# Related work and grouper

# Introduction

In this vignette, we provide a brief, non-exhaustive overview of related work to assign students to projects, in an educational setting. Finally, we introduce our `grouper` package.

## Balancing staff workload and student preferences

One of the earlier papers found was by Anwar and Bahaj (2003). The goal of the educator in that paper was to assign students to two types of project: individual ones and group ones. For the individual projects, students were asked to rank their top four projects from a list of project briefs. Each student was then assigned to a project and a corresponding staff member.

The assignment was carried out using two models. In the first model, the objective was to minimise the total number of projects that each staff managed. In the second model, the feasible solutions from the first model were used to decide upon an assignment that maximised the number of students obtaining their first choice projects.

Compared to the models in `grouper`, the primary difference is in the objective function. In our case, we only work with the student preference; there is no need to balance staff workload since the projects are run within a single course.

For the group project, students were asked to rank their top 3 projects individually. They were then allocated groups that maximised their preferences. Compared to the model in our package, this approach does not allow for self-formed groups, or for larger projects that involve sub-groups.

## OptAssign

In many ways, the model described in Meyer (2009) is similar to ours. The objective function there maximises student preference for project topics. The model in the paper also discusses an extension whereby some groups of students can be favoured for particular topics. This is carried out through the inclusion of weights in the objective function. Another additional feature adds contstraints to ensure that students with certain skills are included in particular topics. For instance, a project topic on “Marketing surveys” may require at least two students with a statistics background in the group.

Overall, this model formulation is very similar to the one in our package. Again, one difference is in the affordance for self-formed groups, and for sub-groups in the project team.

## Students to elective courses

This paper Beroš and Meter (2015) deals with assignment of students to elective courses in Croatia. In short, the institution offers a fixed number of such courses. Every student must be enrolled in a pre-determined number of courses. Each student selects and ranks a certain number of electives. The integer programming solution that is derived here maximises the total student satisfaction, based on these rankings.

## Assigning students to groups based on traits

The master’s thesis from McGuirk (2020) describes a very complex integer linear programming model. The assignment was used to assign students to discussion groups at the University of New Hampshire chemistry department. The complete objective function can be written as:

\[\begin{eqnarray} \text{Minmise:}\; \text{preferences} + \text{sizes} + \text{single-trait} + \text{shared-trait} \end{eqnarray}\]

The first component, preferences, incorporates the ranking that put students put down for a group. The second component was used to control the overall group size. Note that in our formulation, this appears as a constraint. The third component arises as a result of the educators experience in teaching this course. They realised that if a student is the only one with a certain trait, e.g. gender, year-of-study, etc., that student would be disinclined to participate in discussions. This is a very interesting point! The final portion of the objective function applies a penalty if all students in the group share the same trait.

In our formulation, we have avoided using multi-objective functions for the most part. The reason for this decision is that it is very difficult to decide how each component should be weighted. It typically requires a further step of post-assignment sensitivity analysis.

Another similarity with our findings is the recommendation to use Gurobi over open source solvers.

## Student-to-project supervisor assignment

The next article we discuss is Ramotsisi, Kgomotso, and Seboni (2022). The formulation of this model was the result of a thorough investigation into the process by which students are assigned projects that are supervised by faculty members at the University of Botswana. However, similar to Anwar and Bahaj (2003), the objective function in this study aims to maximise the total workload of supervisors. It does not approach the problem solely from the angle of student preferences.

## Automated group assignments in academic setting

In the final work that we discuss, Bonfert-Taylor and Miller (2020) use a probabilistic weighted optimisation routine to perform the group assignment, based on survey input data. Questions in the survey pertain to scheduling, desired attributes of team members, and indications of whether a student may be isolated. For each question, a homogeneity score is computed using the answers from all members of a group. This score is summed over all questions to result in a “fitness” score for each group. A probabilistic hill-climbing algorithm is then used to maximise the average fitness score. Out of the papers discussed on this page, this is the only one that does not use an integer linear programming model.

# Introducing `grouper` package

`grouper` provides two distinct optimisation models, both of which are are formulated as integer linear programs.

The Preference-Based Assignment (PBA) model allows educators to assign student groups to topics primarily to maximise overall student preferences for those topics. The topics can be viewed as project titles. The model allows for repetitions of each project title. It is also possible to allow each project team to be comprised of multiple sub-groups in this formulation.

To execute the optimisation routine, an instructor needs to prepare:

1. A group composition table listing the member students within each self-formed group.
2. A preference matrix containing the preference that each self-formed group has for each topic.
3. A YAML file defining the remaining parameters of the model.

The Diversity-Based Assignment (DBA) model enables educators to assign students to groups and topics with the dual aims of maximising diversity (based on student attributes) within groups and balancing specific skill levels across different groups. These are formulated in a single objective function with weights assigned to each component.

To execute the DBA optimisation routine, the instructor needs to prepare:

1. A group composition table containing:
   - the member students within each self-formed group,
   - the demographics that will be used to compute pairwise dissimilarity between students, and
   - a numeric measure of each student’s skill.
2. A YAML file defining the remaining parameters of the model.

Refer to the remaining vignettes for more information about the model definition and application.

In our package, we use the `ompr` framework for optimisation, which means that you are free to use any solver. In our small examples, we demonstrate the package using the `gplk` solver. However, for more complicated problems, we highly recommend the `gurobi` solver. There is a free academic license for this tool. However, the `ROI.plugin.gurobi` and `gurobi` packages are not on CRAN. The following links will aid in installing the `gurobi` package:

- Installing the R package gurobi
- Guide to installing gurobi optimiser

The following github repository provides instructions on install the gurobi solver:

- Installing `ROI.plugin.gurobi`

# References

Anwar, Arif A, and AS Bahaj. 2003. “Student Project Allocation Using Integer Programming.” IEEE Transactions on Education 46 (3): 359–67.
Beroš, Ivo, and Joško Meter. 2015. “An Integer Programming Model for Assigning Students to Elective Courses.” Croatian Operational Research Review, 511–24.
Bonfert-Taylor, Petra, and Christopher Miller. 2020. “Improving Automated Group Assignments in an Academic Setting.” In 2020 ASEE Virtual Annual Conference Content Access.
McGuirk, Brendan. 2020. “Assigning Students to Groups Based on Preference and Traits.” Master’s thesis, University of New Hampshire.
Meyer, David. 2009. “OptAssign—a Web-Based Tool for Assigning Students to Groups.” Computers & Education 53 (4): 1104–19.
Ramotsisi, Johnson, Mompoloki Kgomotso, and Lone Seboni. 2022. “An Optimization Model for the Student-to-Project Supervisor Assignment Problem-the Case of an Engineering Department.” Journal of Optimization 2022 (1): 9415210.