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The success of Operation Warp Speed in delivering two effective Covid-19 vaccines in record time has stoked public optimism for an end to the pandemic. The difficult science has seemingly been done, and what remains is a simple supply chain problem: how to get shots into arms in the fairest and quickest way.

Although the logistical challenges are certainly solvable, there’s a significant gap between a fairness-based public policy and the most effective solution for the nation as a whole. The goal of prioritizing health care and other first-line workers is politically noble, and thus easy to defend. Practically, however, a holistic view of our goals — public health, restoration of public service, and economic reopening — suggest that a more opportunistic delivery strategy may ultimately save more lives.


For the past 30-plus years, my professional focus has been in decision optimization, the discipline of applying mathematical methods to the solution of problems that arise in the public and private sectors. It is part of the field of operations research, an outgrowth of an effort to engage science to solve difficult tactical and operational issues during World War II.

While the mathematics involved can be quite complex, deciding on a set of objectives — determining what makes one approach better than another — is often the greatest challenge of decision optimization.

The national rollout of vaccines for Covid-19 has sparked much discussion about the best strategy for prioritizing vaccine recipients. As with any decision optimization issue, it is useful to break the problem down into three components: constraints, decision variables, and objectives.


The simplest element to nail down is probably constraints. The vaccine supply is currently limited, and only a certain number of individuals can be vaccinated each day — these are clearly limiting constraints.

Decision variables define the prioritization policy, such as who to vaccinate, when, and whether to offer first doses to all before offering second doses to some. These aren’t easy questions to answer, but they aren’t beyond our capabilities.

The most difficult component to grapple with by far is the objective, meaning how we will define success. As with most complex problems, there won’t be a single objective, but several.

Unfortunately, multiple objectives frequently work against each other, making the determination of appropriate objectives a political rather than a mathematical question. In the case of Covid-19 vaccine distribution, the best example of this is the objective of fairness, the concept that giving priority for getting vaccinated to an individual or group must provide net positive benefit to the population as a whole.

At the extreme, the fairest solution might be to wait until 330 million doses of Covid-19 vaccines are available, deliver them en masse to the entire U.S. population, and repeat the process when an additional 330 million doses become available. Putting aside the practical absurdity of such an approach, it clearly ignores two important goals: minimizing death and serious illness, and allowing public institutions such as schools and businesses to reopen as soon as possible.

As with any multi-objective problem, the challenge is balancing multiple goals — fairness, minimization of sickness and death, and restoring public services and commerce. The relative values of these objectives are difficult social, political, and economic questions, which are all necessary inputs for a decision optimization model. Determining the goals and their relative values makes it possible to develop an objective, mathematically justifiable distribution strategy.

In the early days of Covid-19 vaccine availability, vaccine shortages and surpluses both exist. While the overall demand for vaccine exceeds the number of doses available, the initial distribution strategy has often resulted in substantial number of doses remaining “on the shelf” in various locations. In a conventional business environment, this is expected, and sometimes even encouraged. Companies keep more inventory than they expect to sell because exact demand patterns are unpredictable. The cost of maintaining additional inventory is weighed against the potential of lost sales due to items being out of stock.

The situation with Covid19 vaccine is quite different. Taken as a whole, the vaccine is essentially a single product with a demand that currently exceeds its availability. As such, any doses that remain “in inventory” for longer than absolutely required represent an unnecessary threat to public health and economic recovery. So while delaying the vaccination of lower-priority individuals when doses sit idle may well contribute to the abstract goal of fairness, the greatest good is served by making vaccines available to the greatest number of individuals as quickly as possible.

The concept of fairness has played a large role in recent discussion regarding prioritization of people over 65 versus frontline workers. Clearly, individuals who are at greatest risk of infection should be given priority. But when we see significant numbers of front-line workers declining vaccination, we need to put aside abstract concerns over fairness to ensure that all doses are used rapidly.

The same holds true when there’s a mismatch between vaccines delivered and the people seeking vaccination. Say a primary clinic gets 1,000 doses, but there are few first responders and health care workers in the area who haven’t already been vaccinated. Instead of waiting for the okay to begin vaccinating the next tiers of people, or shipping back the doses to the distributor, it makes sense to use those doses for a wait list of individuals who are on call. Each dose delivered provides a benefit to the community. Each dose sitting in storage is a missed opportunity.

There is no question that maximizing the absolute number of doses must take precedence in distributing Covid-19 vaccines, along with prioritizing individuals and communities with the greatest need. These are consistent with the greater goal of efficiently reaching the entire population. Balancing these objectives is possible and will yield an outcome that best serves us all.

Martin Shell is founding director of Jumpstart Decision Sciences, an analytics consultancy based in greater Boston.

  • So I rec’d the Moderna vaccine 1st dose recently ; fyi I am a single left lobe lung transplant patient from 2010 who suffers from IPF ; I understand science better than most because all my family has PHD’s in science from Columbia , Harvard , Yale and 3 generations from Cambridge University ; myself with a masters and I also know my state has vaccinated over half the population over 65 when I rec’d my dose ; I will not mention it though ; my IPF disease attacks the same lung tissue that covid 19 attack called the alevola blood vessels ; I also know in year 2010 there were only 1752 lung transplants done ; in 5 years there is a 50% death rate ; so to wake up today I feel truly blessed to be able to type this note and say a prayer every morning I open my eyes to this world

  • The United States has ordered far more doses than it can possibly justify. IF through vaccinations we are able to get this pandemic under control by the end of summer, I would be comfortable with the Biden administration releasing the unused doses as foreign aid.

    Lord knows, the need exists, and this would provide a counter to Chinese and Russian efforts to gain favor with third world countries through their vaccines. The greater the proportion of the world’s population that gets vaccinated, the better the outcome for everyone.

  • I think this article is premature. It might not have been premature a months ago, but it is now.
    Because in the meantime, the variants from UK, South Africa and Brazil have all arrived in the US, and it is not at all clear the variants are going to be stopped, or even slowed down, by the vaccines we are using in the US.

    Per one report, tests in South African indicated a vaccine they were pinning their hopes on has only shown 10% efficacy against the new variant.

    I am aware Moderna and Pfizer have each claimed they think their vaccines will work – but their basis for believing that is not clear, it seems to be based on test tube virus/antibody reactions, without any actual data from vaccinated people’s resistance to getting sick. And at the same time Moderna is reported to claim it’s vaccine, as currently formulated, will be very effective – they are also saying they are going to design a ” booster” shot, which will not be a booster, apparently, but rather a new vaccine.
    So, why are they designing a new vaccine if what they have already works ?
    Pfizer likewise has some reactivity in vitro, and extrapolates that claim their vaccine is very likely to still give protection, but will not give an estimate of how much.

    Perhaps I read too much into it, but at the same time, we are being given PSAs about how much better it is to use 2 masks, along with a lot of precise instruction on how to do so.

    My guess is, the authorities know the variants are going to sweep into the country and, as before, since they are not willing to aggressively test the modified vaccines, there will be another year or so of epidemic

    • Indeed – this pandemic is far from over, a third wave being forecasted for March. Until everyone abides by the spread-prevention rules and does not indulge in unnecessary (beach or spring break etc) travel, this virus and its continuous mutations does have the upper hand. Meanhwile, we have to trust that vaccine makers have integrity as they are much aware that they are affecting millions / billions of recipients, as in : the whole human population, globally. I therefore do not think that this article is premature – on the contrary, it hits bulls-eye. And vaccinators should be commended for ensuring vials are fully used with zero waste.

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