Two sides of the "Diet Problem"

Yesterday I contributed a comment to Laura McLay's blog about Operations Research in the USA. She was considering the way that food manufacturers mark the nutritional content of their products. Here are her comments.

I wrote:
There is a similar debate going on in the UK. Our Food Standards Agency has proposed a “traffic light” system showing that certain ingredients are low, medium or high. Some manufacturers have adopted the FSA system, others have refused to use it. Some supermarkets (and in the UK, the food retailing sector is dominated by a few large supermarket chains) have chosen their own systems.

It doesn’t look as if the FSA has used any OR in their research; I would have thought that OR could have helped answer the question that doesn’t really get tackled “What information will people use, and how will they use it?”.

It is possible to see some of the research reports that led to the FSA recommendations at http://www.food.gov.uk/foodlabelling/signposting/siognpostlabelresearch/alt
I was surprised at one response that said 25% of consumers always read nutritional labels. The question which led to this response was badly phrased and it looks as if the response was badly understood. Just watch the shoppers in your local shop; do 25% of them read every label?

Historians of O.R. reckon that Stigler's diet problem was one of the catalysts of the development of linear programming at the end of the 1940's ane early 1950's. I, like many academics, have used nutrition as a simple example of a medium-sized linear programming problem in my classes. Nutrition is additive, and there are one or two interesting constraints on maxima and minima of nutrients in the human diet. Some of them are straightforward, others are expressed as percentages of other nutrients. Many people (myself included) have used data from McDonald's to see if one can find a minimal cost, "Healthy" diet from that chain. [If you have never encountered this problem, then there are two twists in the modelling. The first is the obvious one that the problem really is an integer programming problem. The second is that sachets of sauce are free and contain nutrients; without constraining the number of sachets that you use in a day, the LP solution uses over 40.] The model has a variety of extensions and lessons for the class, for example, concerning shadow prices. [Apologies to those who do not know what a shadow price is; in this case, I used it as a tool to tell you what the maximum price should be for an item that is not in the diet.]

My former colleague, Alan Munford created an integrated database and optimisation tool for mixing feed for animals, who are less choosy about their diets than humans.(Incidentally, Munford's theorem states that for any random variable X, with mean \mu and variance \sigma^2, then for any value k
Probabilty (abs(X-\mu) \ge k^2\sigma^2) \le minimum of((1/k^2),1) [footnote])

My title was "Two sides of the ...". The second side is the one I alluded to in my comment on Laura's blog. People need information. There is an immense amount that you could list about any item of food. What ought to be put on the packaging of processed food? Those with the commonest allergies need to have simple, clear warnings. That is almost straightforward, though there are numerous unusual allergies whose sufferers need to peruse the whole list of ingredients. So those observations give the essentials: common allergies, list of everything. But what about the extra, general information? As I said, the FSA does not appear to have really though this one through, and there is a case for using some O.R. in answering it.



[footnote] Munford's theorem is a joke. Alan introduced it when he was teaching a class of probability, and proved Chebyshev's theorem, which has the inequality
\le (1/k^2). However all probabilities must be less than 1. A few years after this spoof was introduced, a firstyear student told Alan how excited he was to be taught by someone who had a theorem named after them; this student had been taught by one of our graduates who had swallowed the story that this result carried Alan's name.

Digital Britain

Last week the UK government launched a programme based on a report titled "Digital Britain". The aim is to develop the electronic infrastructure of the UK in the next decade or so. The news media have homed in on three proposals from the many (an executive summary of 30 pages seems to go against the desire to be concise). One relates to the funding of the national broadcasting services (BBC), one to the funding of the national broadband network (so every home can have 2MBps broadband by 2012) and the third to the desire to move many FM radio transmissions to Digital by 2015.

Let's look at the second and third from an OR perspective. The proposed funding scheme is a tax of £6 per year on each telephone landline in the UK. (It's not clear if this will be applied pro rata for businesses with internal exchanges.) The media have questioned why such a tax is needed. The government scenario is that the objective of extending the broadband service can only be done by government intervention. An alternative scenario is that commercial operators will develop the broadband provision in response to demand and their financial objectives. So far the operators have done very well without the need for taxes to help. And with the increasing convergence of computer technology and telephone technology, is the scenario seen by the government the correct one?

The third proposal is intriguing. Digital radio in the uK is often referred to as DAB-radio. The government argues that the cost of upgrading the FM network will be about £200million, and this is not worthwhile. Instead, they are looking to manufacturers to develop radios that cost less than £20. So, instead of spending £200million, consumers are expected to replace their radios. Currently, our home has 7 FM radios, plus one in the car. All of these have other functions -- a radio alarm, radios with CD players, an MP3 player with FM radio. So, to replace these will cost rather more than £20 each; unlike TV sets which often have a limited life, radios go on and on and on. Of our 7 household radios, I expect 5 or 6 to be in working order in 2015. Is the scenario of scrapping them a good one? I don't think so.

Finally, the report was launched with a triumphant "We want the UK to be the best in Europe or the world". What about helping other countries to develop in their use of technology? Do we selfishly optimise our bit of the system, or do we think globally and optimise the whole? I favour thinking globally, even if it means that the UK infrastructure is not quite the best in the world!

How not to display data

In an earlier blog, I quoted one of my email signatures which uses the following quotation:
In the information age, somebody has to specialize in the development and presentation of really useful information. Doing that for management and decision-making applications is the core role of Operational Research scientists. (Randy Robinson, the first executive director of INFORMS)

Ever since I read the books "The Use and Abuse of Statistics" and "How to Lie with Statistics" I have been alert to examples of poor communication of data. Today's example comes, I am afraid, from my own university (Exeter).

Here is a map showing the modes of transport used by a sample of employees of the university. I am not sure whether to point the finger at the university or Devon County Council. So what's wrong? A few thoughts to start with.

1) The map covers far too great an area; there should be enlargements around Exeter.
2) The symbols are horrible. A black parenthesis on top of a coloured exclamation mark.
3) When you magnify the map to see the detail (and in most cases, to see the colour) then the symbols are lost.
4) What is the point? Is it to inform?

Let's be positive: could the information be presented in a different way? Suppose that we separated the modes of transport to see where the walkers come from. And those who use public transport? And those who car share? And those who travel less than 2 miles by car? The maps for many of these could be on a large scale. Then we might apply some contours of equal travelling time. But we still haven't answered the question "what is the point?"

Genchi Genbutsu

Genchi Genbutsu is a new expression for me. It was posted in a discussion board, as relevant experience for anyone in O.R.. The wikipedia summary is:
Genchi Genbutsu (現地現物) means "go and see for yourself" and it is an integral part of the Toyota Production System. It refers to the fact that any information about a process will be simplified and abstracted from its context when reported. This has often been one of the key reasons why solutions designed away from the process seem inappropriate.

I don't know why there is so little literature drawing on the parallels between Genchi Genbutsu and practical O.R.; good O.R. requires the modeller to understand what is happening in practice, and you do not learn that by sitting in an office. I suppose that there are eqivalent expressions in English -- "go and see for yourself", "management by walking around", "walk the line". But too many managers (and a few O.R. people) rely on second-hand information.