ATM Algebra


ThinkTank Maths improved a retail bank’s cash refilling operation with mathematical ideas…from a surprising source. So, what do cash machines have in common with cows?

We all know the frustration of a cash machine (ATM) refusing to provide us with cash when we desperately need it.

The reality for the bank is that guaranteeing reliable ATM cash supply is a massive operational challenge. They have to monitor thousands of machines and forecast busy periods, weekends, holidays, public events and even weather to manage the refill schedule for every machine individually according to its specific demand peaks and troughs.

Of course, the bank could choose to refill every machine constantly so that no cashouts ever occur. However, this would increase the cost — and the risks to the delivery teams — exponentially: costs that could be ultimately passed down to the consumer.

So, when a major UK retail bank decided to improve the service quality and efficiency of their ATM operation, they faced a complex dilemma. The existing solutions were focussed only on reducing the probability of machines running out of cash, and were unable to increase the efficiency of the total operation.

Commissioned to study the problem by the bank, ThinkTank Maths (TTM) discovered that from a mathematical perspective, the problem had unexpected similarities to previous work on animal breeding with the Roslin Institute. This allowed TTM to develop an approach that incorporated both the operational constraints and the uncertainty in the cash machine usage data.

In summary, collaborating with the bank and their cash delivery supplier, TTM showed that the new refill scheduling algorithm led to savings of 21% per annum, meaning several million pounds a year.

Seen through the right mathematical lens, very different problems may turn out to be curiously related … and point the way to an unexpected solution with significant value.

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