“Usually, if you’re lucky, someone shows up and says, ‘I have a problem, and I think you can help me,'” said Dr. Josef Kallrath in his Economics and Business seminar on modeling and solving real-world optimization problems. Kallrath works for the Scientific Computing division of BASF, a chemical company, and handles optimization problems on a daily basis.
According to Kallrath, “Real world optimization comes up in a variety of industries” and the basic process for modeling and solving these problems can be applied to all industries. “Most of the problem is not what the customer tells you in the beginning,” joked Kallrath.
By structuring the problem into specific wording and variables, it can easily be turned into mathematical language. By combining data, variables, and situational constraints with experience and know-how, those solving the problem “have this melting pot that produces a wonder drink.”
After turning the problem into mathematical language, an appropriate solver can be selected and used, often a computer-based modeling system. The results can then be interpreted and applied to the original structured problem.
As Kallrath pointed out, “Real-world problems are often very complex and multi-faceted.” For these kinds of problems, Kallrath often uses tailor-made methods or a polylithic approach, which involves stringing together multiple monolithic modeling systems.
Although the polylithic approach is designed to beat the size and complexity of a problem, it requires more experience and a dose of creativity. Kallrath warned this method should be handled with care, noting one “can kill a project easily by over-doing the details.”
From his point of view as an industry employee, Kallrath proposed a triangle of industry, science, and education with respect to optimization problems. Industry was at the peak, the source of real-world optimization problems, and at the base were science, which develops solutions, and education, which prepares students to solve problems.
Kallrath noted a flaw in this pyramid, namely that education normally produces students with textbook knowledge who work for grades, not for understanding. He recommended that modeling be part of curriculum and that students get involved in solving challenging real-world problems early so that the triangle would be more aligned.