestry sought help from Technische Universität München. The problem was much more difficult than the officials thought. The number of possible reassignments of land is very large. As an example, any given area with, say, 300 plots could be reassigned in 10 to the 300th power different possible ways. That is a 10 with 300 zeros. Since brute force evaluation of so many possibilities is impossible, the complexity of the problem needs to be handled mathematically. The Munich researchers used extremely advanced mathematical methods to solve this geometry problem – turning small, scattered farmland plots into larger groupings. They started with a mixed-integer programming formulation that included multiple constraints, such that each farmer would have the overall same quality and amount of land as before. The challenging part to state as a constraint was that each farmer’s lots should be connected. The shape of the land mattered too – a square or round shape is more economical to work than a long string of lots. 

To solve this, the researchers allocated each farmer a center point and would then build the farmer’s fields around that, using a very rigid mathematical formulation to find the optimal solution. However, this is a real-world problem, so the mathematically pure solution was not always practical. The process required room to include additional constraints. What if a farmer wanted to hold on to a particular lot or refused to swap with a certain person? A “black box” just wouldn’t work. 

To make the solution feasible, the researchers went to Bavarian villagers and presented their work as a game. First, they would have the farmers exchange fields with buddies to consolidate their land. Then the researchers presented the optimal solution worked out in FICO Xpress Optimization Suite, using a visual interface that worked like a colored map. The optimal solution was never perfect, so the researchers factored in the complaints and requests for different swaps as new constraints, then optimized again. This iterative approach not only worked – the researchers and farmers thought it was fun!

Key Lesson

One key lesson learned from the Bavarian farmland experience is that stakeholders must use the analytics for the process to work. At first, the farmers volunteered their least profitable plots and failed to discuss either preferences or dislikes that would amount to deal breakers. By the end, the farmers were vocal, and, as they saw the reconfiguration coming together, they were increasingly willing to volunteer their parcels. “Playful analytics” was absolutely necessary to get buy-in and show that they created the solution; it wasn’t being imposed on them. 

The work done by the Technische Universität München researchers represents a mix of a good mathematical solution and a good practical solution. The potential cost savings for just the state of Bavaria are €150 million per year. The foundations of the research algorithms are deep geometric insights that lead to high-quality segmentation of big data. Now that the hard problem-solving was done, the researchers have built an application to offer others to solve similar problems. Various groups are using it already in Germany. In a project with the forestry administration, Dr. Steffen Borgwardt, a postdoctoral fellow in the research group and co-winner of the EEPA, has extended the land-consolidation method to woodland, solving additional challenges.

Optimization has always been a research-intensive endeavor. That’s why companies such as FICO work closely with leading academic institutions to push the envelope of innovation to create better tools and better solutions. Xpress, for example, was partly developed with contributions from academic users, including math and industrial engineering students. What began as a means to test and explore product development in an academic setting has turned into a formal problem-solving partnership program. Faculty and students use the software free of charge to tackle research challenges in real-world operations, often with significant results. In turn, the software developer incorporates academic innovation into better tools.

As in the case above, researchers don’t just use tools to solve problems. They create new methodologies and approaches that drive the field forward. This happened, for instance, in the late 1980s and early 1990s, when researchers were trying to create general purpose mixed-integer programming (MIP) solvers. In the 1960s and 1970s, scientists had created a number of problem-specific MIP solvers that could be used for discrete decisions – decisions that involved assets, resources or activities that could not be subdivided. For instance, in the Army you can optimize food distribution and, if needed, give a soldier half a sandwich. You cannot, however, give a driver half a car or optimize a route by telling the driver to go 50 percent in two directions at once.

To make optimization available to many more problems, it was necessary to create general purpose solvers. One breakthrough emerged from FICO’s collaboration with Institution Catholic University in Leuven, Belgium. Faculty and students at the university figured out how to solve for a broad set of problems. Their implementation of this concept into code was a true innovation industry-wide. (More detail on this research is at

What does an academic partnership between universities and commercial organizations look like?

It starts with companies that have a deep commitment to furthering research. It helps if many of the analytic staff came from research institutions or conducted university research. For example, FICO’s founders, engineer Bill Fair and mathematician Earl Isaac (the F and I stand for their last names, and the company used to be called Fair, Issac), met at the Stanford Research Institute before starting the company in 1956. 

FICO has three levels of collaboration for the academic partnership program based on Xpress. At the most basic level, FICO gives the software for free to approximately 300 academic partner institutions. The software is primarily given to operations research, industrial engineering, mathematics and economics departments. The second level involves developing teaching material with professors who use Xpress in their classes to educate students or conduct research. At the highest level, FICO collaborates with researchers on inventions that the company helps take to market. U.S. schools in the partner program include California Institute of Technology, University of Michigan, MIT, Penn State and the University of Texas. FICO depends heavily on these critical academic relationships and the resulting great ideas. The students have both free access to powerful mathematic tools and also the benefit of help in applying for research grants.

Collaboration is not just about the technology. The program and its many relationships make it easier for student data scientists to expand their work perspectives through studying abroad. Different academic cultures provide exposure to different interpretations and viewpoints. These different perspectives and sometimes different languages also highlight a key element in successful data science: communication. The challenge is not just in the data, algorithms and analytics, but the business or academic drivers of the project and the necessity of a deep understanding of the application of the results in the real world. That only comes with effective communications. 

Another benefit of the academic program is enabling deep research into difficult problems. FICO is not a farming company, but its technology can be used to solve a highly complex farming challenge. As the world continues to produce baffling volumes of data at a swift clip, the need to make sense of it will also increase. Cluster optimization will be a key part of the solution, and companies will rely on their academic partners to delve deep into complex problems and identify the winning formulas for success. ORMS

Oliver Bastert is FICO’s director of product management for optimization.