Author Archives: Laura Albert

PhD development seminar: Time management and work-life balance

I am teaching a PhD development seminar for first year PhD students in industrial engineering and related disciplines. The purpose of this course is to prepare students for the dissertation research in industrial and systems engineering. The course helps set expectations, introduces campus resources to students, and creates a cohort of student to connect students with their peers.

Last week, a student panel composed of three senior PhD students discussed time management and work-life balance. The panelists were fantastic. Below are some highlights from the panel.

I am creating a series of blog posts featuring some of the classes from the semester. Those, along with previous PhD related posts, are tagged with the “PhD support” tag.

Other posts in this series:


Time management and work-life balance for (new) academics

I was on a panel about time management for the 2020 INFORMS New Faculty Colloquium (NFC). I recorded a video sharing my tips for time management with assistant professors in mind. I posted my video on YouTube below.

The live Q&A was fantastic, and I learned a lot from my fellow panelists Professors Tom Sharkey and Jonathan Helm. I want to give a big thank you to Professor Siqian Shen, who organized the NFC.


Presidential election forecasting: a case study

I am sharing several of the case studies I developed for my courses. This example is a spreadsheet model that forecasts outcomes of an election using data from the 2012 Presidential election.

Presidential Election Forecasting

There are a number of mathematical models for predicting who will win the Presidential Election. Many popular forecasting models use simulation to forecast the state-level outcomes based on state polls. The most sophisticated models (like 538) incorporate phenomena such as poll biases, economic data, and momentum. However, even the most sophisticated models are often modeled using spreadsheets.

For this case study, we will look at state-level poll data from the 2012 Presidential election when Barack Obama ran against Mitt Romney. The spreadsheet contains realistic polling numbers from before the election. Simulation is a useful tool for translating the uncertainty in the polls to potential election outcomes.  There are 538 electoral votes: whoever gets 270 or more votes wins.

Assumptions:

  1. Everyone votes for one of two candidates (i.e., no third party candidates – every vote that is not for Obama is for Romney).
  2. The proportion of votes that go to a candidate is normally distributed according to a known mean and standard deviation in every state. We will track Obama’s proportion of the votes since he was the incumbent in 2012.
  3. Whoever gets more than 50% of the votes in a state wins all of the state’s electoral votes. [Note: most but not all states do this].
  4. The votes cast in each state are independent, i.e., the outcome in one state does not affect the outcomes in another.

It is well known that the polls are biased, and that these biases are correlated. This means that there is dependence between state outcomes (lifting assumption #4 above). Let’s assume four of the key swing states have polling bias (Florida, Pennsylvania, Virginia, Wisconsin). A bias here means that the poll average for Obama is too high. Let’s consider biases of 0%, 0.5%, 1%, 1.5%, and 2%. For example, the mean fraction of votes for Obama in Wisconsin is 52%. This mean would change to 50% – 52% depending on the amount of bias.

Using the spreadsheet, simulate the proportion of votes in each state that are for Obama for these 5 scenarios. Run 200 iterations for each simulation. For each iteration, determine the number of electoral votes in each state that go to Obama and Romney and who won.

Outputs:

  1. The total number of electoral votes for Obama
  2. An indicator variable to capture whether Obama won the election.

Tasks:

(1) Create a figure showing the distribution of the total number of electoral votes that go to Obama. Report the probability that he gets 270 or more electoral votes.

(2) Paste the model outputs (the electoral vote average, min, max) and the probability that Obama wins for each of the five bias scenarios.

(3) What is the probability of a tie (exactly 269 votes)? 

Modeling questions to think about:

  1. Obama took 332 electoral votes compared to Romney’s 206. Do you think that this outcome was well-characterized in the model or was it an expected outcome?
  2. Look at the frequency plot of the number of electoral votes for Obama (choose any of the simulations). Why do some electoral vote totals like 307, 313, and 332 occur more frequently than the others?
  3. Why do you think a small bias in 4 states would disproportionately affect the election outcomes?
  4. How do you think the simplifying assumptions affected the model outputs?
  5. No model is perfect, but an imperfect model can still be useful. Do you think this simulation model was useful?

More reading from Punk Rock Operations Research:

How FiveThirtyEight’s forecasting model works: https://fivethirtyeight.com/features/how-fivethirtyeights-2020-presidential-forecast-works-and-whats-different-because-of-covid-19/

Files

  1. The assignment
  2. A shell spreadsheet with basic data to share with students
  3. A spreadsheet with the solutions

More teaching case studies


SIR models: A teaching case study to use in a course about probability models

This past summer, I created a few examples about COVID-19 to use in my course on probability models. I’ll post those materials here as I teach with them. Here is the first case study that introduces SIR models for modeling the spread of infectious disease. SIR models are widely used in epidemiology.

Infectious disease modeling: framing and modeling

Assume we have a constant population with N individuals. We can partition the population into three groups:

  1. Those who are susceptible to disease (S[n], i.e., not infected).
  2. Those who are infected (I[n])
  3. Those who are recovered (R[n]).

We assume a discrete time model, where we are interested in how the number of susceptible, infected, and recovered individuals vary according to time. Therefore, we start at time n=0 and index these values by n. The time between time n and n+1 could represent, say, a week.

A new strain of influenza or a novel coronavirus emerges. Susceptible individuals can become infected after exposure, and infected individuals can recover. Recovered individuals have immunity from reinfection.

New infecteds, result from contact between the susceptibles, and infecteds, with contact rate beta/N, which represents the proportion of contacts an infected individual has. Infecteds are cured at a rate (gamma) proportional to the number of infecteds, which become recovered.

Question #1: Come up with an expression to relate N to S[n], I[n], and R[n].

Question #2: Develop recursive expressions for S[n+1] based on S[n] and perhaps other variables.

Question #3: Then, do the same for I[n+1] and R[n+1].

Question #4: What are the boundary conditions?

Question #5: How would you estimate the total number who become infected by time n? 

Discussion questions:

  1. What other diseases fit this model?
  2. What are some possible ways to reduce the infection rate?
  3. What are some possible ways to increase the recovery rate?
  4. How does a vaccine effect this model?
  5. There is an interruption in the production of the vaccine, and your state will only receive 20% of the vaccines that you need before influenza season begins. Vaccines will slowly be released after this level. What are some criteria we could use to decide how to distribute these vaccines? What else can you do?

The second part performs computation in a spreadsheet. The assignment is here. We use the CDC 2004-5 data from a population of 157,759 samples taken from individuals with flu-like symptoms and 3 initial infections. Let n=0 represent the last week in September, the beginning of influenza season. Then, we compute these numbers in a spreadsheet to see how the disease may evolve. Next, we fit the model parameters (beta and gamma) using data that was collected by minimizing the sum squared error (SSE). Finally, we assess the impact of a vaccine. 

Files:

  1. The assignment.
  2. The solution.
  3. The assignment for the computational part.
  4. A google spreadsheet with the calculations (create a copy or download)

More examples


PhD development seminar: getting started with research

I am teaching a PhD development seminar for first year PhD students in industrial engineering and related disciplines. The purpose of this course is to prepare students for the dissertation research in industrial and systems engineering. The course helps set expectations, introduces campus resources to students, and creates a cohort of student to connect students with their peers.

I am creating a series of blog posts featuring some of the classes from the semester. Those, along with previous PhD related posts, are tagged with the “PhD support” tag.

Other posts in this series:


PhD development seminar: first steps in writing

I am teaching a PhD development seminar for first year PhD students in industrial engineering and related disciplines. The purpose of this course is to prepare students for the dissertation research in industrial and systems engineering. The course helps set expectations, introduces campus resources to students, and creates a cohort of student to connect students with their peers.






I am creating a series of blog posts featuring some of the classes from the semester. Those, along with previous PhD related posts, are tagged with the “PhD support” tag.

Other posts in this series:


Pooled testing: a teaching case study to use in a course about probability models

This summer, I created a few examples about COVID-19 to use in my course on probability models. I’ll post those materials here as I teach with them. Here is the first example.

Pooled testing to expand testing capacity

In July 2020, many states struggled to process COVID-19 tests quickly, with some states taking more than a week to process tests. Many statisticians have proposed pooled testing to process tests quicker and effectively expand testing capacity to up to four times the regular capacity. Pooled testing works when few tests come back positive.

Pooled testing came about in the 1940s, when government statisticians needed a more efficient way to screen World War II draftees for syphilis. “The Detection of Defective Members of Large Populations,” by R. Dorfman in 1943 contains a methodology for pooled testing.

Pooled testing works as follows:

  • Tests are grouped that pool n samples together, where each sample reflects an individual’s test sample.
  • Pooled test results are either positive or negative. They come back positive if at least 1 of the n individual samples are positive.
  • For tests that come back positive, tests are rerun individually with the unused portions of the original samples to see which individuals test positive, achieving the same results but faster. A total of n+1 tests are performed.
  • For tests that come back negative, no further testing is needed. We conclude all individuals are negative. One total test is performed, which reduces the overall tests.
  • When pooling is not used, one test per individual yields n tests for the group.

Consider a group of 40 asymptomatic individuals that are tested for COVID-19 in pooled groups of size . Let  denote the number of groups tested, and let  capture the number of groups that test positive (a random variable). We assume that an individual tests positive for COVID-19 with probability  (New York data from July 2020).

  • Express g as a function of n.
  • Express X and its distribution based on g, n, and q.
  • Let the random variable T denote the total number of tests run. Derive an expressive for T as a function of  as well as fixed parameters n and g.
  • Consider test groups of size n = 4, 5, 8, 10, 20. Which group size yields the fewest number of tests performed, on average? (Hint: Find E[T]).
  • How does your answer to the last question change if q = 0.02, 0.02, 0.075? (Note: Dane County had q = 0.02 and Wisconsin had q = 0.075 at the end of July 2020. At the time I wrote this in early October 2020, more than 20% of COVID tests are coming back positive in Wisconsin).

You can read more on the New York Times article that inspired this case study.

Files:

  1. The assignment.
  2. The solution.
  3. A google spreadsheet with the calculations (create a copy or download)

PhD development seminar: first steps in research

Last year, I developed a new PhD development seminar for first year PhD students in industrial engineering and related disciplines.

The purpose of this course is to prepare students for the dissertation research in industrial and systems engineering. The main focus is on initial steps and skills required to get started with research. Topics include understanding degree requirements, first steps in research, conducting a literature review, working with citation managers, time management, research ethics, data management, technical writing, and research organization. I invite a number of guest speakers to class sessions to introduce topics, connect students with campus resources, and answer questions.

By the end of the semester: each student should achieve these learning outcomes

  • Understand requirements for a PhD in Industrial Engineering or other PhD program.
  • Understand expectations for a dissertation and how to get started with research.
  • Understand what campus resources are available for writing, finding resources at the library, mental health, and others.
  • Understand research concepts such as research safety, research ethics, time management principles, setting expectations, meeting milestones, and plagiarism.

The course helps set expectations, introduces campus resources to students, and creates a cohort of student to connect students with their peers.

I am again offering the course in Fall 2020 but in a virtual format. So far, we are off to a great start. I will create a series of blog posts featuring some of the classes from the semester. Those, along with previous PhD related posts, are tagged with the “PhD support” tag.

First steps in research

This week’s class was about first steps in research, where two professors discussed how they helped new PhD students started on research. Professors Vicki Bier and Doug Wiegmann came to class and were wonderful. Some of their terrific advice was captured in my tweetstorm below.

Stay tuned for more blog posts about the course.


Resilient voting systems during the COVID-19 pandemic: A discrete event simulation approach

Holding a Presidential election during a pandemic is not simple, and election officials are considering new procedures to support elections and minimize COVID-19 transmission risks. I became award of these issues earlier this summer, when I had a fascinating conversation with Professor Barry Burden about queueing, location analysis, and Presidential elections. Professor Burden is a professor of Political Science at the University of Wisconsin-Madison, a founding director of the Elections Research Center, and an election expert.

I was intrigued by the relevance of location analysis and queueing theory in this important and timely problem in public sector critical infrastructure (elections are critical infrastructure). I looked into the issue further with Adam Schmidt, a PhD student in my lab. We created a detailed discrete event simulation model of in-person voting, and we analyzed it using a detailed study.

We present an executive summary of our paper below. Read the full paper here: https://doi.org/10.6084/m9.figshare.12985436.v1

 

Resilient voting systems during the COVID-19 pandemic:
A discrete event simulation approach

Adam Schmidt and Laura A. Albert
University of Wisconsin-Madison
Industrial and Systems Engineering
1513 University Avenue
Madison, Wisconsin 53706
laura@engr.wisc.edu
September 21, 2020

Executive Summary

The 2020 General Election will occur during a global outbreak of the COVID-19 virus. Planning for an election requires months of preparation to ensure that voting is effective, equitable, accessible, and that the risk from the COVID-19 virus to voters and poll workers is minimal. Preparing for the 2020 General Election is challenging given these multiple objectives and the time required to implement mitigating strategies.

The Spring 2020 Election and Presidential Preference Primary on April 7, 2020 in Wisconsin occurred during the statewide “Stay-at-home” order associated with the COVID-19 pandemic. This election was extraordinarily challenging for election officials, poll workers, and voters. The 2020 Wisconsin Spring Primary experienced a record-setting number of ballots cast by mail, and some polling locations experienced long waiting times caused by consolidated polling locations and longer-than-typical check-in and voting times due to increased social distancing and protective measures. A number of lawsuits followed the 2020 Wisconsin Spring Primary, highlighting the need for more robust planning for the 2020 General Election on November 3, 2020.

This paper studies how to design and operate in-person voting for the 2020 General Election. We consider and evaluate different design alternatives using discrete event simulation, since this methodology captures the key facets of how voters cast their votes and has been widely used in the scientific literature to model voting systems. Through a discrete event simulation analysis, we identify election design principles that are likely to have short wait times, have a low-risk of COVID-19 transmission for voters and poll workers, and can accommodate sanitation procedures and personal protective equipment (PPE).

We analyze a case study based on Milwaukee, Wisconsin data. The analysis considers different election conditions, including different levels of voter turnout, early voting participation, the number of check-in booths, and the polling location capacity to consider a range of operating conditions. Additionally, we evaluate the impact of COVID-19 protective measures on check-in and voting times. We consider several design choices for mitigating the risks of long wait times and the risks of the COVID-19 virus, including consolidating polling locations to a small number of locations, using an National Basketball Association (NBA) arena as an alternative polling location, and implementing a priority queue for voters who are at high-risk for severe illness from COVID-19.

As we look toward the General Election on November 3, 2020, we make the following observations based on the discrete event simulation results that consider a variety of voting conditions using the Milwaukee case study.

  1. Many polling locations may experience unprecedented waiting times, which can be caused by at least one of three main factors: 1) a high turnout for in-person voting on Election Day, 2) not having enough poll workers to staff an adequate number of check-in booths, 3) an increased time spent checking in, marking a ballot, and submitting a ballot due to personal protective equipment (PPE) usage and other protective measures taken to reduce COVID-19 transmission. Any one of these factors is enough to result in long wait times, and as a result, election officials must implement strategies to mitigate all three of these factors.
  2. The amount of time spent inside may be long enough for voters to acquire the COVID-19 virus. The risk to voters and poll workers from COVID-19 can be mitigated by adopting strategies to reduce voter wait times, especially for those who are at increased risk of severe illness from COVID-19, and encourage physical distancing through the placement and spacing of voting booths.
  3. Consolidating polling locations into a few large polling locations offers the potential to use fewer poll workers and decrease average voter wait times. However, the consolidated polling locations likely cannot support the large number of check-in booths required to maintain low voter wait times without creating confusion for voters and interfering with the socially distant placement of check-in and voting booths. As a result, consolidated polling locations require high levels of staffing and could result in long voter wait times.
  4. The NBA has offered the use of its basketball arenas as an alternative polling location for voters to use on Election Day as a resource to mitigate long voter wait times. An NBA arena introduces complexity into the voting process, since all voters have a choice between their standard polling location and the arena. This could create a mismatch between where voters choose to vote and where resources are allocated. As a result, some voters may face long wait times at both locations.

We recommend that entities overseeing elections make the following preparations for the 2020 General Election. Our recommendations have five main elements:

  1. More poll workers are required for the 2020 General Election than for previous presidential elections. Protective measures such as sanitation of voting booths and PPE usage to reduce COVID-19 transmission will lead to slightly longer times for voters to check-in and to fill out ballots, possibly causing unprecedented waiting times at many polling locations if in-person voter turnout on Election Day is high. We recommend having enough poll workers to staff one additional check-in booth per polling location (based on prior presidential elections or based on what election management toolkits recommend), to sanitize voting areas and to manage lines outside of polling locations.
  2. To reduce the transmission of COVID-19 to vulnerable populations during the voting process, election officials should consider the use of a priority queue, where voters who self-identify as being at high-risk for severe illness from COVID-19 (e.g., voters with compromised immune systems) can enter the front of the check-in queue.
  3. In-person voting on Election Day should occur at the standard polling locations instead of at consolidated polling locations. Consolidated polling locations require many check-in booths to ensure short voting queues, and doing so requires high staffing levels. Election officials should ensure that an adequate number of voting booths (based on prior presidential elections or based on what election management toolkits recommend) can be safely located within the voting area at the standard polling locations, placing booths outside if necessary.
  4. We do not recommend using sports arenas as supplementary polling locations for in-person voting on Election Day. Alternative polling locations introduce complexity and could create a mismatch between where voters choose to go and where resources are allocated, potentially leading to longer waiting times for many voters. This drawback can be avoided by instead allocating the would-be resources at the sports arena to the standard polling locations.
  5. The results emphasize the importance of high levels of early voting for preventing long voter queues (i.e., one half to three quarters of all votes being cast early). This can be achieved by expanding in-person early voting, in terms of both the timeframe and locations for early in-person early voting, adding new drop box locations for voters to deposit absentee ballots on or before Election Day, and educating voters on properly completing and submitting a mail-in absentee ballot.

The results are based on a detailed case study using data from Milwaukee, Wisconsin. It is worth noting that the discrete event simulation model reflects standard voting procedures used throughout the country and can be applied to other settings. Since the data from the Milwaukee case study are reflective of many other settings, the results, observations, and recommendations can be applied to voting precincts throughout Wisconsin and in other states that hold in-person voting on Election Day.

Resilient voting systems during the COVID-19 pandemic: A discrete event simulation approach

 


Optimization with impact: my journey in public sector operations research.

Today, I gave a keynote talk at the Advances in Data Science & Operations Research Virtual Conference, presented by Universidad Galileo in collaboration with INFORMSttt. It’s the first INFORMS conference made for Latino America that brings together the scientific community from the areas of operations research, business intelligence, and data science. Dr. Jorge Samayoa, the General Chair, and Dr. José Ramírez, the Executive Chair, were wonderful hosts.

My keynote talk was entitled “Optimization with impact: my journey in public sector operations research.” My slides are below.

 

References from my talk include:

Media Engagement

  1. L.A. Albert. 2020. Engaging the media: Telling our operations research stories to the public. SN Operations Research Forum 1 (14) https://doi.org/10.1007/s43069-020-00017-0
  2. Many of my media appearances are here.

Cyber-Security

  1. Zheng, K., Albert, L., Luedtke, J.R., Towle, E. 2019. A budgeted maximum multiple coverage model for cybersecurity planning and management, IISE Transactions 51(12), 1303-1317.
  2. Zheng, K., and Albert, L.A. A robust approach for mitigating risks in cyber supply chains, Risk Analysis 39(9), 2076-2092.
  3. Zheng, K., and Albert, L.A. Interdiction models for delaying adversarial attacks against critical information technology infrastructure. Naval Research Logistics 66(5), 411 – 429.
  4. Enayaty-Ahangar, F., Albert, L.A., DuBois, E. 2020. A surey of optimization models and methods for cyberinfrastructure security. To appear in IISE Transactions. https://doi.org/10.1080/24725854.2020.1781306

Aviation security

  1. McLay, L. A., S. H. Jacobson, and J. E. Kobza, 2006. A Multilevel Passenger Prescreening Problem for Aviation Security, Naval Research Logistics 53 (3), 183 – 197.
  2. Lee, A.J., A. McLay, and S.H. Jacobson, 2009. Designing Aviation Security Passenger Screening Systems using Nonlinear Control. SIAM Journal on Control and Optimization 48(4), 2085 – 2105.
  3. McLay, L. A., S. H. Jacobson, and A. G. Nikolaev, 2009. A Sequential Stochastic Passenger Screening Problem for Aviation Security, IIE Transactions 41(6), 575 – 591.
  4. McLay, L.A., S.H. Jacobson, A.J. Lee, 2010. Risk-Based Policies for Aviation Security Checkpoint ScreeningTransportation Science 44(3), 333-349.
  5. Albert, L.A., Nikolaev, A., Lee, A.J., Fletcher, K., and Jacobson, S.H., 2020. A Review of Risk-Based Security and Its Impact on TSA PreCheck, To appear in IISE Transactions.

Fire and Emergency Medical Services

  1. McLay, L.A., A Maximum Expected Covering Location Model with Two Types of Servers, IIE Transactions 41(8), 730 – 741.
  2. McLay, L.A. and M.E. Mayorga, 2010. Evaluating Emergency Medical Service Performance Measures. Health Care Management Science 13(2), 124 – 136.
  3. McLay, L.A., Mayorga, M.E., 2011. Evaluating the Impact of Performance Goals on Dispatching Decisions in Emergency Medical Service. IIE Transactions on Healthcare Service Engineering 1, 185 – 196.
  4. McLay, L.A., Moore, H. 2012. Hanover County Improves Its Response to Emergency Medical 911 Calls. Interfaces 42(4), 380-394.
  5. McLay, L.A., Mayorga, M.E., 2013.  A model for optimally dispatching ambulances to emergency calls with classification errors in patient priorities. IIE Transactions 45(1), 1—24.
  6. Toro-Diaz, H., Mayorga, M.E., Chanta, S., McLay, L.A., 2013. Joint location and dispatching decisions for Emergency Medical Services. Computers & Industrial Engineering 64(4), 917 – 928.
  7. Chanta, S., Mayorga, M. E., McLay, L. A., 2014. Improving Rural Emergency Services without Sacrificing Coverage: A Bi-Objective Covering Location Model for EMS Systems. Annals of Operations Research 221(1), 133 – 159.
  8. Grannan, B.C., Bastian, N., McLay, L.A. A Maximum Expected Covering Problem for Locating and Dispatching Two Classes of Military Medical Evacuation Air Assets. Operations Research Letters 9, 1511-1531.
  9. McLay, L.A., Mayorga, M.E., 2013. A dispatching model for server-to-customer systems that balances efficiency and equity. Manufacturing & Service Operations Management 15(2), 205 – 200.
  10. Ansari, S., McLay, L.A., Mayorga, M.E., 2015. A Maximum Expected Covering Problem for District Design, Transportation Science 51(1), 376 – 390.
  11. Ansari, S., Yoon, S., Albert, L. A., 2017. An approximate Hypercube model for public service systems with co-located servers and multiple response. Transportation Research Part E: Logistics and Transportation Review. 103, 143 – 157.
  12. Yoon, S., Albert, L. An Expected Coverage Model with a Cutoff Priority Queue. Health Care Management Science 21(4), 517 – 533. DOI: https://doi.org/10.1007/s10729-017-9409-3.
  13. Yoon, S., and Albert, L.A. A dynamic ambulance routing model with multiple response. To appear in Transportation Research Part E: Logistics and Transportation Review. https://doi.org/10.1016/j.tre.2019.11.001
  14. Yoon, S., Albert, L.A., and V.M. White 2020. A Scenario-Based Ambulance Location Model for Emergency Response with Two Types of Vehicles. To appear in ­Transportation Science.