Much of the UK is facing a supply chain crisis. Due to disruptions in transportation and staff shortage, supermarket shelves are empty and restaurants have to change their menus.
Major retailers have their lowest stock levels since 1983, so the country’s retail sector is ready for stock shortages over Christmas.
British Chambers of Commerce warned that there could be a sharp decline in economic growth due to the crisis, which has been made worse by Brexit and the pandemic.
The situation may seem dire, but math whizzes are hard at work using algebra to try to manage the disruption.
For example, when a delivery arrives at your home, this is after an equation has been solved and a missing number found. As The Guardian put it, ‘Algebra is the maths that delivers’.
Algebra’s key feature is its ability to find previously unknown numbers given certain conditions.
Talking to The Guardian, principal data scientist at Ocado Technology, Anna Moss, said: “Stocking warehouses is a complicated problem.”
Fancy job title aside, Anna Moss’ role ensures that the amount of stock ordered from suppliers is balanced, enough to satisfy the demand from customers whilst not exceeding warehouse storage facilities and creating food waste.
Moss could be called a maths mogul. Many of her mathematical research has been published in academic journals.
Linear algebra is the foundation of logistics math. This is the area of algebra where variables, such as warehouse stock data, are processed in ways that don’t depend on any power or square. Linear algebra would allow for y = 4x to be performed, but not y = 2×2.
Linear algebra is a way to find solutions for sets of equations which, when combined, contain all the information you need to determine the relationships among the variables.
This format of equations acts as a kind of mathematical spreadsheet. It can process large amounts of data in a single operation, which allows the mathematician the ability to find the relationships between them.
The same process is at work behind Google search technology, flight scheduling and parcel delivery when even your virtual shopping basket is delivered to your device via linear algebra in the logistics routing information through the internet. This linear algebra is used to develop algorithms.
As reported by The Guardian, Keith Moore of US logistics company Autoscheduler.AI, said: “You can think of this as computational algebra.”
It’s in place with one sole purpose, to deliver successfully to every customer, on time and in full (OTIF), but as supermarkets in post-Brexit Britain know all too well, this is never actually possible.
Moore continued: “Even at a single distribution centre, they are collecting gigabytes of data every minute and that data changes constantly. It’s not just impractical to have analysts and people sitting in a room doing math to make decisions, it’s completely unfeasible.”
This is why the appropriate algebra is programmed into software – the exact algorithm at work is a trade secret.
This algebra, however, is not like secondary school algebra questions. It has a lot of variables. “All these criteria are given weights based on their relative importance and this weighted combination serves as a single value to be optimised,” Moss states.
“In addition, our problem keeps changing all the time, as customers place new orders and edit the existing ones. Our algorithms have to cope with these on-the-fly changes.”
For home delivery for example, there are optimal delivery routes to consider and location of warehouses relative to your address. Moss commented: “We know the travel distances between all pairs of these locations. The problem is to find the best van routes or the way to assign orders to vans and determine the sequence for each van in which to deliver its assigned orders.”
The maths is prevalent at all stages of the supply chain and essentially allows businesses to assess what the best options are for them, something which has been thrown up in the air thanks to the widespread disruption.
Although algebra may not be the most popular subject at school in our teens, and we are still trying to understand the concept, it is one of the many ways that the world turns and, in such situations as we are now, attempts to balance things again.
As Moss put it: “I consider myself lucky. I still enjoy doing maths and have a chance to do the things that both truly interest me and make a difference to society.”