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.
Friday, 24 June 2011
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 ....
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 ....
Wednesday, 11 May 2011
Lateral thinking
The term "lateral thinking" was coined by Edward de Bono in 1967, and it has become widely used since then. I found myself admiring how some people had been thinking laterally when I was following a country footpath the other day.
Stiles and footbridges on such footpaths work better if they provide some kind of grip for shoes and boots. In some places, this is done by wrapping the wooden planks in chicken wire to make for a ridged surface. However, I noticed that several stiles and bridges now use decking planks instead. These are grooved to provide grip. The popularity of decking means that such planks are readily available, whereas there would be insufficient demand for such planks if the only consumers were people making stiles and footbridges.
Similarly in O.R.; there are solutions which would not be affordable unless some other group of users were also going to use a similar solution and the expense could be shared ... or even completely paid by the others. The moral is to think laterally when a solution has to be implemented.
Stiles and footbridges on such footpaths work better if they provide some kind of grip for shoes and boots. In some places, this is done by wrapping the wooden planks in chicken wire to make for a ridged surface. However, I noticed that several stiles and bridges now use decking planks instead. These are grooved to provide grip. The popularity of decking means that such planks are readily available, whereas there would be insufficient demand for such planks if the only consumers were people making stiles and footbridges.
Similarly in O.R.; there are solutions which would not be affordable unless some other group of users were also going to use a similar solution and the expense could be shared ... or even completely paid by the others. The moral is to think laterally when a solution has to be implemented.
Wednesday, 27 April 2011
Back to the blood donor session
I have written about the sequence of queues in a blood donor session earlier. Yesterday my appointment was later in the session and the system had reached a steady state; so I could observe where the bottlenecks were in the system. I had to wait a long time for the initial medical assessment, but I think that this was because the person in charge was operating a sort of feedback so that he didn't have too many people waiting at the next queue -- or too few either. What surprised me was that there was a long delay once I was on the couch; but I realised that it was a combination of rare events which meant that the nurses were busy elsewhere.
I wonder whether anyone in the blood donor service in the U.K. -- or elsewhere -- monitors where there are bottlenecks in sequences of queues. Not the long delays between doctors and hospitals, but the process within one system?
I wonder whether anyone in the blood donor service in the U.K. -- or elsewhere -- monitors where there are bottlenecks in sequences of queues. Not the long delays between doctors and hospitals, but the process within one system?
Learning from mistakes
One of the stories of the early days of operational research during the second world war relates to the study of where warplanes were damaged when they returned to the U.K.. Each plane which landed was examined, and the places where there were holes in the wings and fuselage were plotted on a schematic. Once sufficient data had been collected, it was clear that the holes were clustered in certain sections of the warplanes. The story goes that someone in the O.R. team pointed out that the important lessons were not about the location of the holes, but about which parts of the schematic had no holes. These were the places where no planes had survived to return, and therefore indicated the vulnerable parts of the planes. These were those which needed extra protection.
I was reminded of this when I read an article in the newspaper about the American surgeon Atul Gawande. He is obsessed with failure in the medical services, and especially surgery. Most operations in hospitals go successfully, but the interest should be concentrated on those operations which go wrong. He asks the question: "Why?". Atul is especially concerned about surgery in the developing world, with the aim of saving lives. So he has written about failure, how it happens, how we learn from it, how we can do better. And he is working with the World Health Organisation to develop tools to help surgeons.
The simplest tool he has popularised is a checklist, that should be followed before every operation "Is this the right patient? Is this the right limb?". It takes two minutes, but saves lives and complications. However one item in the list is expensive; an oxygen monitor. So, Atul has identified this as the obstacle to implementing the checklist, and has persuaded a company to make them cheaply and there is a charity Lifebox which helps provide them.
So how can we learn from this in O.R.? Gene Woolsey has written about lessons that he learnt from some mistakes, but generally we crow about our successes and say little about our failures. Maybe practitioners ought to examine their failures more closely? I remember a couple of my projects which came to nothing because ai took the textbook attitude that the initial description indicated there was very little relevant data, and I said so. The clients reached the conclusion that the project was doomed from the outset. Maybe academics can also learn from mistakes. I advised my research students to document their "Dead ends" in the research programme.
I was reminded of this when I read an article in the newspaper about the American surgeon Atul Gawande. He is obsessed with failure in the medical services, and especially surgery. Most operations in hospitals go successfully, but the interest should be concentrated on those operations which go wrong. He asks the question: "Why?". Atul is especially concerned about surgery in the developing world, with the aim of saving lives. So he has written about failure, how it happens, how we learn from it, how we can do better. And he is working with the World Health Organisation to develop tools to help surgeons.
The simplest tool he has popularised is a checklist, that should be followed before every operation "Is this the right patient? Is this the right limb?". It takes two minutes, but saves lives and complications. However one item in the list is expensive; an oxygen monitor. So, Atul has identified this as the obstacle to implementing the checklist, and has persuaded a company to make them cheaply and there is a charity Lifebox which helps provide them.
So how can we learn from this in O.R.? Gene Woolsey has written about lessons that he learnt from some mistakes, but generally we crow about our successes and say little about our failures. Maybe practitioners ought to examine their failures more closely? I remember a couple of my projects which came to nothing because ai took the textbook attitude that the initial description indicated there was very little relevant data, and I said so. The clients reached the conclusion that the project was doomed from the outset. Maybe academics can also learn from mistakes. I advised my research students to document their "Dead ends" in the research programme.
Tuesday, 12 April 2011
The Geograph Project
Six years ago, I signed up to take part in the Geograph project in the U.K. http://www.geograph.org.uk/
This is a mixture of eduaction and fun, and a challenge and a game. Photographs of places (not people) are linked to the Ordnance Survey (O.S.) grid-square in which the picture was taken. The O.S. maps are divided into squares with side 1km (i.e.metric) and any place in the U.K. can be located by a grid reference. I am sitting at SX 9309 9189 which locates me to within 10 metres. Some webpages will accept that and locate my home on a map or satellite.
The aim of those who signed up at first was to be the first to obtain a photograph for a grid square, and I recorded first "Hits" for about 100 of them. Most of mainland Britain has now been "Geographed" so participation for many people means extending the range of pictures. Within many grid squares there are numerous sites and sights to record, and those who are part of the project try to extend the range in various ways, and to add more squares to their personal tally. At the time of writing, I have photographs recorded in 1118 squares with a further 36 where my picture is only of a close-up detail.
So where does the link with O.R. apply? It first comes with the problem of planning an expedition to add further squares to that total. This could be seen as a variant of the orienteering problem, of finding ones way around check-points in the shortest time. Except that there are no check-points, all one wants are pictures from a square. So in an ideal world, one could stand at the corner of four grid-squares, and turn north-east, south-east, south-west and north-west and take pictures in each direction with negligible distance covered. To get a further two squares, you would have to walk one kilometre to the next intersection and take two more squares. Or you could walk 1.414.km diagonally and photograph three more squares. (I say walk, but obviously, you can travel in any way that you like.) So, travelling horizontally or vertically means that you obtain 4+2N pictures with a distance of N kilometres, i.e. an average of 2+4/N pictures per km. travelling diagonally gives 4+3N pictures for a walk of 1.414N kilometres, an average of
2.121 +2.828/N pictures per km. If you want 6 pictures, walk along a grid line.
If you want 7, go diagonally, If you want 8, go along a grid line, If you want 9 or 10, go diagonally. My reckoning is that for 21 pictures or more, the diagonal is best, but below that, you need to compare the strategies.
Letting H be along a grid line, D be diagonal
5H, 6H, 7D, 8H, 9D, 10D, 11H, 12H, 13D, 14H, 15D, 16D, 17H, 18H, 19D, 20H,
The problem is more serious than this because roads and paths do not allow one to wander at will. So the problem becomes more realistic when you start to impose such constraints, and to impose the obvious condition of returning to the start point. That is left for a future occasion.
This is a mixture of eduaction and fun, and a challenge and a game. Photographs of places (not people) are linked to the Ordnance Survey (O.S.) grid-square in which the picture was taken. The O.S. maps are divided into squares with side 1km (i.e.metric) and any place in the U.K. can be located by a grid reference. I am sitting at SX 9309 9189 which locates me to within 10 metres. Some webpages will accept that and locate my home on a map or satellite.
The aim of those who signed up at first was to be the first to obtain a photograph for a grid square, and I recorded first "Hits" for about 100 of them. Most of mainland Britain has now been "Geographed" so participation for many people means extending the range of pictures. Within many grid squares there are numerous sites and sights to record, and those who are part of the project try to extend the range in various ways, and to add more squares to their personal tally. At the time of writing, I have photographs recorded in 1118 squares with a further 36 where my picture is only of a close-up detail.
So where does the link with O.R. apply? It first comes with the problem of planning an expedition to add further squares to that total. This could be seen as a variant of the orienteering problem, of finding ones way around check-points in the shortest time. Except that there are no check-points, all one wants are pictures from a square. So in an ideal world, one could stand at the corner of four grid-squares, and turn north-east, south-east, south-west and north-west and take pictures in each direction with negligible distance covered. To get a further two squares, you would have to walk one kilometre to the next intersection and take two more squares. Or you could walk 1.414.km diagonally and photograph three more squares. (I say walk, but obviously, you can travel in any way that you like.) So, travelling horizontally or vertically means that you obtain 4+2N pictures with a distance of N kilometres, i.e. an average of 2+4/N pictures per km. travelling diagonally gives 4+3N pictures for a walk of 1.414N kilometres, an average of
2.121 +2.828/N pictures per km. If you want 6 pictures, walk along a grid line.
If you want 7, go diagonally, If you want 8, go along a grid line, If you want 9 or 10, go diagonally. My reckoning is that for 21 pictures or more, the diagonal is best, but below that, you need to compare the strategies.
Letting H be along a grid line, D be diagonal
5H, 6H, 7D, 8H, 9D, 10D, 11H, 12H, 13D, 14H, 15D, 16D, 17H, 18H, 19D, 20H,
The problem is more serious than this because roads and paths do not allow one to wander at will. So the problem becomes more realistic when you start to impose such constraints, and to impose the obvious condition of returning to the start point. That is left for a future occasion.
Monday, 4 April 2011
More on parking meter risk
Last November I speculated about different policies for scheduling the collection of cash from parking meters.
http://iaoreditor.blogspot.com/2010/11/parking-meter-risk.html
On Monday morning last week, the meters in our residential street were emptied. It struck me that whatever rules you have for collecting cash, this was not optimal. There are no parking restrictions at the weekend, so these meters had been full of their money for three nights and 66 hours. Fortunately, the local crime figures have not recorded any vandalism of parking meters in the past year.
http://iaoreditor.blogspot.com/2010/11/parking-meter-risk.html
On Monday morning last week, the meters in our residential street were emptied. It struck me that whatever rules you have for collecting cash, this was not optimal. There are no parking restrictions at the weekend, so these meters had been full of their money for three nights and 66 hours. Fortunately, the local crime figures have not recorded any vandalism of parking meters in the past year.
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