Dividing a large learning cohort into smaller teams for group work, discussion, or other activity is a common requirement in many learning contexts. It is easy to automate the formation of randomly assigned teams, but there can be rules, guidelines, and goals guiding the desired team composition to support learning objectives and other goals which can complicate manual and automated team creation.
The approach described in this document provides a technical framework and implementation to support specifying team formation objectives in a declarative fashion and can automatically generate teams based on those objectives. There is also a description of how to measure and evaluate the created teams with respect to the specified objectives.
The team formation objectives currently supported are team size and diversification and clustering around participant attributes. Diversification in this context is defined as the goal of having the distribution of a particular attribute value on each team reflect the distribution of that attribute value in the overall learning cohort. For example, if the overall learning cohort has 60% women and 40% men, a diversification goal on gender would attempt to achieve 60/40 female/male percentages on each team or, more specifically, to achieve the female/male participant counts that are closest to 60%/40% for the particular team size.
Clustering is defined as the goal of having all team members share a
particular attribute value. For example, if there is a job_function
attribute with values of Contributor, Manager, and Executive a
clustering goal would be to have each team contain participants with a
single value of the job_function attribute to facilitate sharing
of common experiences.
Cluster variables can also be multi-valued indicated by a list of
acceptable values for the participant. For example, if there is a
working_time variable with hour ranges 00-05, 05-10, 10-15,
15-20, and 20-24. A participant might have the values ["00-05", "20-24"] indicating that both those time ranges are acceptable.
In order to balance possibly conflicting objectives and goals of the team formation process we allow a weight to specified for each constraint to indicate the priority of the objective in relation to the others.
The problem of dividing participants into specified team sizes guided by diversity and clustering constraints can be stated as a Constraint Satisfaction Problem (CSP) with a set of variables with integer domains and constraints on the allowed combinations.
There is a very efficient constraint solver that uses a variety of constraint solving techniques from the Google Operational Research team called Google OR-Tools CP-SAT that we are using for this team assignment problem.
The remainder of the document describes how to frame the team formation problem in the CP-SAT constraint model to be solved by the CP-SAT solver.
The input to the team formation process is a set of participants with
category-valued attributes, a target team size, and a set of
constraints. The specification of the constraints is done with a
dictionary with keys attribute names from the participants data frame as
keys, a type of diversify or cluster, and a numeric weight.
>>> from team_assignment import TeamAssignment
>>> import pandas as pd
>>> participants = pd.DataFrame(
columns=["id", "gender", "job_function", "working_time"],
data=[[8, "Male", "Manager", ["00-05", "20-24"]],
[9, "Male", "Executive", ["10-15", "15-20"]],
[10, "Female", "Executive", ["15-20"]],
[16, "Male", "Manager", ["15-20", "20-24"]],
[18, "Female", "Contributor", ["05-10", "10-15"]],
[20, "Female", "Manager", ["15-20", "20-24"]],
[21, "Male", "Executive", ["15-20"]],
[29, "Male", "Contributor", ["05-10", "10-15"]],
[31, "Female", "Contributor", ["05-10"]]]
)
>>> constraints = pd.DataFrame(
columns=["attribute", "type", "weight"],
data=[["gender", "diversify", 1],
["job_function", "cluster", 1],
["working_time", "cluster", 1]]
)
>>> target_team_size = 3
>>> ta = TeamAssignment(participants, constraints, target_team_size)
>>> ta.solve()
>>> ta.participants.sort_values("team_num")
id gender job_function working_time team_num
4 18 Female Contributor [05-10, 10-15] 0
7 29 Male Contributor [05-10, 10-15] 0
8 31 Female Contributor [05-10] 0
0 8 Male Manager [00-05, 20-24] 1
3 16 Male Manager [15-20, 20-24] 1
5 20 Female Manager [15-20, 20-24] 1
1 9 Male Executive [10-15, 15-20] 2
2 10 Female Executive [15-20] 2
6 21 Male Executive [15-20] 2
>>> ta.evaluate_teams()
team_num team_size attr_name type missed
0 0 3 gender diversify 1
1 0 3 job_function cluster 0
2 0 3 working_time cluster 0
3 1 3 gender diversify 0
4 1 3 job_function cluster 0
5 1 3 working_time cluster 0
6 2 3 gender diversify 0
7 2 3 job_function cluster 0
8 2 3 working_time cluster 0
>>>For a detailed log of changes see CHANGELOG.md.