In elective services, the worst sin of all is under-utilising the valuable resources you have available. It costs you financially (both as lost income and incurred expenditure), and it pushes up the waiting list and waiting times. So hospitals generally try to avoid this sin, and fill capacity up as much as possible.

However, you find that unpleasant things start happening as you push utilisation up towards the magic 100 per cent mark. Suddenly you are faced with lots of questions, such as:

1. When all your appointment slots are full, how do you book urgent patients at short notice? How many slots should you hold back for them?
2. Should those urgent slots ever be used for non-urgent patients?
3. What should you do if an urgent referral comes in, but still no slots are available?
4. When patients are cancelled by the hospital, should they get preferential treatment when you rebook them?
5. Are the answers to these questions different, depending on whether you run a fully- or partially-booked appointments system?

The good news is that there are answers to all these questions, which means that you can utilise your elective capacity at 100 per cent. In fact 100 per cent utilisation is so desirable, that we took it as a basic assumption when beginning our research into the best tactics for booking elective patients.

Our research (which studied over a million years of simulated bookings) threw up some other results too.

Firstly, it is good to be as precise as possible about how long each urgent patient can safely wait, and book them accordingly. This finding was expected from the work we conducted on waiting lists in the 1990s, but it was good to have it confirmed in simulation.

Secondly, fully-booked services perform almost as well as partially-booked services, if (and it’s a big if) the level of disruption is the same. Of course the whole point of running a partially booked service is to reduce the number of cancellations caused by staff taking annual leave, so there should be less disruption under partial booking (and so even better performance compared with a fully-booked one). (Set against that, you have greater certainty to patients in a fully-booked service, so take your choice…)

Thirdly, it doesn’t make very much difference whether you can arrange for any potential long-wait patients to accept a rebooking, if slots remain empty at short notice. This counter-intuitive result holds both for waiting times on their own, and for a basket of measures that takes disruption into account. Why? Simply because in a well-managed service there should be very few opportunities to rebook patients into short-notice slots; the slots are generally full.

Fourthly, there is good news on offering a choice of bookings to patients. You can offer slots in up to three different weeks without significant impact on waiting times or other aspects of performance. It might even reduce your DNA and rebooking rates.

Finally, we looked at another booking technique that is used in some hospitals: rippling. What is rippling? Imagine you have an urgent patient to book, but no empty slots that are soon enough. So you cancel the least-inconvenienced routine patient. Now what do you do with this cancelled patient? You could rebook them into the next available slot, which might be a long time in the future. Or you could cancel another routine patient in a couple of weeks time to make space, then cancel another a couple of weeks after that, and so on until you reach the next empty slot. So lots of patients are delayed a little, instead of one patient being delayed a lot.

Now that you’ve got your head around all that, you can forget it. Rippling isn’t a good idea. The disruption caused to patients by all those rebookings will always outweigh the benefits of shorter individual delays. “But what about my waiting time targets?”, you ask? Well, that is what the allowance is for, that lets 5 or 10 per cent of patients wait longer than the time limit.