Try to give applicants one of their first-choice projects, by randomly assigning them a project, weighted by number of places remaining.
Each applicant was able to select more than one (assumed equal) first-choice project, and similarly more than one second-choice project.
import random
import numpy as np
import pandas as pd
# Show all the data
pd.options.display.max_rows = 200
pd.options.display.max_columns = 50
pd.options.display.max_colwidth = 1000
Load the applications and then filter out the ones that we don't want to allocate projects to (e.g. withdrawn, duplicates or withdrawn).
all_applicants = pd.read_excel('Applicants.xlsx')
all_applicants.shape
(109, 17)
For the purposes of this example, redact the actual data:
# Don't run this code in production
# ------------------------------------------------------------
# Redact personal data
columns_to_redact = [
'Name', 'Preferred Name', 'Organisation', 'Email address', 'Role', 'Research interests',
'Please confirm you can meet the following requirements', 'JASMIN username', 'GitHub username',
'Please state the limitations on your availability', 'Any other information',
]
for column in columns_to_redact:
all_applicants[column] = "*** redacted ***"
# Shorten project names
from itertools import chain
first_choices = all_applicants['First-choice projects of interest (tick all that apply)'].str.strip(';').str.split(';')
projects = dict.fromkeys(chain(*first_choices)) # Want to do set(chain(*first_choices)) but the order is not determinate
for replace_with, to_replace in enumerate(projects, start=1):
replace_with = f'Project {replace_with} title...'
all_applicants['First-choice projects of interest (tick all that apply)'] = (
all_applicants['First-choice projects of interest (tick all that apply)']
.str.replace(to_replace, replace_with, regex=False)
)
all_applicants['Second-choice projects of interest (tick all that apply)'] = (
all_applicants['Second-choice projects of interest (tick all that apply)']
.str.replace(to_replace, replace_with, regex=False)
)
# ------------------------------------------------------------
Now filter out:
#included = (
# all_applicants['Email address'].str.endswith('.ac.uk') |
# all_applicants['Email address'].str.endswith('@metoffice.gov.uk')
#)
included = all_applicants['Include'] == 'Yes'
applicants = all_applicants[included].copy()
applicants.shape
(90, 17)
applicants.head(2)
| Name | Preferred Name | Pronouns | Organisation | Email address | Role | Research interests | Include | First-choice projects of interest (tick all that apply) | Second-choice projects of interest (tick all that apply) | Please confirm you can meet the following requirements | Do you already have a JASMIN account? | JASMIN username | GitHub username | Happy for name/institution to go on website? | Please state the limitations on your availability | Any other information | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | *** redacted *** | *** redacted *** | He/Him | *** redacted *** | *** redacted *** | *** redacted *** | *** redacted *** | Yes | Project 1 title...;Project 2 title...; | Project 7 title...;Project 4 title...; | *** redacted *** | Yes | *** redacted *** | *** redacted *** | Yes | *** redacted *** | *** redacted *** |
| 1 | *** redacted *** | *** redacted *** | He/him | *** redacted *** | *** redacted *** | *** redacted *** | *** redacted *** | Yes | Project 1 title...; | Project 7 title...;Project 10 title...; | *** redacted *** | No - we will allocate you a temporary account | *** redacted *** | *** redacted *** | Yes | *** redacted *** | *** redacted *** |
We have given each project a number:
projects = [
"Project 1 title...",
"Project 2 title...",
"Project 3 title...",
"Project 4 title...",
"Project 5 title...",
"Project 6 title...",
"Project 7 title...",
"Project 8 title...",
"Project 9 title...",
"Project 10 title...",
"Project 11 title...",
]
The online form concatenates the choices, so split them into a list:
first_choices = applicants['First-choice projects of interest (tick all that apply)'].str.strip(';').str.split(';')
second_choices = applicants['Second-choice projects of interest (tick all that apply)'].str.strip(';').str.split(';')
first_choices.head(2)
0 [Project 1 title..., Project 2 title...] 1 [Project 1 title...] Name: First-choice projects of interest (tick all that apply), dtype: object
Given the number of projects and number of applicants, we might assume about 8 people per team:
len(applicants) / len(projects)
8.181818181818182
However we have some double-groups with a questions that can be split in two, so we will aim for a group size smaller than this.
Encapsulate the assignment alogirthm in a function.
In summary:
def assign_participants(ideal_group_sizes, random_state=1234):
random.seed(random_state)
assignments = pd.Series(
index=first_choices.index,
dtype=pd.CategoricalDtype(categories=projects),
)
# Start by trying to assign those people who only chose one first-choice project
for applicant, choices in first_choices.items():
if len(choices) == 1:
assignments.loc[applicant] = choices[0]
# Then randomly assign first choice projects, starting with those who chose two
# first-choice projects. Weight random choices by inverse exponential of number
# of existing assignments to that project
def get_weights(choices, assignments):
group_sizes = assignments.value_counts()
weights = [
# Penalise if greater than ideal group size
1 / np.exp(group_sizes[choice] - ideal_group_sizes[choice])
for choice in choices
]
# Normalise
return [weight / sum(weights) for weight in weights]
for applicant, choices in first_choices.items():
if len(choices) == 2:
choice = random.choices(choices, get_weights(choices, assignments))[0]
assignments.loc[applicant] = choice
# Now continue for applicants with any remaining number of first-choices
for applicant, choices in first_choices.items():
if len(choices) > 2:
choice = random.choices(choices, get_weights(choices, assignments))[0]
assignments.loc[applicant] = choice
return assignments
Manually tweak the ideal_group_sizes paramater until the final group sizes are about right:
assignments = assign_participants({
'Project 1 title...': 14,
'Project 2 title...': 13,
'Project 3 title...': 8,
'Project 4 title...': 12,
'Project 5 title...': 6,
'Project 6 title...': 8,
'Project 7 title...': 7,
'Project 8 title...': 6,
'Project 9 title...': 8,
'Project 10 title...': 7,
'Project 11 title...': 9,
})
assignments.value_counts()
Project 1 title... 13 Project 4 title... 13 Project 2 title... 12 Project 5 title... 7 Project 6 title... 7 Project 7 title... 7 Project 10 title... 7 Project 3 title... 6 Project 8 title... 6 Project 9 title... 6 Project 11 title... 6 dtype: int64
applicants['Assigned project'] = assignments
applicants.head(2)
| Name | Preferred Name | Pronouns | Organisation | Email address | Role | Research interests | Include | First-choice projects of interest (tick all that apply) | Second-choice projects of interest (tick all that apply) | Please confirm you can meet the following requirements | Do you already have a JASMIN account? | JASMIN username | GitHub username | Happy for name/institution to go on website? | Please state the limitations on your availability | Any other information | Assigned project | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | *** redacted *** | *** redacted *** | He/Him | *** redacted *** | *** redacted *** | *** redacted *** | *** redacted *** | Yes | Project 1 title...;Project 2 title...; | Project 7 title...;Project 4 title...; | *** redacted *** | Yes | *** redacted *** | *** redacted *** | Yes | *** redacted *** | *** redacted *** | Project 2 title... |
| 1 | *** redacted *** | *** redacted *** | He/him | *** redacted *** | *** redacted *** | *** redacted *** | *** redacted *** | Yes | Project 1 title...; | Project 7 title...;Project 10 title...; | *** redacted *** | No - we will allocate you a temporary account | *** redacted *** | *** redacted *** | Yes | *** redacted *** | *** redacted *** | Project 1 title... |