Tuesday, 17 June 2008


I recently read a review of the book:
Guesstimation: Solving the World's Problems on the Back of a Cocktail Napkin by Lawrence Weinstein & John A. Adam

The authors encourage their readers (and their students) to have a feel for the size of numbers, and developing the skill of estimating reasonably accurately the scale or size of some measurable event or situation. The publisher's website for the book gives some examples, as well as a pdf of the first chapter. Something in the latter intrigued me. Suppose that there is a lottery with a hundred million tickets. If all those tickets were piled high, what would the height be?

In the UK, there is a National Lottery with about fourteen million different entry tickets. Like many university lecturers, I have used it for examples of simple (and not so simple) probability and statistics. So I started to wonder how high the pile of cards would be for the UK National Lottery. Following Weinstein and Adam, you start by thinking how thick a ticket would be, and conclude it is somewhere between 0.1 mm and 0.2 mm (a pack of 500 sheets of paper for the computer printer is 5cm thick, and lottery tickets are thicker). If we work with the smaller figure, we are talking of a stack 1,400,000 mm high, or 1,400 metres, or 1.4 kilometres. The figure is more than this, but less than twice, so we may as well call it 2km. Now we have a sense of the small probability of winning. 2km is higher than the highest mountain in the UK. Put that stack down, along a straight road; now it will take 20 minutes to walk from one end to the other, with just one card being the winner.

Guesstimating the size of things has more serious applications than this, but I am pleased to see that a publisher thinks it is worth putting a book like this in the marketplace. O.R. people use guesstimates quite often, to get a feel for the rightness of an answer, or a feel for the problem. In the early days of O.R., in the UK in the second world war, Winston Churchill heard of a ship crossing the Atlantic with a load of dried egg and asked one of his scientific advisers to estimate from the tonnage of the ship how many eggs were in the ship. The serious business of war was held up while the adviser worked it out, on the back of an envelope. Weinstein and Adam would be proud!

Monday, 16 June 2008

Multicriteria cities

According to a survey that seems to have been flashed around the world like a viral email, Copenhagen is the "best" place to live in 2008. The magazine "Monocle" (a "Lifestyle magazine" which is not in the journals abstracted for IAOR) took measurement on several criteria, weighted them and came up with a ranking which placed the Danish capital at number 1.

Operational researchers are familiar with problems of multiple criteria measurement. The cynical O.R. person will mutter about adding apples to oranges and trying to work out what the result is. Everyone will have their views on the best place to live, and what makes it so good. And that list will almost certainly not coincide exactly with the criteria used by the magazine. Let me admit that I like Copenhagen, perhaps because my late friend Ellen had a flat which was ten minutes walk from the gates of Tivoli Gardens, and so could hardly have been more convenient for visiting the place. Even without that personal experience, it is a very pleasant city, but my criteria would not have included (for instance) Monocle's number of international flights from the city airport, nor the ease of buying drinks at 1a.m..

So, seeing such analysis of multiple criteria optimisation, the O.R. person ought to reflect on how difficult it is to measure the "hard to measure" and on how to work with clients and decision-makers when some of the consequences of choice are determined by aesthetic and qualitative scales.

Tuesday, 10 June 2008

Governments, swimming pools and models

The UK government has announced that it intends to subsidise swimming pools in England, with the aim of making entry free of charge to all the pools which are managed by councils. The subsidy will be introduced gradually, starting with the over-60s and under-16s. By 2012, everyone will be able to use public swimming pools free of charge. This excludes pools owned by companies, sports clubs, hotels and educational establishments. This is to try and encourage more people to take part in sport, and it is claimed that the most likely form of exercise for people to take up is swimming. There will also be money for new Olympic sized swimming pools.

Now I enjoy swimming, and go to the pool several times each week. When I started work at the university, one of the free perks of the job was being able to stroll to the open-air pool that was five minutes walk away from my office, and swim. The pool was free for staff and students. Now there is a charge, and I have moved my regular swimming to the public pool managed by Exeter city council. But, even though the pool was free, it didn't mean that everyone used it. Removing the charge for some goods or service doesn't automatically bring in more customers.

So I wonder what kind of modelling has been done by the UK government in advance of this announcement. The claim is that it will bring two million more people into regular exercise. As an O.R. person, I wonder what model yielded that figure, about 3% of the UK population. And how do you really measure "regular"? If the figure is accurate, what does it mean for the numbers of people using a typical swimming pool on a typical day? Most pools have lane swimming for serious swimming. Before 9am, Exeter's pool has two "fast" lanes, one "medium" and one "slow". The fast lanes are crowded when there are six or seven people in each, the medium one can take a few more, and swimming in the slow one is awkward when there are 20 in it. Can you recognise a queueing problem here? When does the congestion in a service system get so bad that arrivals turn away?

Swimming pools provide several further O.R. related questions. I used to ask one of my modelling classes how big the hot water tank that feeds the showers should be for a set of public showers. For simplicity, these showers often have no control over temperature, simply an on-off button or tap. So the water temperature cannot fluctuate too much. Therefore, the heating system must be able to maintain the water temperature within a small range, putting design limitations on it.

Another problem comes with lane swimming. There is a heuristic which says that it is safer if alternate lanes go in opposite senses, clockwise, anti-clockwise, clockwise ... across the pool. Why? Because adjacent lanes are swimming together, and a swimmer only needs to avoid those coming towards themselves on one side, not two. But overtaking in lane swimming is an art, which leads to models of congestion. Assuming that I am two metres tall, then if I make a turn after the person in front of me, then to overtake them, I need to swim an extra two metres in the time that it takes for us both to complete a length -- unless they give way. So you need to be in the region of 10% faster than the person ahead to complete overtaking in a normal pool. And if there is a third person behind, then that person will see congestion. It is rather like two similar speed trucks overtaking on a two or three lane road -- it takes time and there are people held up behind. Swimming has the complication of turning at the ends of the pool. But there's a research possibility: "The similarities and differences of lane swimming and overtaking trucks." You read it here first!