The Power of Pooling

One of the central lessons from the waiting time unit of my operations management course is "the power of pooling"¹: a single centralized system can result in lower waiting times than many independent systems. The reason for this is that when you have separate systems, it's possible to have a backlog in one, while servers remain idle in the other. This is inefficient! A (properly designed) centralized system ensures that whenever there is a queue, all servers are busy.

This observation explains why companies prefer to use national (or even international) hotlines, rather than having customers call into their local branch. It's also just sexy enough to make headlines on slow news days: see for example this article titled "A Long Line for a Shorter Wait at the Supermarket."

Unfortunately, people often remember "a single line is better", without internalizing why it's better. Let's consider the grocery store setting mentioned in the article above: will using a single line really reduce average waits? I don't think so. In a grocery store, customers typically go to the shortest line. If one line empties, someone will leave the line they are in and go to the idle cashier. This shows that checkout lines are not truly separate systems: generally, if there is a backlog of customers, all cashiers will be working. In other words, grocery stores get the power of pooling regardless of whether they use a single line or separate lines.

There are still good reasons to use a single line. The biggest is probably fairness. We've all been in the position of getting into a slow line, only to watch in frustration as customers in a different line are served promptly. Aware of this risk, many of us spend our time in line questioning our decision, and scanning to see whether we should switch lines. Using a single line relieves us of this burden, and ensures that customers are served in the order they arrived.²

Implications for COVID Vaccination

In most states, there are many organizations administering the vaccine. In theory, having many vaccination sites should reduce the distance that people need to travel. However, it can also make the process of booking an appointment a nightmare. Consider the following FAQ from a recent New York Times article:

There are a lot of different websites. Which one do I use?

Be prepared to try several, and to try them repeatedly. Some of the vaccination centers in the city are run by the local government, but others are not. Then there are the state-run centers, and hospitals and other medical providers are also receiving doses.

There are articles from all over the country complaining about decentralized registration, giving advice for scoring an appointment, and lauding volunteers who help others book appointments.

Is the presence of so many different systems to blame for the slower-than-hoped-for vaccine rollout? Probably not. While there may be isolated instances of appointment slots going to waste, my sense is that most slots are claimed shortly after they become available. In other words, this situation is analogous to the grocery store lines: customer jockeying will ensure that cashiers (vaccination centers) are fully utilized. However, as discussed earlier in this post, the presence of multiple systems opens serious questions about fairness. Successfully booking an appointment requires comfort with technology, information about where vaccines are being administered, and time to constantly refresh your web browser. This favors younger and more affluent registrants, despite the fact that elderly and low-income communities have been harder hit by the virus.

Brainstorming Solutions

It seems natural to use a centralized system to schedule all appointments: allow people to register for a state-wide waiting list, and notify them when it is their turn.³ Several states have started to do this, including my home state of Minnesota. However, often these registration systems only apply to vaccination centers run by the state.

Even if the central portal is used for all vaccination centers, booking an appointment could remain daunting for many. In my ideal world, we could move away from a "first-come, first-served" registration system (which favors those with time and technology) to a system that allows people to indicate hours of availability each week, and then schedules them at a nearby vaccination center. This would give people a window of several days to sign up (enhancing equity), and the scheduling algorithm could prioritize the elderly and other high-risk individuals, while ensuring that all slots are filled. Barring this change, I would want to see states working to make registration easy by clearly showing not only locations that are administering the vaccine, but also available appointment times at each location. Furthermore, state employees should be available to help the elderly (and others) book appointments.

Conclusions

Although using a single centralized system would not significantly increase the rate of vaccination, it could help make sure that appointments are distributed more equitably, and given to those (such as the elderly) who are at greatest risk. Moving away from "first-come, first-served" appointment scheduling could further enhance equity.

What do you think of these ideas? What other ideas do you have to improve our vaccine distribution system? Type your thoughts into the comment box below!