Tuesday, 28 April 2009

Nappies, Diapers and decisions

From time to time, someone in the media raises the question "is it better to use disposable nappies (diapers) or cloth ones?" As Tina and I are childless, we have not had to face this problem in person. However, the debate about the answer is a classic case (as in Operational Research) of identifying the system in which you have defined the problem. The family is isolated from the problem of waste disposal, and concentrates on the costs and time needed for using either cloth or disposable. The waste disposal contractor (often local government in the UK) is concerned about the cost of landfill and is not bothered about the family. Society is concerned (ideally) with the total impact of a baby's lifetime in nappies. In the developed world, the option seen in Africa and Asia of letting the child run around without any nappy does not exist.

The speaker on local radio yesterday was a waste disposal person, and from his position, cloth nappies are best. But that is simply to look at the subsystem. According to several websites, and written reports, the choice is too close to call. Cotton growing, manufacture and then washing of soiled items, cause so much environmental impact that it matches the impact of disposable nappies in landfill. I haven't seen this in the O.R. literature.

Coincidentally, the book that I am currently reading (Hungry City: How Food Shapes Our Lives by Carolyn Steel) alludes to a problem which I have not seen in the reasoned discussion of the choice. How easy is it to dry a lot of nappies in a small modern British house or flat? Carolyn Steel raised the question of modern homes which are designed with minimal space in the kitchen, and British building regulations allow construction of houses with very limited floor area. So I wonder whether the answer to the question depends on how big your home is? There's a research area!

Wednesday, 22 April 2009

The secretary problem, and ants

An article has appeared online today in a leading biology journal (Proceedings of the Royal SOciety Series B) about the behaviour of ants, choosing their nesting sites. For an abstract go here.

One of the authors' keywords (why do we speak of keywords when there may be two or more?) is "Sequential search" and that links to several O.R. models for decision making. The best known is the "Secretary problem" where an employer interviews a succession of candidates for a job, and after each interview must say "yes" or "no". The aim is to find the best, or to maximise the rated value of the one selected, or to maximise the probability that the best has been chosen, or .... And it seems to me that the ants in the research paper are solving their own "secretary problem" because the authors report that very few ants in a colony go back to a nest site that they have rejected. It is not the first time that biologists have observed sequential search in living creatures; it happens with birds looking for mates, and selecting nest sites. Long before Richard Bellman, ants and birds were solving dynamic programming problems!

I admit to having a soft spot for the secretary problem. An article that I wrote for an mathematics website for schools is probably the one which has been read by more people around the world than any of my other publications.

Tuesday, 21 April 2009

Psychology and swimming pool management

In my blog of 10 June 2008, I commented on the introduction of free swimming in the UK for over-60s. Then I asked whether there had been any modelling of the likely effects; no answer yet! But the scheme has started, and the swimming pool in Exeter (Pyramids) has adopted an interesting policy to restrict the take up. It is a sort of rationing. The management has to record the number of "free" users. There is also a fear that, as Devon is a holiday destination, there will be significant numbers of users from outside the city and county during the holidays. (This is a genuine fear, as the take-up of free bus travel for the over 60s has been considerable in the holiday areas of the UK.)

So, the pool has a policy that over-60s must register and pay a small fee (£2) for a card; once this has been done, then swimming at that pool is free. Using the swipe card allows a record to be kept of usage. The fee is very small (less than the price of one entry to the swimming pool) but I suspect that the psychology of having to pay even such a small fee will be enough to deter some holiday-makers. A very subtle way of reducing demand, generating a small bit of profit on the scheme, and maintaining records.

Monday, 20 April 2009

Lessons for O.R. from the primary school

The same article in "The Independent" mentioned the primary school at St Ives; there was a thought-provoking quote from its head teacher (Joanne Dean) too. She too stressed the need for lifelong learning for everyone (including the O.R. profession!).

We never think to ourselves:
"That's it; I have learnt all I need to know."
It never happens

Lessons for O.R. from the junior school

Britain's "The Independent" daily paper carries a supplement on education most weeks. Last Thursday (16th April) there was a page about two schools in St Ives, Cornwall. Although St Ives is a popular holiday destination, many local people are not well off, as tourism is low paid, seasonal work. The Junior School had problems when it was inspected in about 2003, and the head teacher, Sue Smith (no relation) was drafted in to sort things out. The feature covered many of her achievements and philosophy.

Two quotes struck me as being relevant to the O.R. profession. First, a homily from her office wall:

In times of change, the learners will inherit the earth whilst the knowers will be beautifully equipped to deal with a world which no longer exists.

Second, the response to Sue Smith's question at the start of school assembly, "What are we doing?":

We are thinking, looking, listening, not talking, and concentrating.

Why the relevance to O.R.? For the first one, it is a reminder that learning never stops; as O.R. professionals, we are agents of change in systems, and that rebounds on us -- we need to be people who learn and change in turn. And for the second, those five characteristics should be the ones we show when we face a new management problem; maybe the fourth is not so relevant, and might be replaced by "Not talking irrelevantly".

Tuesday, 14 April 2009

Travels in a mathematical world

Throughout my career in O.R., I have had a dilemma about the role of mathematics in what I do. When I talk to other people on a casual, friend to friend basis, I often say that I do mathematics, and immediately add that I do the "Interesting stuff, the stuff with everyday applications". When I talk to clients or those sponsoring projects, I may talk about modelling. With students, I will talk about the mathematics that lies behind models, but will stress that these models need to be appropriate, easy to understand, and applied with political and psychological insights. As has been said many times, "A manager would rather live with a problem s/he can't solve than a solution s/he can't understand".

So I am not sure whether or not I ought to be recommending the website:
www.travelsinamathematicalworld.co.uk. It has accounts of careers in mathematical areas, as part of a process of making information about these available to a wide readership or listeners to podcasts. I came across the account by Professor Mike Maher, whose title is Professor of the Mathematical Analysis of Transport Systems at the (UK) University of Leeds. He describes the use of O.R. models in several areas of transport, mainly traffic assignment. He concludes:

"The skills that I enjoy employing are modelling skills - taking a real-world problem, and trying to formulate it as s mathematical problem with sufficient realism that the outputs can be taken seriously but simply enough to stand a chance of solving it. Then formulating some method, an algorithm, by which the problem can be solved efficiently and robustly. And in the field of transport, there is no shortage of problems!"

Isn't that what O.R. is about? Especially, I hope, "enjoyment".

The two-envelope paradox

Over the weekend, I received an email from Moshe Sniedovich in Melbourne. He will probably be flattered to be described as one of the world's outstanding O.R. scientists, but that is my opinion. His great strength is to be able to look at accepted wisdom and question it, taking what is sometimes described as "A sideways look". Anyway, his email alerted me to his developing web directory entitled "Decision-Making Under Severe Uncertainty". The URL is


It is well worth browsing through, especially if (like me) you have a streak of skepticism at the pronouncements of experts.

Today I browsed the article he has written about the two-envelope paradox.

I have just left on your desk two indistinguishable envelopes, each con-
taining some money. I do not know how much money is involved, except
that one envelope contains exactly twice as much as the other.
You can select an envelope, open it, and either keep the money you find
in it – no questions asked – or swap envelopes and keep the money you
find in the other envelope, in which case the money in the first envelope
that you opened will self-destruct.

What should you do? According to the paradoxical analysis, you should always swap, as this will increase the expected amount you will gain. But, in a delightful essay/paper, Moshe explains the mathematics behind this situation. Enjoy!