Three methods for robust grading

We propose three strategies by which a professor of a university course can assign final letter grades tak- ing into account the natural uncertainty in students’ individual assignment and final numerical grades. The first strategy formalizes a common technique that identifies large gaps in the final numerical grades. For the second and third strategies, we introduce the notion of a borderline student , that is, a student who is close to, but below, the breakpoint for the next highest letter grade. Using mixed-integer linear programming and a tailor-made branch-and-bound algorithm, we choose the letter-grade breakpoints to minimize the number of borderline students. In particular, the second strategy treats the uncertainty implicitly and minimizes the number of borderline students, while the third strategy uses a robust- optimization approach to minimize the maximum number of borderline students that could occur based on an explicit uncertainty set. We compare the three strategies on realistic instances and identify over- all trends as well as some interesting exceptions. While no strategy appears best in all cases, each can be computed in a reasonable amount of time for a moderately sized course. Moreover, they collectively provide the professor important insight into how uncertainty affects the assignment of final letter grades.