Saturday, 31 March 2012

Petrol, Postage and Pasties: Don't Panic at the pumps

Some very strange figures have been published by the Retail Motor Industry (RMI) about the increase in sales of fuel because of the panic buying earlier this week.  Yesterday (Friday 30 March 2012) the RMI released sales figures for the change in daily sales, looking at the previous day (Thursday 29 March 2012) compared with the average for the previous week.  Here they are:

Fuel Volume - Uplift Against Previous Week
Thursday 29/03 
Diesel                  +76.8%
Unleaded             +171.8%
Super Diesel       +375.9%
Super Unleaded  +358.1% 

Leaving aside my refusal to place any credence on the third and fourth significant digits in the statistics, there are several oddities here. 

First, why the variation between fuel types?  A possible reason for the difference between diesel and unleaded is that diesel is more often found in vans and commercial vehicles, and perhaps(?) professional drivers haven't panicked. 

Second, why the differences between "ordinary" and "super"?  One might think that "super" fuels are a smaller part of the market, and that measurement errors account for the change -- but in a market of hundreds of thousands of litres per day then the changes are really going to be significant and not within measurement error.  It would be interesting to see an analysis of what type of driver routinely buys "Super" fuel.  My hunch -- and it is only a hunch -- is that one contributing factor to those massive increases could be because there have been some drivers who normally purchase "ordinary" fuel at a supermarket who have changed to an independent filling station which sells "super" fuel.  And perhaps once there, people have bought whatever they could. 

Third, given these figures, why has the "uplift" for diesel and super diesel not been similar to the "uplift" for unleaded and super unleaded?  There is some deep psychology here which would repay study!

Finally, the RMI press release (here) talks about the supply chain.
... the pinch point in the supply chain remains the movement of fuel from terminal to forecourt.

The average retail fuel usage is near to 100 Million litres every day. This would require 2300 tankers to replenish the petrol stations assuming the tanker has a 44,000 litre capacity.

Figures for Thursday 29 March suggest that the number of tanker movements required will be nearly double; taking into account back log from earlier in the week. The UK haulage industry does not have that capacity.

The good news for today (Saturday 31 March) is that demand is more or less back to normal.  The bad news is that my three questions about the figures are not answered.

There is scope here for some O.R. model-building.  Collect some more data about sales, but be more specific about the location of sales.  Collect the data day by day and also note where filling stations ran out of fuel.  With these figures, and some interviews, you could start to build a model to advise fuel companies about their priorities when there are problems in the supply chain. 

But, of course, there is yet another O.R. aspect to the panic effect.  Drivers are playing a complex game with the supply network when they decide that their vehicle must have enough fuel and the network is under stress.  So, if the result of the model for the fuel company is implements, then the game will change and consumer behaviour will change as well. 

Thursday, 29 March 2012

Petrol, Postage and Pasties: (3) Pasties

The third item of news from this week concerns the way that hot take-away snacks are taxed.  After the UK government Budget last week, in a short time a hot Cornish pasty or similar hot take-away will be charged VAT at 20%.  But the same pasty at room temperature will not be subject to VAT at all.  The story and video are here.  Newspapers and the media have nicknamed this the "Pasty Tax"

The UK Government has a large team of OR analysts, and generally there are models to predict the effect of changes in taxation.  So it is likely that someone considered the financial consequence of changing the collection of VAT on take-away food.  But, given the instant reaction in the media, it should have been fairly obvious that this change would lead to confusion among retailers, and among the public buying hot food.  The comments from "the man on the street" and those in the snack food business could have been foreseen.  They come under the heading of elementary psychology. 

Once upon a time, Operational Research was regarded as an interdisciplinary subject.  Models about public finance would have been developed by economists, mathematicians and psychologists together.  It looks as if there wasn't enough input from the last discipline.  Even if there was nobody around with an academic background in psychology, training in O.R. ought to have included aspects of it.

Petrol, Postage and Pasties: (2) Postage

This week Britain's Royal Mail announced that the price of a first class stamp will rise from 46pence to 60pence at the end of April 2012, and the price of a second class stamp will rise from 36pence to 50pence on the same date.  The Independent carried an article in its Business section headed "Royal Mail may be sealing its demise with rises in prices".  What was interesting was the paragraphs about modelling. 

The figures indeed suggest that increasing the price of stamps has ensured that revenues have fallen less quickly than the volume of letters. But if you increase prices by too much you run the risk of it being counter-productive. People will see sending anything through the post as a luxury and cut back sharply. The fall in revenues that results from this might not be compensated for by the sharp rise in prices. Losses will escalate.
Royal Mail has naturally done lots of modelling that argues against this outcome. The trouble is that when businesses do modelling to see how a controversial measure might work in practice they usually get the sort of results that they want. Particularly if they hire consultants to do the modelling for them. 

However, there is no prior experience of a 30% price rise, so any model of the effect of such a change on the volume of mail is speculation - it is extrapolation beyond the range of validity of the data.  And so the model becomes a piece of fiction, and the mantra "Garbage In, Garbage Out" applies.  Royal mail has claimed that other countries have similarly priced postal services, but not all models of elasticity of demand transfer between countries.

I know that Royal Mail has used Operational Research in the past, but I hope that this model was not created by an OR person; please, please, don't build models without defensible data!

Petrol, Postage and Pasties: (1) Petrol

Three stories in the UK news where an OR modelling approach could contribute to the debate.  Let's start with petrol (or rather, vehicle fuel).  There is a threat of a strike by the majority of fuel tanker drivers (news story here) which would mean that filling stations could run short of fuel.  The threat has been reduced because the union and employers have gone to arbitration.
However, public announcements about the talk of the strike have provoked a panic reaction by drivers.  There are queues for fuel, and some filling stations have run out of fuel.  And once these panics have started, then more people think that there is a need to stock up on fuel, so the queues get worse.  Behaviour changes, as drivers choose to purchase more fuel, or to fill up more frequently.
Letters in the press, and callers on the phone-ins on radio, suggest an assortment of solutions.  The usual is to ration drivers ("no more than X litres" or "no more than £Y in value").  This has little effect on behaviour, because the ration is usually set higher than the median amount that drivers purchase at a time under normal circumstances.  It is not a deterrent, because one of the principal changes in behaviour is to buy fuel when the tank is half-full, rather than quarter-full.  The inventory of fuel carried by a typical vehicle normally varies between quarter-full and three-quarters-full, and when there is a panic, it tends to be fuller,  and the range is smaller.  Another popular solution is reverse rationing, that customers must buy at least some minimum amount of fuel.  There are advantages to this idea, as the consequence is thought to be fewer customers of the kind who change their behaviour to "fill up every time I see a source of fuel".  However, not all vehicles are created equal.  So a minimum of 20 litres may be OK for many larger cars, but cannot be suitable for a motor-cycle or small car.  And policing the scheme is very difficult. How does the cashier deal with someone who has bought less than that minimum?
Operational Research models of the situation are limited in their validity, because they are dealing with the unpredictability and irrationality of human behaviour.  Most OR models are rational!

Tuesday, 20 March 2012

An all-round approach to problem solving

Until the 1970s, the colleges of the University of Cambridge offered students benefits known as Entrance Scholarships and Entrance Exhibitions.  These were monetary awards to supplement other sources of finance that the student was receiving.  With inflation, the significance of the value declined, although there continued to be kudos for having obtained a scholarship or exhibition.   Eventually the colleges changed the system.  When I sat the scholarship examinations in 1967, I took exam papers in mathematics and physics.  One of the physics examination papers was designed to test one's ability to bring together many aspects of physics, and did not simply test whether you knew about light rays, or how an electric motor worked.  They were all, of course, unseen.  Even at this distance, I can recall some of the questions, either from the questions that I tackled to win my scholarship, or from those that I used as preparation. 

So dear reader: "A copper plate is placed on the north bank of the River Thames at Greenwich where the river is tidal.  A similar copper plate is placed on the opposite, south, bank.  The north bank is connected by a copper cable to the positive terminal of an ammeter, and the negative terminal is connected to the south bank plate.  What readings will the meter show over a twenty-four hour period?"

Another, which I am reasonably sure was in the questions I answered read: "Explain what happen when a balloon is burst with a pin, drawing attention to the reasons that the balloon goes 'pop'".  Tina and I have been talking about this, because we have had to perform a related experiment.  Three or four weeks ago, we started to make two papier-mache eggs for a sermon illustration at Easter, using balloons as the former.  So we pasted strips of newspaper onto the balloons, allowed the paper to dry, and added further layers of paper soaked in dilute paste.  Eventually we decided that the eggs were firm enough.  So last night we burst the balloons.  But, we had talked in advance about what we expected.  Would the glue hold the balloon in shape?  Would the tension in the latex tear it away from the papier-mache?  Would there be any "pop"?   So what happened?  The air gradually escaped through the pin-holes with a quiet hiss.  The glue held the balloon firmly in place.  Over the weeks, the air pressure inside the balloons had reduced, but had not reached the air pressure outside.  Now comes the next stage of decorating these large eggs!

Part of my postgraduate programme in operational research was examined in a similar way, with a question which was designed to bring together material from across the syllabus.  The Lancaster "Jumbo" examinations were eight hours long.  At 9am, one was presented with a case study to analyse and report on by 5pm.  They were artificial case studies, based on a hidden model, and there was no indication of how to approach each one.  Setting them was an art.  Later in my academic life, I devised two similar case studies, which we used in a different setting to examine undergraduate students in the Mathematical Statistics and Operational Research degree at Exeter as part of their communications skills course.  They are hard work to create!  Mine were both based on queue models, but brought in statistical analysis and cost-benefit analysis.

It strikes me that both examinations - Cambridge scholarship and 8 hour case study - are testing something which is desirable for all students to have achieved, and that is an understanding of their material without the artificial boundaries of one area of their subject material.

ps: The ammeter will show a current.  It will follow a sine wave (approximately) over time with a wavelength of about 12.5 hours.  This is because the salty water is a moving conductor passing through a magnetic field (the earth's magnetic field).  As the tide goes in and out, the direction of the flow of electrical current will reverse.

Friday, 16 March 2012

Multivariable optimisation in the home

Over the years, I have seen several presentations of projects that use nonlinear optimisation in design.  Some of these can be loosely classified as consumer matters.  One of the interesting ones was about the design of telephoto lenses for compact cameras.  The variables were concerned with the position of the lenses and their nature, so a typical lens involved 20 to 30 variables.  There were several objectives, such as cost, weight, sharpness of image (at several focal lengths).  I used to use this as an everyday example, though sometimes I talked about the design of jet engines as a further example of nonlinear multivariable optimisation, following another interesting presentation.  (My PhD thesis was also about nonlinear multivariable optimisation, applied to the design and operation of water supply systems.)

Latterly, although it was not a subject that I have ever heard talked about in seminars on nonlinear multivariable optimisation I used to refer to the design of the arms of a domestic dishwasher.  Where should the holes be placed?  How many?  What direction should they be?  One could discuss the engineering problems in outline, and think of objectives.  And as I loaded the dishwasher at home, I used to think that here was a successful application of operational research in the design of an everyday object. 

From time to time, though, my belief in the rationality of the design of the dishwasher has been shaken, especially when the crockery comes out with a coating of tiny tea-leaves or fragments of vegetables.  And to these experiences, this week I had the interesting experience of trying to work out why two of the jets were blocked.  The arms cannot be opened, so the way to get rid of the blockage was a heuristic (good bit of OR) called "shake the arm and add water".  Eventually several apple pips and an apple stalk emerged.  Obviously the design brief did not include provision for straining the water that goes into the arms.  Of course, a good O.R. scientist would have investigated the implementation of the solution to the nonlinear multivariable optimisation problem before allowing it to be incorporated in the design. 

Friday, 2 March 2012

When was your public transport delayed?

On Wednesday 29th February 2012, the 1045am X38 express bus from Exeter to Plymouth broke down outside Ashburton.  A replacement bus was sent from Exeter, as the breakdown was almost exactly midway between the two possible depots for spare buses.  And, as you will have gathered, I was on the 1045am bus.  Tina and I were on a day-trip from the smaller city of the county to the more populous.  There were about twenty passengers on that particular service.  We reached Plymouth about 45 minutes later than the schedule, having caught up time on the second part of the journey because there were no passengers to pick up.  Four of the passengers decided to walk the mile to Ashburton, and didn't wait for the replacement.  Another one phoned for a friend who collected her from the broken-down bus.

Afterwards, we shared memories of times when we had been delayed on public transport buses.  For each of us, despite having travelled to school by bus for most of our school lives, there were very few such occasions.  Tina had been on a couple of buses which had broken down when she was on her way to school.  I recalled the time when (aged 6) the older pupils (aged 10) on our bus organised a crocodile of pupils to walk the last mile to school when a bus broke down.  (Yes, we were unaccompanied by adults, and yes, it was the 10 year olds who led us.  Would it happen today like that?)  But generally, our bus trips had been free of breakdown or accident.  Delays were due to adverse weather conditions.  Tina recalled London smogs in the 1950s.  I recalled bus trips in snow during bad winters, and delays when the River Severn burst its banks in Worcester.  There were times when a road had been blocked by a serious accident, and once, on a journey from London to Exeter, slow traffic meant that the driver's rest period had to be taken before we reached Exeter. 

Then we compared this with experiences on the railway.  Again, it had been rare for us to be delayed because the engine had broken down.  But, far more often, we had been delayed because of another event on the rail network.  And that made us think about how rail and bus transport differ in their reliability.  The reliability of buses is slightly affected by problems of the reliability of other buses, and slightly affected by problems to the infrastructure.  The reliability of rail services depends much more significantly on a combination of the performance of other vehicles and the rail network. 

So here's an aspect of measuring the performance of two forms of transport.  You cannot simply look at the performance of the individual vehicles; having a closed system (like rail tracks, and limited access points such as stations, ports for ships, airports for planes) means that you need to look wider than the vehicles themselves. 

It is worth remembering that in terms of injuries per passenger mile, elevators (lifts in the UK) are the safest form of passenger transport.  But they don't run from Exeter to Plymouth.