Friday, 24 June 2011

The Science of Better Owl Deliveries

Dear Muggle Friend
As you know, J K Rowling was a student at the University of Exeter in Devon, in the south-west of England. Many people have commented on the way that the author has used links from Devon in her books. Perhaps the best known is "Ottery St Catchpole", which is a very poorly concealed reference to Ottery St Mary; there are also references to Topsham, Ilfracombe and Chudleigh (spelt Chudley by JKR). However, there are further links. The name "Catchpole" is a reference to the former professor of theology at the university; JKR studied in the same building as the department of theology. The name Muggle may be connected to a missionary couple from an Exeter church whose surname is Muggleton. The word "goyle", commonly assumed to refer to gargoyles, is also a Devon dialect term meaning a valley.

But this is all about Operational Research (or Operations Research as Americans call it). Whichever name you use, it is abbreviated "OR". In both the USA and UK, OR is referred to as the "Science of Better". When JKR was at the University of Exeter, there was a successful undergraduate course in "Mathematical Statistics and Operational Research" which was usually known as "MSOR". It may be argued that the author was aware of the abbreviation "OR" and it came to appear in numerous names in the books. DumbledORe is an obvious example, along with the DiggORy family, and on the opposing "side" are the DementORs and lORd VoldemORt. There is the "ORder of the Phoenix" as well. I hope that you are convinced that OR runs through the series of Harry Potter books(?)

One application of OR in the book series is clearly used at Hogwarts. This is the owl post. Postal and delivery services around the world use OR to ensure efficient delivery of letters and packages. The pattern of deliveries used by the Owl post office in Hogsmeade shows many similarities to that used in the muggle world. However, there are a few differences. First, in Hogwarts, the owls have been studied and colour coded to divide them into short and long deliveries. This corresponds to a separation which is seldom used in postal services these days, that of marking letters "local" so that they did not need to be sent to a sorting office. Most postal services have used OR to determine that it is better to sort all post in one place, and hence have adopted the use of zip codes or postal codes. Second, provision is made in the Owl post office for rest and recuperation for owls. In the books, the time for this depends on the length of the owl's flight. In modern postal services, cars/planes/vans/trains carry long distance mail and do not need to rest. The concept of one messenger carrying a package all the way from sender to recipient (as owls do) is seen to be inefficient and has been rejected by postal organisations (with the possible exception of those engaged in espionage).

However, in one regard, postal services can learn from the owl post office. In some episodes from the books and films, deliveries are synchronised for many students at Hogwarts. Although many delivery companies offer "timed deliveries", these are normally timed to within a particular time window ("before 9am", "between noon and 4pm" and so on). I have applied for research funding to explore how to learn from the owls and improve the punctuality and precision of mail services.

I hope that you have learnt a little from this letter, which is my contribution to the June 2011 INFORMS challenge. You may even believe some of it.

Tuesday, 7 June 2011

Critical mass for academic research

The current issue of the magazine "Mathematics Today" (vol 47, no 3, dated June 2011) includes an article Critical Masses of Research Groups in the Mathematical Sciences
in which the authors (Ralph Kenna and Bertrand Berche) have analysed the research ratings of academic groups in the United Kingdom, as recorded in the Research Assessment Exercise of 2008 (RAE2008). It is based on more extensive work that they have published (Critical mass and the dependency of research quality on group size).

In summary, the authors plotted the outcome of RAE2008 (measured as a quality between 0 and 100) against the size of the research group that reported to RAE2008. This yielded scatter diagrams, which can be interpreted as being piecewise linear, with no, one or two "knees" or breakpoints where the slope changes. Small groups get small scores, and the score increases rapidly as the group size increases. At a critical size, the slope is reduced, and the score increases more slowly. A second "knee" means that the slope is reduced still further, almost to flatness.

The interpretation of the "knees" is that they represent critical sizes for research groups. The lower one is the smallest viable size; less than this, and the quality of the research falls sharply. The upper one represents an upper limit, beyond which adding extra researchers will not add to the quality of the output.

Having said that, the authors report that in pure mathematics, the lower critical mass is at most 2, and the upper one is at most 4. For applied maths, the figures are 6 and 13.

But for statistics and O.R., the critical sizes are 9 and 18. In other words, to produce good academic output, O.R. scientists and statisticians need to be in a large group. Our work makes us gregarious; we work well with other people around us. Since I read the article, I have wondered why this should be, and concluded that it is in the nature of academics in these disciplines that they work together well, they have complementary skills, and those skills are heterogeneous, and they like to collaborate in teams. It chimed with my experience and observations. At various times I have been in groups of between 9 and 18, where we worked well together, and the interplay of ideas flowed. I have also been in a smaller group, and then there was much less academic stimulation. One might think that this would also be true of applied mathematicians, but I suspect that they are more homogeneous in academic expertise than those in stats/O.R.. And the pure mathematics area is much more dependent on individuals with their ideas and theories than those who work with mathematical models and statistical data. (Pure mathematicians -- I love you a lot! -- but you will probably admit to flying solo much of the time.)

Many years ago, I found a spoof paper which was written by M.V.Wilkes under the pseudonym H.W.O.Petard on the optimum size of an establishment. It argues that time gets wasted by people reporting to one another ....