Vaccines have been on everyone’s mind for a long time now. The COVID-19 pandemic has been with us in the UK for around a year. Getting access to a vaccine has been viewed by many as our only path back to some form of normality.
The biotechnology labs and pharmaceutical companies have done their part and delivered numerous efficacious vaccines. Following this, the next major step in vaccinating the population is the distribution of the vaccine throughout the country. Logistics and supply chain management plays a very important role in this process.
The UK has had access to vaccines for a number of months now. However, there are still countries waiting for their first doses. Thinking about the logistic of vaccine distribution is still a pertinent issue. This blog given some of my musings about the details one must consider for to complete this monumental task.
Problem definition
On the face of it the problem is very simple: determine the transportation links from the vaccine manufacturing plant to the distribution centres.
However, the actual problem is not that simple. I will go through some of the many aspects that must be considered in this very messy problem
Vaccines
There are a number of COVID-19 vaccines available in the world today. Lets focus on two of them:
- Oxford-AstraZeneca (OA for short)
- Pfizer-BioNTech (PB for short)
These have very different characteristics that impact the logistics. Most importantly, the OA vaccine can be stored in a regular fridge. The PB vaccine, however, has very strict temperature requirements. The Wikipedia page states that the PB vaccine must be stored at “−80 and −60 °C until five days before vaccination when it can be stored at 2 to 8 °C (36 to 46 °F), and up to two hours at temperatures up to 25 °C or 30 °C”. New reports suggest that these temperature requirements can be relaxed. In any case the temperature requirements of the PB vaccine makes the logistics problem very interesting.
Transportation
The vehicles here are very important. The OA vaccine just needs a fridge. So that should be covered fairly easily by regular cold storage vehicles. The PB vaccine needs very cold storage. This requires special vehicles. Also, every step in the PB vaccine journey is an opportunity for it to thaw out–impacting its efficacy. Thus, we want to limit the number of “hops” in the vaccine journey.
Who gets the vaccine?
A very important question that has had a lot of people trying to answer. The simple answer is: the most vulnerable. Why do we care about this for the logistics problem? Because we are working with a scarce resource, both the vaccine and time. The different priority groups may need different distribution locations. For example, the distribution of people aged over 70 throughout the UK could be vastly different to the distribution of people aged between 50 and 60. This leads in to the next point.
Distribution centres
Where do we set up the distribution centres? This really depends on who is getting the vaccine at that particular time. This can change over time, since the demand for the vaccine by different groups will change over time. This brings in a very interesting time element into the logistics problem.
Rate of manufacture
We can assume this is given and that the vaccine is manufactured as quickly as we can distribute. However, this could quickly become a bottleneck. I am sure that this is a feature that governments are keeping a close eye on. A question for a later blog is whether the manufacturing or the supply chain is more efficient.
Efficacy and cost
Finally, the OA and PB vaccines have vastly different efficacy. But they also have vastly different costs. Another factor, for the UK at least, the OA vaccine is manufactured in the UK, which could reduce the transportation time and costs. Where the PB vaccine is manufactured in Germany.
We must also take into account the costs of opening distribution centres and the cost of staff to administer the vaccine. Finally, transportation and warehousing costs must be taken into account.
The logistics optimisation problem
This is what we are here for: the logistics optimisation problem. Lets break it into parts:
- At the base of it we have a classical vehicle routing problem, with some extra elements.
- There is a heterogenous fleet, one for the OA vaccine and one for the PB vaccine. We could use the PB vehicle to transport the OA vehicles, but not the other way around.
- There is also a hop constraint for the PB vaccine.
We also need to consider the distribution centres.
- A facility location problem will be solved to identify the distribution centres.
- There is a time element, so the distribution centres can change based on the current demand
All the while we need to consider the purchase, distribution, staffing, transportation and warehousing costs.
What we end up with is an optimisation problem integrating a facility location with time dependent demand and vehicle routing problem with heterogenous fleet.
One very important thing that I am missing is the last-mile journey of the vaccine. It is likely that there will be two or more different vehicle sizes, one for transshipment across the country and another for local distribution. I am conveniently ignoring that here.
Summary
This is definitely an optimisation problem that I would like to work on. It sounds incredible challenging from an optimisation point of view. However, I think that the most challenging part is coordinating all of the organisations that control the manufacturing, transportation, warehousing and distribution. As a mathematician, we can just see the pure problem. In practice, a logistics problem on this scale is much messier.
