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?

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.

Tuesday, 12 April 2011

The Geograph Project

Six years ago, I signed up to take part in the Geograph project in the U.K.

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 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.

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.