The PPE Matching Problem consists of optimally matching a set of requests, D, made by donors interested in donating Personal Protective Equipment (or PPE, such as masks, gowns, gloves, etc) with a set of requests, R, made by recipients interested in receiving PPE. Requests are characterized by a timestamp (date), a type and quantity of PPE to donate or request, and a donor or recipient id. The input of the problem also includes a matrix M of distances between donors and recipients. The objectives are multiple, and include maximizing the recipients' fill rate, minimizing the total shipping distance, minimizing the holding time of PPE, and minimizing the number of shipments of each donor.
During health crises like the Covid-19 pandemic, organizations such as GetUsPPE.org provide a platform that aims at connecting prospective donors of PPE to prospective recipients of PPE. Requests by donors and recipients are collected over time. Every delta days, the organization solves the PPE Matching Problem, in order to direct each donor to ship a certain quantity of PPE to a given recipient.
Our package provides an open-source framework for researchers interested in developing and testing methodologies to solve the PPE matching problem.
The user only needs to implement a function ppestrategy(D,R,M), which solves the PPE matching problem. Our testing framework evaluates the performance of that user-defined solution method on real-world requests received by GetUsPPE.org in the early months of the Covid-19 pandemic (April-July 2020).
In a virtual environment with Python 3.6+, ppe_match can be installed via pip
pip install ppe_match
from ppe_match import TestingFramework
from ppe_match import TestingFramework
# Initialize the testing framework with default parameters
s = TestingFramework()
# Run the testing procedure
s.run()
# Retrieve the decisions made throughout the simulation
s.get_decisions() # Pandas dataframe that can be stored
# Retrieve the performance metrics
s.get_metrics() # Pandas dataframe that can be stored
The last five metrics are the average holding time, the average number of shipments per donor, the average unit-miles, the average fill rate, and the average fill rate excluding zeros.
res = s.get_metrics()
res.tail(5)
By defining a weight for each of the five summary metrics, the user can easily obtain a single metric.
import numpy as np
# set weights of different objectives
avg_holding_time_weight = 1
avg_shipments_weight = 10
avg_unit_miles_weight = 1
fill_rate_weight = 100
fill_rate_0_weight = 100
weights = np.array([avg_holding_time_weight,avg_shipments_weight,avg_unit_miles_weight,fill_rate_weight,fill_rate_0_weight])
# retrieve the five metrics above
metric_values = res['value'].tail(5).values
# compute dot product
metric_values.dot(weights)
To test a new matching solution method, start by defining a function that takes as input the current date (date, a datetime object), the current donor and recipient requests (Dt and Rt), and the distance matrix between donors and recipients, M. Dt is a DataFrame with columns (don_id,date,ppe,qty), Rt is a DataFrame with columns (rec_id,date,ppe,qty), M is a DataFrame with columns (don_id,rec_id,distance). The function must return the DataFrame Xt of matching decisions (don_id, rec_id, ppe, qty).
For example, a proximity match strategy that matches each donor's request with the closest recipient's request is implemented as follows:
import pandas as pd
def proximity_match_strategy(date,Dt,Rt,M):
# prepare the result DataFrame (X^t)
Xt = pd.DataFrame(columns=['don_id','rec_id','ppe','qty'])
ppes_to_consider = set(Dt.ppe.unique())
ppes_to_consider = ppes_to_consider.intersection(set(Rt.ppe.unique()))
# for each ppe to consider, match each donor request with the closest recipient request
for ppe in ppes_to_consider:
donors_ppe = Dt[Dt.ppe == ppe].copy()
recipients_ppe = Rt[Rt.ppe == ppe].copy()
for _, drow in donors_ppe.iterrows():
if len(recipients_ppe) == 0:
break # if we don't have any more recipient with this ppe, consider the next ppe
# find the closest recipient to drow.don_id
dr = M[(M.don_id == drow.don_id)].merge(recipients_ppe,on='rec_id').sort_values('distance').iloc[0]
dqty = drow.qty # donor's qty
rqty = recipients_ppe.loc[recipients_ppe.rec_id == dr.rec_id,'qty'].values[0] #recipient's qty
qty = min(dqty,rqty) #qty to ship
if qty == 0:
logger.info('qty is zero')
if qty == rqty:
recipients_ppe = recipients_ppe[recipients_ppe.rec_id != dr.rec_id] # remove recipient
else:
recipients_ppe.loc[recipients_ppe.rec_id == dr.rec_id,'qty'] -= qty #update recipient's qty
Xt.loc[len(Xt),:] = [dr.don_id, dr.rec_id,ppe,qty]
return Xt
On the other hand, a first-come-first-matched (FCFM) strategy that matches the i-th donor's request with the i-th recipient's request is implemented as follows:
import pandas as pd
def FCFM_strategy(date,Dt,Rt,M):
# prepare the result DataFrame (X^t)
Xt = pd.DataFrame(columns=['don_id','rec_id','ppe','qty'])
# the ppe to consider are the intersection of the PPEs in the table of current donors Dt (D^t) and the table of current recipients Rt (R^t)
ppes_to_consider = set(Dt.ppe.unique())
ppes_to_consider = ppes_to_consider.intersection(set(Rt.ppe.unique()))
# for each ppe to consider, match the i-th donor request with the i-th recipient request
for ppe in ppes_to_consider:
donors_ppe = Dt[Dt.ppe == ppe]
recipients_ppe = Rt[Rt.ppe == ppe]
n = min(len(donors_ppe),len(recipients_ppe))
for i in range(n):
don = donors_ppe.iloc[i]
rec = recipients_ppe.iloc[i]
qty = min(don.qty,rec.qty)
# add
Xt.loc[len(Xt)] = [don.don_id,rec.rec_id,ppe,qty]
return Xt
Once you have implemented your own matching strategy (let us call it my_strategy), run the test on the GetUsPPE.org data set by passing the function to the TestingFramework constructor:
s = TestingFramework(strategy=my_strategy)
The ppe_match package contains the implementation of two strategies illustrated above: the first-come-first-matched strategy (strategies.FCFM_strategy) and the "proximity matching" strategy tested by Bala et al. (2021) (strategies.proximity_match_strategy).
Users interested in embedding our framework in a simulation procedure may be interested in generating random variations of our data set, in order to test their code on multiple data sets. To that end, the code below implements a "bootstrap" procedure that randomly reorders the actual donor (recipient) requests by reassigning to each donor (recipient) request the timestamp of another random donor (recipient) request. In other words, in each bootstrap execution, the same recipients (and donors) make exactly the same requests as in the original data, but they make them in a different order every time. The function generate_data_for_bootstrap takes as input the donor and recipient requests and two random seeds for the reordering. It returns two new donor and recipient requests as pandas DataFrames.
import pandas as pd
def generate_data_for_bootstrap(donor_path,recipient_path,random_seed_donors,random_seed_recipients):
"""function that generates a donor table and a recipient table through resampling
:param donor_path: the path of the original donor table
:type date: str
:param recipient_path: the path of the original recipient table
:type date: str
:param random_seed_donors: random seed for the resampling of donor requests
:param random_seed_recipients: random seed for the resampling of recipient requests
:return: two DataFrames D2 and R2: the new donor requests and the new recipient requests
"""
D = pd.read_csv(donor_path,index_col=0)
R = pd.read_csv(recipient_path,index_col=0)
# donors
D = D.reset_index().drop(columns=['index'])
date = D.date.copy()
D2 = D.sample(frac=1,random_state=random_seed_donors).reset_index().drop(columns=['index'])
D2['date'] = date
# recipients
R = R.reset_index().drop(columns=['index'])
date = R.date.copy()
R2 = R.sample(frac=1,random_state=random_seed_recipients).reset_index().drop(columns=['index'])
R2['date'] = date
return D2,R2
The next code shows how to use the function above to run the testing procedure on randomly generated data.
import os
from ppe_match import TestingFramework
D2,R2 = generate_data_for_bootstrap('anon_donors.csv','anon_recipients.csv',1,2)
D2.to_csv('anon_donors_2.csv')
R2.to_csv('anon_recipients_2.csv')
# Initiate the testing framework with default parameters
s = TestingFramework(donor_path = os.path.join(os.getcwd(),'anon_donors_2.csv'),recipient_path=os.path.join(os.getcwd(),'anon_recipients_2.csv'))
# Run the testing procedure
s.run()
# Retrieve the decisions made throughout the simulation
s.get_decisions() # Pandas dataframe that can be stored
# Retrieve the performance metrics
s.get_metrics() # Pandas dataframe that can be stored
Path to the data set containing the donors' requests. See expected format in the data folder.
Expected input type: csv
Default: anon_donors.csv (which is the anonymized table of donors' requests from GetUsPPE.org)
Path to the data set containing the recipients' requests. See expected format in the data folder.
Expected input type: csv
Default: anon_recipients.csv (which is the anonymized table of recipients' requests from GetUsPPE.org)
Path to distance matrix between donors and recipients. See expected format in the data folder.
Expected input type: csv
Default: anon_distance_matrix.csv (which is the anonymized distance matrix from GetUsPPE.org)
User defined strategy to allocate PPE The function must have the following arguments:
ppestrategy(date, Dt,Rt,M)
where,
dateis a datetime with the current dateDtis a pandas.DataFrame object whose rows contain the current donor requestsRtis a pandas.DataFrame object whose rows contain the current recipient requestsMis a pandas.DataFrameobject that reports the distance between each donor and each recipient.
Default: proximity_match_strategy
pd.dataframe of decisions with columns (don_id, rec_id, ppe, qty). Each row represents the decision of shipping from donor don_id to recipient rec_id qty units of PPE of type ppe.
Day Interval set for framework to iterate over. Default: 7 (days)
Maximum quantity limit for donor to donate (helps filter out dummy entries or test entries) Default: 1000 (ppe units)
Boolean flag to save intermediate input objects (donors, recipients, and distances) and outputs (decisions) as csv Default: False
If set to True intermediate data will be saved for every iteration as follows:
output
├── 2020-04-09
├── decisions.csv
├── distance_matrix.csv
├── donors.csv
└── recipients.csv
├── 2020-04-16
├── decisions.csv
├── distance_matrix.csv
├── donors.csv
└── recipients.csv
├── ...
Sets the directory where the intermediate files and results will be saved Default: output/
Tests a strategy function by simulating the arrival of the requests given in the input data
Returns the list of all matching decisions made during the test.
Returns the performance metrics described in Section 4 of the research article. The metrics are reported at the PPE level, the recipient level, and the "overall" level (see Section 4). The "overall" metrics are at the bottom of the DataFrame.
Sets the logging level to DEBUG if True Default: False (Loglevel sets to WARN)