Methods for assigning students to groups: a study of alternative objective functions
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#2002 Operational Research Society Ltd. All rights reserved. 0160-5682/02 $15.00 www.palgrave-journals.com/jors
Methods for assigning students to groups: a study of alternative objective functions KR Baker* and SG Powell Dartmouth College, Hanover, NH, USA This paper describes the problem of forming work groups. The motivating problem is often described as maximizing the diversity of members within groups, and also as minimizing the differences among groups. We review the formulations of this problem in the literature, paying particular attention to the different criteria that have been suggested. We compare the various criteria by solving a number of test problems using standard techniques and then examining the possibility that using one criterion will produce a result that is desirable on other criteria. Ultimately, we recommend a composite procedure for solving large versions of the group formation problem. Journal of the Operational Research Society (2002) 53, 397–404. DOI: 10.1057=palgrave=jors=26001307 Keywords: diversity; heuristic; algorithms
Introduction A number of academic programmes assign students to groups in a systematic fashion. Typically, the goal in this process is to spread certain traits throughout the class, not allowing them to cluster in a few groups. Stated another way, the goal is to create diverse groups, so that students will have the experience, and the challenge, of working with people unlike themselves. This paper describes research into procedures for forming diverse student groups. We attack the problem using both heuristic and optimizing methods. We extend previous work on this problem by elaborating different alternatives for the objective function, and we report the results of a computational study comparing several alternatives. Our results suggest that an objective function that counts the number of special attributes in each group and then sums the absolute deviations between pairs of groups performs best over a wide range of cases. However, as a practical matter, we recommend running at least six alternative heuristics and picking the best solution. We confronted the problem of creating diverse student groups at the Tuck School of Business, where there has been a long tradition of assigning students to class sections and to work groups. In the late 1990s, access to a new information system in the admissions department made it possible to obtain much of the requisite data automatically from a computerized database. Instead of using tedious manual
*Correspondence: KR Baker, The Amos Tuck School of Business Administration, Dartmouth College, Hanover, NH 03755-9002, USA. E-mail: [email protected]
techniques to create groups, the school turned to the use of computer-based algorithms. Two versions of the problem were solved: the first involved assigning the entering class of about 200 to four sections, and the second, within sections, involved assigning the 50 section members to ten study groups. Although the motivating application for our work is the assignment of students
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