The length of queues will be proportional to “headroom”, and small changes in supply or demand can made a big difference to headroom, and therefore to the lengths of the queue.
Let me explain:
Suddenly we are waiting a month for a plumber, a year for a car, five years for an operation. We vaguely suspect it’s due to the invasion of Ukraine, or Brexit, or the post-Covid boom, or the Great Resignation (people deciding not to come back to work after lockdown, at least not full time).
But each of these things is surely only a 5% or 10% factor, so why have queues doubled or more?
Headroom:
Suppose you have 9 customers (or patients) a day and you can actually serve 10 if you need to – you have 10% headroom.
Or if you sell 90 cars a month but you have 100 cars available, that’s also 10% headroom.
There’s a formula for the length of the queue for any resource, which is that it’s (100-H)/H where H is the headroom, so if you have 10% headroom it’s 90%/10% = 9 people waiting
And if you have 20% headroom it’s 80%/20% = 4 people waiting
(Don’t worry about the formula, don’t question it, it just is what it is!)
80 vs 100
So you can see that if you’re happily at 20% headroom, with a queue of 4 (4 cars, 4 plumbing jobs waiting, 4 days or weeks, 4 months, whatever) – and if the demand goes up from 80 to 90, or if the supply drops from 100 to 90, then you now only have 10% and the queue has doubled to 9. A 10% change leads to a 100% change in the queue!
90 vs 95
And worse, if demand goes up, say from 80 to 90, AND the supply of cars drops from 100 to 95, the headroom becomes only 5% and the queue goes up from 4 to 19!
95 vs 96
And if we start at 90 and 100 and demand goes up to 95 and supply comes down from 100 to only 96 then we have only 1% headroom and the queue will be 100 – ELEVEN times what it was before. A month’s wait becomes a year! 6 minutes for an ambulance becomes over 60.
Or if the number of nurses drops from 10,000 to 9,500
And the requirement for nurses increases from 9,000 to 9,400,
the headroom has gone from 10% to 1% and the queues have gone from 10 to 99, so a month has become a year. (And for each person who you bring to the front and see in a week, someone else has to wait TWO years).
So – small increases in demand and small decreases in supply make huge differences to waiting times.
What can be done?
Look after supply – make sure you don’t make your systems less efficient by adding any extra bureaucracy or unnecessary tasks, and make sure you treat your workforce well so 10% don’t leave. Invest in Maintenance: Make sure you don’t have 10% of your machines or printers or vehicles broken down, or 10% of your people off sick. Look after your suppliers too – treat them well so you are the last person they let down.
Keep an eye on demand – put your prices up rather than increase the amount of work you are trying to do. Don’t promise what you can’t deliver. Get rid of high maintenance customers.
Recruit if you need to – if you can. Remember that you need some headroom to keep a good service (queues down) – probably 20%. For every 10 people you think you need, you need to actually employ 12. And I’m not talking about sickness and holidays, this is on top of that. So if 10 people only really do the work of 8 after sickness and holidays, and you think you need 10, then you need 12 to be at 100% and 14 to have the required headroom.
And you need to factor this into your cost calculations, perhaps charging more.
onwards and upwards!
Chris
PS But why do queues build up when we have headroom? Surely we can cope? (I told you not to question the formula). The answer is because of fluctuations in demand – it’s never smooth. Try rolling two dice, one for arrives and one for people being served, and see what happens!!
