Tuesday, 28 September 2021

"First signs of stabilisation in fuel supply crisis"

Reports Sky News.

The whole thing is an absolutely fascinating example of irrational human behaviour. Being a natural born trouble maker with a bit of spare time, I queued twice over the weekend to unnecessarily fill up two of my cars -  I would have done the third one but I noticed the MOT had expired (it's gone in today). It made me all nostalgic for the 1970s or East Germany.

There is a whole branch of applied maths for Queueing Theory, and no doubt they'll be analysing the heck of out this for years to come.

I always assumed that it would sort itself out within a week or so. On average (say), motorists fill up every two weeks, a petrol station can handle three times its normal volume and everybody bunches and fills their cars over a five day period (14 ÷ 3, rounded). Then theoretically for the next nine days (14 - 5), very few people need to or will bother filling up at all.

Except heavy users, they have no choice. And people who are would rather fill up again even if the tank is three-quarters full, which are unknown unknowns. The effect will be minor - while people just topping up spend much the same amount of time in the queue, at the pump, faffing about in their cars before driving off (what the heck are they doing?) and manoeuvring their way back into the traffic they are only buying smaller amounts of fuel per visit, so total fuel sold per petrol station per day is the same (more customers x smaller volumes).

Maybe we will reach a steady state where everybody tops up a quarter tank every three or four days, which is the same amount of fuel purchased, just more time in longer queues? Which will dwindle to every week, and hence to every fortnight again.

I don't know how this will pan out, but it is very interesting.


Rich Tee said...

Interesting letter in today's Daily Telegraph that pointed out that setting a maximum spend of £30 per customer encourages small fill-ups. It is more sensible to set a *minimum* spend of £30, which would force motorists to wait until they needed to do a large fill-up.

Mark Wadsworth said...

RT, that is a brilliant idea.

Mark Wadsworth said...

RT, actually, to finesse it a bit, it would have to be fuel tank only, not putting £20 in the tank and then filling up a few jerry cans to get over the line.

ontheotherhand said...

I think I heard a figure on radio 4 this morning from some Fuel association that the average spend on normally £25. Then some lesson from fuel protest 2000 that it takes 3 weeks for behaviour to return to normal.

I took a half tank this morning which is irrational given the circumstances, but it gave me a warm fuzzy good citizen feeling like I get when I vote.

ontheotherhand said...

There was also condemnation of forecourts who had put the price up 10p. I don't agree. Price will moderate excess demand, reward those that have better organised logistics, and provides extra funds to pay overtime if needed.

Mark Wadsworth said...

OTOH, I calculated the 'every fortnight' number in my head, I heard somebody who knows about this stuff use that number on the radio. Does this tie in with £25? That doesn't sound like a full tank, does it?
Either way, this is a maths puzzle so you have to make assumptions.

Well done for the unnecessary topping up. Makes me proud to be British.

Also agreed on price rises, if I had a petrol station, I would have gone for 50p/litre extra.

Lola said...

I tend to fill from nearly empty about every three to four weeks. About 55/60 quids worth (as was). Average MPG about 32 (diesel SUV - i live in the sticks.). OTOH a petrol i10 of my daughters fills up rarely for about 20 quids and does 40 to 50 mpg. So 25 quids average fill looks about right.

Macheath said...

The president of the AA has spoken of motorists reportedly putting in less than £2.50 worth of fuel, presumably after a long wait, which surely takes irrationality to unprecedented levels.

Perhaps I am too cynical, but it reminds me of the 1980s practice of jamming government switchboards by assigning activists to ring repeatedly from every available payphone (the trick was to put the phone down when the pips went so it didn’t cost anything). It would be relatively easy, these days, to rally the troops via social media and, judging by my local paper’s breathless coverage of the queues, the amount of political capital to be gained by the sacrifice of a few hours might well seem worth it for some.

mombers said...

Never understood why people don't fill up completely. Unless you're really skint and can't afford it, you're wasting time and fuel doing it twice. Americans took to doing it in the early 2000s, assuming that dirt cheap gasoline surely would be even cheaper again in a few days

mombers said...

Re queues, what really irks me is when a supermarket has one queue per till. You can easily get stuck behind someone doing something benign or silly, whereas a single queue for two or more tills improves this greatly

Lola said...

Mombers - queuing at tills. Agreed. I mostly buy Shell V Power (diesel and petrol) and I have the Shell app on my 'phone so I can fill up without going in the shop. Very handy. I'll probably install the BP and Esso apps as well.

ontheotherhand said...

Macheath, it is not the queues that are the problem, it is the surge in demand for petrol leading to empty stations. If everyone got £2.50 or even £25 worth rather than a rush for full tanks, it might take a few minutes longer to queue, but petrol would be available 24hrs.

Mark Wadsworth said...

L, I'm surprised it's that low, but would appear to be correct.

McH, yup, that's irrationality at a new level.

M, surprisingly, real life studies shows that having one queue for several tills - while seeming 'fairer' - actually slows things down, that's why most places don't do it.

OTOH, it is the queues that are the problem. If a petrol station can deal with 100 customers per hour at normal times, then if 110 or 150 people turn up, you quickly get long queues. I like TR's idea about MINIMUM spend.

Macheath said...

OTOH, surely the it is the images of queues that are directly responsible for the surge in demand - reason enough for activists with cars to form a line outside a petrol station for the express purpose of generating such an image to be disseminated via social and broadcast media. Human nature, sadly, will do the rest.

MW, It’s complicated, but perhaps the optimal solution is rationing by maximum spend in the early stages, enabling more people to keep using their cars in the short term, switching to a minimum spend to prevent unnecessary top-ups once the initial crisis is past and deliveries are available. The point of the changeover would require some serious number-crunching/algebra - more your field than mine - but there should be a way to calculate it.

Mark Wadsworth said...

McH: "The point of the changeover would require some serious number-crunching/algebra - more your field than mine - but there should be a way to calculate it"

Queuing Theory is way beyond me - you have to do statistics and probability and take unpredictable human behaviour into account, so with extreme cases like this, you can only work it our afterwards.

I guess that garages will work out the optimum for themselves by trial and error, they will then copy strategies that seem to work until they all end up doing the same thing. It's the free markets in action and it will all sort itself out.