A food-delivery platform handles 220,000 orders a day. About 1.8% of orders raise a refund dispute. Automated rules settle most of them but 22% reach a human agent who spends roughly 9 minutes per case. A fully loaded agent costs about £38,000 a year and delivers about 1,500 productive hours. Roughly what does the manual tail cost per year?

The assumptions stated

Four numbers and nothing else: order volume, dispute rate, the share of disputes that escape automation, and the handling time. Everything else is arithmetic.

The arithmetic shown

1. Disputes per day: 220,000 × 1.8% = 3,960.
2. Disputes reaching a human: 3,960 × 22% = 871 per day.
3. Per year: 871 × 365 ≈ 318,000 cases.
4. Agent hours: 318,000 × 9 minutes = 2,862,000 minutes ≈ 47,700 hours.
5. Agents needed: 47,700 ÷ 1,500 ≈ 32 FTE.
6. Cost: 32 × £38,000 ≈ £1.2m a year.

Real staffing is worse than the ideal, because arrivals are peaked around the dinner window and you cannot staff a queue to 100% utilisation without the wait exploding. Add 25% to 30% for cover and shrinkage and the honest answer is £1.2m to £1.6m a year.

Which assumption dominates the error

Handling time, not volume. Volume and dispute rate are measured and stable; 9 minutes is an average over a long tail where a photo-evidence case takes 25 minutes and a duplicate-charge case takes 2. If the true mean is 14 minutes the answer is £1.9m. Measure handling time by dispute reason before costing any automation, because the reason code is also what tells you which slice is automatable.

What the number rules in and out

• It rules out a platform-scale programme. £1.2m a year will not fund a team of eight for two years. A business case has to clear the run cost of whatever it builds.
• It rules in a narrow attack on one reason code. If 40% of manual cases are one reason and that reason is deterministic, 13 FTE of effort (≈£490k a year) is reachable with a few engineer-months.
• The rule of thumb: automate a reason code when annual manual cost for that code exceeds roughly three times the build cost plus its annual run cost. Below that, a better agent tool that cuts 9 minutes to 6 returns a third of the cost for a fraction of the effort.

Why the other options fail

• About £120k a year drops a factor of ten somewhere, usually by costing the daily agent count rather than annualising the case volume. It makes the tail look like rounding error and the conversation stops.
• About £12m a year comes from using 90 minutes rather than 9, or from costing all 3,960 daily disputes as manual. It is the error that gets an automation programme funded on a number that will never be realised, which is the expensive direction to be wrong in.
• About £120m a year treats every order as a dispute. It is worth sanity-checking against revenue: a cost that large would exceed the platform's gross margin on those orders, so the model must be wrong.

When this estimate is the wrong tool

When the manual tail exists for a reason other than cost. If disputes are the only place a human sees how the delivery network is failing, the queue is a sensor as well as a cost, and automating it blind removes the feedback that keeps the first-time-right rate up.