Journal article
Three methods for robust grading
European journal of operational research, Vol.272(1), pp.364-371
01/01/2019
DOI: 10.1016/j.ejor.2018.06.019
Abstract
•Evaluating student performance is fraught with uncertainty.•We present three algorithms for assigning final grades that consider uncertainty.•We discuss and illustrate each method on an anonymized class of students.
We propose three strategies by which a professor of a university course can assign final letter grades taking 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 overall 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.
Details
- Title: Subtitle
- Three methods for robust grading
- Creators
- Samuel Burer - S346 Pappajohn Business Building Department of Management Sciences, Iowa City, IA 52242-1994United StatesVeronica Piccialli - Dipartimento di Ingegneria Civile e Ingegneria Informatica Università degli Studi di Roma ”Tor Vergata” via del Politecnico, 1 00133 Roma, Italy
- Resource Type
- Journal article
- Publication Details
- European journal of operational research, Vol.272(1), pp.364-371
- Publisher
- Elsevier B.V
- DOI
- 10.1016/j.ejor.2018.06.019
- ISSN
- 0377-2217
- eISSN
- 1872-6860
- Language
- English
- Date published
- 01/01/2019
- Academic Unit
- Business Analytics
- Record Identifier
- 9984083260902771
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