How to ration scarce resources fairly

Michael Maiello | May 27, 2021

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Collections Operations Management

Among the many failures in America’s early COVID-19 disaster response, unprepared federal authorities mismanaged the allocation of emergency medical equipment as the pandemic mushroomed. Decisions by the Federal Emergency Management Agency “were inconsistent and lacked transparency, which frustrated state officials,” according to Yale’s Vahideh Manshadi, Chicago Booth’s Rad Niazadeh, and Yale PhD student Scott Rodilitz.

To be fair, the government stockpile of emergency medical and personal protective equipment was designed to help manage localized emergencies, not a pandemic. But rationing—during a pandemic or in other disaster-response settings—can be done fairly and efficiently, the researchers say.

A challenging time to keep things equitable

The researchers looked to April 2020, as COVID-19 infections spread across the US, to test their model. This series of maps illustrates when each state’s demand for emergency medical equipment had been projected to peak, which forced officials to calculate how much of the nation’s stockpile to deploy and how much to hold back from week to week.

When states were projected to hit peak demand for medical equipment in April 2020

First wave
Five states over April 1–7
Data visualization: A US map highlighting a group of states whose projected average demand had been 15,366 extra ICU beds, with a standard deviation of 3,287: Louisiana, Michigan, New Jersey, New York, and Vermont.

Second wave
Seven more states plus Washington, DC, over April 8–14
Data visualization: A US map highlighting a group of states whose projected average demand had been 2,193 extra ICU beds, with a standard deviation of 710: Alaska, Connecticut, Delaware, Maine, Massachusetts, New Hampshire, Washington, and the District of Columbia.

Third wave
Another 17 states over April 15–21
Data visualization: A US map highlighting a group of states whose projected average demand had been 9,719 extra ICU beds, with a standard deviation of 3,600: Alabama, Colorado, Georgia, Illinois, Indiana, Minnesota, Mississippi, Nebraska, Nevada, New Mexico, North Dakota, Ohio, Oklahoma, Pennsylvania, Rhode Island, Tennessee, and Utah.

Remaining 20 states after April 21
Data visualization: A US map highlighting a group of states whose projected average demand had been 3,831 extra ICU beds, with a standard deviation of 1,763: Arizona, Arkansas, California, Florida, Hawaii, Idaho, Iowa, Kansas, Kentucky, Maryland, Missouri, Montana, North Carolina, Oregon, South Carolina, South Dakota, Texas, Virginia, West Virginia, Wisconsin, and Wyoming.

Manshadi et al., 2021

They developed a method they call projected proportional allocation that makes a good-faith effort to deploy public resources not only to alleviate current suffering but also to care for future victims who would be left out in a first-come, first-served system.

As the coronavirus started spreading from the early hot spots, government planners realized the disease would quickly go nationwide and had to decide how to allocate resources among communities already suffering and those next to become infected. Faced with global shortages of equipment, FEMA struggled to keep up, prioritizing deliveries to medical facilities in danger of running out within 72 hours, according to congressional testimony by administrator Peter Gaynor. That left some communities on their own as a FEMA stockpile of protective medical gear that would normally have lasted a year ran out in weeks. 

The researchers base their proportional allocation alternative on the theory of justice proposed by the late philosopher John Rawls, which defines fairness from the vantage point of a neutral observer. Accordingly, they aim to maximize the well-being of the worst-off communities. The goal is to balance equitability and efficiency, plus to be simple and transparent, two qualities that are particularly important for public policy, they say. In order to achieve this, their model takes the complicated correlation structure of future demands into consideration when making allocation recommendations for a community in need. It then relies on a straightforward statistical analysis of likely needs and outcomes, which tend to be difficult to predict with high precision in various communities during a pandemic such as COVID-19. 

Using April 1, 2020, projections by the Institute for Health Metrics and Evaluation at the University of Washington, the researchers split US states into four groups on the basis of when they were expected to hit peak demand for ICU beds. They then ran 10,000 simulations using their mathematical model for distributing medical and protective equipment. The output was a fill rate (FR) that determines what fraction of a community’s need can be met while maintaining enough of the emergency stockpile for future needs.

The researchers calculate that their model, which focuses on maximizing the FR across all communities, outperforms other rationing policies by as much as 33 percent when assessed using their metric for efficiency and fairness. A limited supply of crucial goods is a common problem in catastrophes such as natural disasters, and their approach can also be used in those settings. “Our framework lends itself to extensions such as considering generalized objectives and rationing multiple types of resources,” they write. “More broadly, it serves as a base model for theoretically studying sequential allocation problems with an objective beyond utility maximization.”