The blog of the former editor of IAOR

Moving on

2011-09-05T09:30:00.000-07:00

This is my last post with this blog. Now that Preston White is established as editor-in-chief of IAOR, it seems best to stop blogging as "IAOReditor".

So I am launching ORinDevon.blogspot.com as my new blog site.

I remember when networks used the mail

2011-07-29T05:04:00.000-07:00

INFORMS asked us to blog about O.R. and Social Networks.

Once upon a time, O.R. people networked using the mail. In those days, academics would often have a network of people interested in the same branch of O.R., and would circulate drafts of papers by post for comment and criticism. And we networked at conferences, study groups and lectures.

When the OR Society (UK) held its conference in Exeter in 1991, they asked me to chair the event. I invited various speakers from outside the O.R. community to speak at the event. Two were academics. from geography and medicine. Independently they commented that the atmosphere of an O.R. conference was different from the experiences of their disciplines in conferences. They both said that it was much more friendly, and they sensed that O.R. people were less competitive. The networking was both social and sociable.

And then came USENET and the sci.op-research discussion group, which I followed and contributed to over the next ten years. It made for an international gathering, though there were the regular contributors who had a word to say about everything. There were those who thought that they could get help with student homework free of charge, and every so often we had contributions who thought that "op" meant "optical". On balance, I think that the overall cost-benefit of using the discussion group was limited. I could have done more usefully with my time than follow it. But there were days when it was valuable.

And now there are discussions of a kind on LinkedIn and Facebook relating to O.R.; very few people are contributing ... even to the group that hates linear programming.

As an example of a concept used in O.R., both of these recognise that their users form a graph, with each friendship represented by an edge between the nodes of people. So there are suggestions of people that you may know who are two edges away from you. I laugh at some of these. I am "friends" with my wife's sister and her children. But I don't know their circle of friends in the place where they live, even though Facebook tells me that we have many mutual friends. Facebook has an app which plots a friend graph, which in my case is reasonably small. It has several cliques. But I would know that without the app.

So, for O.R., following the new social networks are probably not cost-effective. All in all, I hope that O.R. people will continue to network at conferences, study groups and lectures, and that they will always be both social and sociable events.

The importance of experience

2011-07-13T07:26:00.000-07:00

Three lessons were drummed into us as students of O.R., and I have tried to pass them on to my students.

(1) do not analyse numerical data by machine before you have looked at that data by hand; the analyst needs to have a "feel" for the numbers.
(2) do not assume that the decision-maker who is identified for you by the management is actually the decision-maker; somebody on the spot may actually take decisions which the management do not know about.
(3) observe as much of the system as possible, first hand. Walk the line!

On our trip last week to South Wales, the importance of number (3) became clear. But I doubt if the organisation actually has an O.R. team, but they needed O.R. advice.

We went out to an inn for our evening meal. Like most inns serving food, there was one queue for ordering food, and another for drinks. Food orders were passed to the kitchens and waiting staff, and drinks, of course, were served at once. However, on Wednesday evenings, it was Curry Night. If you ordered a curry at the food counter, then you could have a drink included in the price. This meant that the young lady at the food counter had to leave her place and collect the drink that you had ordered from her. Hence she had to do an increased workload on an evening when there was increased demand at the food queue. Customers for food had long queues, while there were no queues for drinks. Service time could be speeded up in various ways ... passing a token to the drinks bar ... having an extra person to serve at the food queue, all or some of the time. It could also be reduced by having a printed list of what "free drinks" were available, rather than for the staff to have to recite them. All of this could have been noticed if someone with authority had actually observed the queue process, rather than assume that the normal system could cope on the Curry Night.

Result: two very nice curries, reasonable drinks, but lost profits because we didn't go back to the long queue for a sweet.

Mini supermarkets

2011-07-11T08:26:00.000-07:00

A news item at the weekend told that one of the big four UK supermarkets has opened a small city centre store for the first time. Morrisons were joining others (Tesco & Sainsbury and Co-operative) who have both large out-of-town stores and basic outlets in city centres.

The story claimed that the decision had been taken because of the recession, affecting the number of people who shop out-of-town. But the other stores know that there are different clienteles for different types of shop, so there is almost certainly an underlying decision to try and reach the clientele who shop regularly in their city centres. Maybe the recession drew the management's attention to the need to do this?

I don't know how many O.R. scientists work at Morrisons. But I hope that any who are there have read about a study that one of the others commissioned, which led to a change in the way that it handled distribution to its city-centre shops. The study showed that the principles of distribution were significantly different to such stores, compared with the model that was used for out-of-town stores. The O.R. person involved spent three months travelling in the cabs to observe what actually happened, which was not what the staff in head office thought happened. And as numerous O.R. studies have shown, it is always important for the O.R. staff to get involved on the front line, or sharp end.

What's in that truck?

2011-07-11T08:14:00.000-07:00

Last week Tina and I drove from Exeter to South Wales for a two day break (it rained a lot!). On the motorway (M5) we started to pass the time by looking at the articulated lorries coming on the other carriageway. The first "game" was to look out for those labelled with the major British supermarkets. We decided that the rules were to see how long it took before we had a hand of five: Asda, Morrison, Sainsbury and Tesco, plus one wild card from Waitrose, Co-operative, Somerfield etc. We weren't sure whether or not to count M&S, as their lorries might be carrying clothes ... but decided that the big supermarkets also deal in clothes and much else. (Yes, British readers will know that Somerfield doesn't exist as an entity these days, but the Co-operative which has taken it over has not completed the conversion of its fleet. We even spotted a truck whose trailer read Somerfield, pulled by a tractor labelled Co-operative.)

In the first hour, we completed three hands of five, an indication of how much traffic there is into the south-west of England. But we were also interested in the other labelled food trucks. Once, when I was consulting for a major confectionery company, I remarked that you never saw lorries with their name on the side. I was told that when the company started in the UK, they linked to a local haulage company in the same town, and that haulage company continued to carry all the confectionery; the two companies had grown together. So there are many household names which never appear on the sides of articulated lorries in the UK.

But there were two companies we commented on, one selling yoghurts and dairy products, the other selling pasties and pies. How many yoghurts fit into a 40-ton trailer? Allowing for packaging and pallets, we suggested about 30,000 (assuming about 1kg each). And about the same time for the pies, possibly a few more. How many of these products would be sold in one day in a major supermarket? We estimated at least 10 and at most 1000, for both "large" and packages of four. So by the rules of guesstimation, we plumped for 100 per day (geometric mean). With two products, that meant each lorry carried enough for about 150 supermarkets. And with thousands of supermarkets across the country, one could see why it was economical for these companies to haul such large quantities of their products from factory to distribution centre in large trucks.

Next time we use the motorway, we'll be looking out for other named products on the move, and wondering whether the owners have made the decision to run their own fleets for commercial reasons or because it has "just happened".

Networks and social networks

2011-07-02T13:43:00.000-07:00

I was teaching a course on graphs and networks a few years ago, soon after Facebook became popular, and I mentioned that the graph of connections between the students in the room, defined by their Facebook "friends" would be an interesting one. Within 24 hours, several students had asked to be friends; I said that I felt it would compromise me to be linked to some but not all the class. However, we were able to discuss aspects of graph properties that related to Facebook.

I have a love of practical uses of graphs and networks, so was delighted to find a new one. It is the "Map of the World Drawn Entirely Using Facebook Connections" (found here among other places). Based on a large number of connections in Facebook, lines are drawn between them, and the colour of the line relates to the number of connections. Many people have links within their home city, still more are linked within their home country, and then there are international ones.

There are several fascinating aspects to the map. National coasts are very learly defined. Look at Florida, for instance. There are numerous links within the state, and these so outnumber the links to neighbouring states, that the coast of southern USA is clear. The same is true of the west of Britain. There are not many links between Wales and the west of England, so that the Bristol Channel is clearly marked. It is hard to see the boundaries between most countries, though Spain is clearly separated from France and Portugal, and (hardly surprisingly) the boundaries of Israel are well marked.

The author comments on the emptiness of China, Brazil and Russia. There are empty spaces in the world's deserts as well -- in Australia, the Sahara, and Central Asia.

The more I look at the map, the more I find of interest. A wonderful illustration of the power of mathematics and Operational Research.

The Science of Better Owl Deliveries

2011-06-24T07:41:00.000-07:00

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.

Critical mass for academic research

2011-06-07T08:05:00.000-07:00

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 ....

Lateral thinking

2011-05-11T04:11:00.000-07:00

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.

Back to the blood donor session

2011-04-27T04:49:00.000-07:00

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

2011-04-27T04:31:00.000-07:00

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.

The Geograph Project

2011-04-12T09:21:00.000-07:00

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.

More on parking meter risk

2011-04-04T07:45:00.000-07:00

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.

Why OR in sports? Some reflections

2011-03-17T14:54:00.001-07:00

Why is OR applicable to sports?

Many sports have a score, a number, to be maximised or optimised - hence there is a link to OR

Most sports have limited resources, to be used optimally - hence OR, The resources may be the team, or time, or money

Many sports operate sequentially, with decisions being made in order - just like in dynamic programming

Sports events require transport and supply chains - areas where OR has expertise

In a separate blog, I have mentioned the range of sports which have provided abstracts in IAOR. Most of those links are to strategy in the sport itself. My other blog on the subject considers the problems of scheduling transport.

Transport to sports events

2011-03-17T14:42:00.001-07:00

When I studied OR as a postgraduate, we were presented with several scenarios to reflect on their logistical problems. One was related to sports transport.

An event is scheduled at time T1 and finishes at time T2. Spectators arrive by public transport in advance of time T1. Their arrivals are spread over a considerable period, as their plans vary. Some may want to be very early, others arrive in the last few minutes. But the general distribution of their arrivals is widely spread. So the transport provision has to reflect this ... with vehicles scheduled over a wide range of times before T1.

On the other hand, at time T2, all those who arrived by public transport are ready to depart at the same time. So the public transport has to be concentrated into a much smaller time window.

These are the same sorts of problem that one meets in other circumstances, but the size of the crowds at some sports events make the contrasting problems particularly difficult.

OR has been used by the organisers of the recent Olympics to cope with this scheduling problem. And already, the London Underground OR team is planning how to cope with the 2012 Games.

OR in Sport - the index

2011-03-17T14:36:00.000-07:00

This month's suggestion from INFORMS is that bloggers should write about OR in Sport.
The problem that I have about this is knowing where to start. When I edited IAOR, there were numerous research papers that were included in IAOR, and I cross referenced them by sport. So my records show that there were abstracts relating to the following sports:
athletics
baseball
basketball
cricket
croquet
curling
darts
football
golf
hockey
horse racing
karate
netball
Olympics
orienteering
skating
skiing
tennis
volleyball
yachting
So, this is my first contribution - an index!

Reducing wood waste

2011-03-15T09:56:00.000-07:00

It is interesting to see how technology can be used to create something which is ethically and aesthetically pleasing. I have been pointed to the website of a company called Bolefloor who make wooden floorboards. But these are not rectangular boards, they follow the natural curves of the wood, so that there is less waste in shaping the boards.

So, here is their process:
1) take a tree
2) saw it and plane it into planks of uniform thickness (21mm)
3) scan the shape of the edges
4) now optimise -- how can the floor of a room be made of these planks, like a jigsaw, with plain or tongue-and-groove edges, to minimise the waste? Here is the O.R. content, though it looks as if it was people who come from the computer science academic regime who did it.
5) shape the edges and ship to the customer.

Result - a beautiful, unique floor.

Puzzles and logic

2011-03-01T08:39:00.000-08:00

My father had a selection of books of mathematical puzzles, and as a youngster I used to enjoy trying to solve them. Later, we subscribed to a Sunday newspaper, the Sunday Times, which had a weekly "Brainteaser". These were problems of logic and mathematics which we enjoyed solving together. Much to my mother's dismay, some Sunday lunchtime meals were disturbed as he and I debated how to solve the problem.

These were puzzles where the first stage was to sort out the logic needed to solve them. Recently, a number of puzzles have become popular, such as Sudoku. These need logic (and minimal mathematical skill) but the logic is more or less the same each time. I am interested in the reasoning behind the setting of such problems; how can you guarantee that the puzzle can be solved and has a a unique solution?

The Independent newspaper has carried Sudoku puzzles for several years; recently, it has carried a range of puzzles. We have been looking at the ones that are called "Maths Puzzle". These are based around the nine digits 1-9, arranged in a square, with two mathematical operators between the three digits in each row, and between the three digits in each column. Then, at the three row ends and three column feet, are the results of the "sum". The challenge is to work out where the nine digits are placed, given the six results and the twelve operators. See "Maths Puzzle" for an example.

So, I wonder how such problems are set. With nine digits, the checking could be done by brute force very quickly, and that is how I suspect it is verified. The newspaper's problems have an easy puzzle, with two digits entered, and a hard one with one digit entered. Tina and I tackle the problems ignoring those digits. Much more need for logic.

And the O.R. link? The solution is a problem of combinatorial optimisation.

Games and the Acts of the Apostles

2011-02-11T08:57:00.000-08:00

One of the standard textbooks in operational research a generation ago was "Fights, Games and Debates" by Anatol Rapoport. Rapoport distinguished between Fights, where you want to overpower your opponent, Games, where you want to outwit your opponent, and Debates, where you want to convince your opponent. Last week our home group Bible study was looking at chapter 25 and I commented that the story there illustrated those three situations.

The fight: in 25v7, When Paul came in, the men who had come down from Jerusalem stood around him. They brought many serious charges against him, but they could not prove them.

The game: in 25v3, They requested Festus, as a favour to them, to have Paul transferred to Jerusalem, for they were preparing an ambush to kill him along the way.

The debate: in 25v8, Then Paul made his defence: “I have done nothing wrong against the Jewish law or against the temple or against Caesar.”

As is clear from the whole chapter, the various parties present were not working to the same agenda, and hence they never communicated with one another.

Optimal search

2011-02-08T06:12:00.000-08:00

A contribution to the February 2011 INFORMS blog theme, "OR and Love"

Way back in 1997, there was a news story about a psychologist who had published work about optimal strategies for finding a marriage partner. Seeing the report, I wrote a tongue-in-cheek letter to the national newspaper (The Independent) which pointed out that the mathematics behind this was familiar. I also wrote that it had created opportunities for light-hearted examination questions. The newspaper published my letter ... and a few days later I received an email from a mathematician at the University of Cambridge who wanted me to expand on the letter. It is a small world; that mathematician had tutored me as an undergraduate, but hadn't made the association of the signatory of the letter with one of his ex-students. He wanted to use my piece as part of a series of interesting mathematics for schoolchildren.

So I wrote a piece, still light-hearted, and it appears as "Marriage, mathematics and finding somewhere to eat" concerned with optimal stopping (the secretary problem). Cambridge provided the illustrations and a simple interactive game of "Googol".

Since then, that piece has been widely read, and I have had feedback from all over the world. (How I wish that my more serious written work was so widely read!) One friend told me that the item had been posted on her staff-room notice board, and she had acquired considerable kudos when she revealed that the author was a friend of hers.

I followed the article up with correspondence with the psychologist, which never led to a publication, but we learnt a lot from each other. Over the next year, I collected a stack of publications about this problem of optimal search, including several concerned with the mating habits of birds and animals, and the search habits of birds looking for nest sites.

Falling in love is not something to be modelled by O.R. techniques, but finding a partner can be simply modelled as a secretary problem. "A succession of potential candidates present themselves, and you can accept them or reject them. If rejected, you cannot go back and change your mind. What is your strategy to find 'the best'?" There are various variations on the problem.

But there were two bizarre twists to the story, as I heard from adults who had read this article for schoolchildren.

First came an email from an American lady. She asked, I assume seriously, if I could advise her whether her current partner was the right one for her. She asked for a mathematical formula which she could apply to him, to see if he was the best.

Second, another lady wrote (I forget where she came from) asking for my advice about increasing the pool of potential partners. Again, I think it was serious, but again I had to reply that there was no mathematics or other O.R. techniques which could be used in such circumstances.

One thing that the secretary problem does not address is how to approach the problem when both partners are using the search strategy! But dating agencies which encourage sequential search start with an assignment problem ... another O.R. and love technique.

Epidemics and advertising

2011-01-15T07:26:00.000-08:00

I first learnt the power of stochastic models when I had lectures by the late Professor David Kendall (famed for the Kendall notation for queue models http://en.wikipedia.org/wiki/Kendall%27s_notation). He spoke about a simple model of an epidemic, and how that model gave rise to a statistical distribution for the number of people who would be infected. To add variety to his lectures, he spoke of the way that the model could be modified to describe the spread of a rumour (when someone spreads the message to someone who has already heard it, he realises it is a rumour and stops spreading it).

(Incidentally, I wonder whether David Kendall and I come from the same branch of the Kendall family, as my mother was a Kendall before she married.)

Since then, models of epidemics have become very much more sophisticated, but the essentials remain the same. As I write, the UK government is concerned with the spread of influenza in the population. The Labour opposition claims that the advertising about risk should have been started much earlier. In response, the government have spoken about the need to time the adverts for greatest effectiveness. I suspect that there are O.R. models in the background.

Advertising too long in advance is of limited value -- it will be forgotten. It needs to be at a time when it may affect the behaviour of people, who may be infected or susceptible. So the timing needs to be linked to models of the spread of the current 'flu virus. Hence two models need to be linked -- one about the effectiveness of advertising, the other an epidemiological one. But these models are bound to be in the background and, once again, O.R. is the "hidden science".

Marmalade, seasonality, production planning

2011-01-15T06:52:00.000-08:00

It's the middle of January, and this is the time of year to buy Seville oranges. And to make real "English" marmalade, you must have Seville oranges. However, these oranges are only available for a few weeks, from early January to early February. Commercial producers can preserve the fruit and spread the production over the rest of the year, but amateurs have a short window for home production. It is seasonality, but seasonality of supply of raw material, not seasonality of demand.

So yesterday and today we have been making marmalade. Just over 20 pounds of it. (This is one product in the kitchen which we measure in pounds, not in the metric way, because the glass jars we use are "one pound jars" or "12 ounce jars" even though they are labelled 454 grammes, or 340 grammes.) This was two batches in our large jam pan, and my forecast is that it will last us until early 2012. Forecasting demand for twelve months is not generally advisable in industry or commerce, but in our case we know that the rate we use it is about 20 to 24 pounds per year, and we buy a little each year to add variety to the diet, to support charities who sell home-made marmalade, to try other flavours, and because my family know that a jar of "interesting marmalade" will be a welcome present for birthday or Christmas. Given all this, our actual demand for our own marmalade is less than 20 pounds per year, so next year will probably be a "one batch" January. So here is a matter of "make-to-stock" production planning!

The basic recipe can be varied in many ways; extra fruit can be added, in which case the quantity of sugar needs to be increased. This year, for the first time, we have added some fresh pomelo.

Who would have thought that something so mundane could illustrate facets of operational research.

Here's the recipe for a basic batch, which we keep written in one of the cookbooks on an old 80 column punched card!

3lb Seville oranges
2 lemons
5.25 pints water
6lb sugar, which may be mixed granualted and demarara
0.5oz margarine or butter

1: peel the fruit and cut the peel into slivers of the size you like (ours are about 2cm by 2mm [it is easier to give small sizes in metric units])
2: put the peel into 2.25 pints of water and simmer gently for 90 to 120 minutes
3: chop the peeled fruit roughly (we either quarter the fruit or cut it into 4 or 5 slices) and put it all as pith in a large jam pan with 3 pints of water and simmer alongside the peel
4: Drain the pith into a bowl or pan through a colander, and scrape the pith through the colander as well, to give "body" to the marmalade.
5: unless you have two jam pans, now you need to wash the jam pan
6: add the drained liquid from the bowl to the jam pan, add the peel and its liquid, add the sugar and boil steadily ("rolling boil") until a test shows that it has reached setting temperature. (We take a small amount, put it on a saucer, cool it in the freezer for 30 seconds and then see if it wrinkles. Other methods exist.)
7: remove from heat, add the margarine/butter and stir to remove the scum on the liquid. Leave to cool for 6-10 minutes
8: meanwhile, wash your jars, and place in a cool oven to dry and sterilize at about 100 deg C,
9: Carefully fill each jar, and finish off as usual for home-made preserves.

The school which was too small

2011-01-11T03:39:00.001-08:00

The current INFORMS blogging challenge/theme is about "O.R. and politics". It reminded me of a student project a great many years ago. It was never suitable for a research paper write-up, but a blog is an appropriate place to recount what happened.

The city had expanded, and a large housing estate had been built. Part of the development was a new primary school. However, before the estate was complete, the school became overcrowded. It was too small. Not much could be done to provide more space. The local politicians were embarrassed and the local media were not slow to blame them. The student (B) and I were asked to help the council officers make better decisions in the future.

So we interviewed people, read literature, and did our best to become familiar with aspects of planning. We quickly realised that the whole mess was multi-criteria, and many criteria were non-numerical. One of the attributes of O.R. should be the ability to cut through messes. For simplicity, here, we reduced the problem to a two way table. One dimension was the forecast demand, reduced to “Low”, “Medium”, “High” and the size of school “None”, “Small”, “Medium”, “Large”. In each of the twelve cells we wrote down aspects of the consequence of the two dimensions, and then iterated through meetings in which stake-holders could contribute their ideas. So the table of twelve cells became a tool for thinking with for planners and decision-makers. It could be – and was – used in other new developments in the city and region. Nothing high-tech, but we had helped to make the mess less messy. B went on to a career in O.R. and other messy problems.

Among the gems that we learnt along the way were the following:
(1) It takes about five years from initial ideas to opening a school, so the children who will use the school are being born at about the time of those initial ideas;
(2) Families with pre-school children are much more mobile than others, so it is not possible to forecast demand by local surveys of families;
(3) The forecasts made in the past had gone awry because of world-wide economic upheaval;

O.R. at the blood donor session

2011-01-11T03:13:00.000-08:00

When I taught queue models in O.R. at the university I encouraged students to give blood at the regular donor sessions held on campus. It was a good example of queues in series -- arrive -- register -- health check -- give blood -- refreshments, and I urged the students to observe and consider how the system could be improved.

Yesterday when I gave blood, I arrived before the system had reached a steady state and there was little delay. Wonderful! As I lay on the couch, it was possible to watch the donor next to me and the machinery used to shake the blood. The plastic bags holding the donated blood rested on a tray which was programmed to rock. What was odd was that the rocking was intermittent. Up, down, up, down, pause. Repeat. Someone had designed it so that it rocked twice and then paused. Why? Was this an optimal way of rocking the blood? Someone had designed the mechanism, and that design had involved finding a numerical solution to "Rock N times, at rate R per minute, pause S seconds"

Politics in a developing country

2011-01-11T02:50:00.000-08:00

Location-allocation problems appear in many settings, and O.R. scientists have been involved in numerous cases. My research student (S) was concerned for the location of primary health-care facilities in his home country. He came equipped with the data about the villages and towns in one province. Populations, location of existing facilities, which villages had suitable infrastructure, distances between the population centres, and the government's policy for expanding health services in their five-year plan. So he set out to study where facilities should be located if one had a blank sheet to start with, given the five-year plan. Then he added constraints, because it would not be politically expedient to close facilities, so these had to remain even if they were not in the optimal solution. He was anxious to develop a system that could be replicated on a PC in his country, and this was part of S's work.

One constraint which had to be imposed was that each sector of the province should have the same number of facilities, and that the expansion plan should ensure that no sector had more than one more than any other. This was to keep local leaders and government staff happy. So the expansion gave each sector two facilities, then expanded these to three. Given the existing facilities, and the uneven distribution of population in the sectors of the province, these constraints meant that the location of facilities would not be as good as it could be.

So S completed his research, and presented it in his thesis and in seminars. At one of these, an astute member of the audience asked how S could be confident that the province would implement the solution. Developing country politics is not always what westerners are used to, and an O.R. solution might not be accepted by politiicians. "Well," said S, "my father works in the provincial governor's office. The governor will take his advice." He had never disclosed this in his research.

This is my first contribution to INFORMS Blog challenge/theme for January 2011 "O.R. and Politics"

O.R. and some French roads

2010-12-20T07:49:00.000-08:00

I am always intrigued when I find references to some kind of modelling which is identifiable as O.R. in obscure places. A book on the historical geography of France has provided two such observations. ("The Discovery of France" by Graham Robb)

Writing about the mid nineteenth century, "In the Landes, where carriages sank in the sand up to their axles, the engineer Chambrelent calculated that once a road reached a certain length it would be destroyed by the process that built it: 'In travelling to the point where it will be used to prolong the road, one cubic metre of stone or gravel wears out more than one cubic metre of road.'"
The modelling must have been based on some observations and statistical analysis.

Then, about roads later in the nineteenth century, "The chief engineer in the Limousin, Pierre Tresaguet, had insisted that a limit sould be placed on [road] gradients. ... The old road east of Morlaix still includes a needless climb of 15 per cent (1 in 7) because the blundering military Governor of Brittany, the Duc d'Aiguillon, preferred straight lines to the more accommodating curve of the older road that runs alongside. Thanks in part to Tresaguet, it is unusual now to find a climb in excess of 8 per cent (1 in 12). This was thought to be the steepest gradient that a fully laden mule could manage. British mountain roads seem to rise in fits and starts like step pyramids. French mountain roads go much higher, but more steadily, and can comfortably be climbed for hours by a fully laden cyclist."

So far so good; the road builders were given a constraint which had been thought about in terms of the users of the road. But there's a twist in the footnote to these comments, indicating that other people didn't make observations:

"To judge by the army handbook of 1884, it is fortunate that most road building was left to civil engineers:
Gradient on which troops can still march in good order: 25 per cent;
Gradient manageable by mounted horses and light carriages: 33 per cent;
Gradient manageable by mules: 50 per cent;
Escarpment that an infantryman can still cross by using his hands: 100 per cent (completely vertical)"

OR and the holidays (2)

2010-12-20T01:31:00.000-08:00

This blog post contributes to the INFORMS monthly blogging theme. Look for the INFORMS blog to summarize the blogs at the end of the month.

A Christmas tradition in the U.K. is the office Christmas party, when everyone in the company gets together for some kind of celebration. This year, the economic situation has meant that some companies have cut back on the expense of these events. However, my wife Tina's company held one on Friday evening, and the director invited spouses and partners to attend. More importantly, as an O.R. problem, he arranges taxis for everyone to and from the event. To save money, each one is shared by several people, collected on the way from the most distant employee.

So here is the O.R. problem. How many taxis should be ordered, and which routes should they take? It should be recognisable as a "Vehicle routing problem" for which there are numerous soilution approaches. The constraints and interesting features include:
1) some calls have one pick-up, others two; a route which is feasible for one size of taxi may not be feasible for a smaller one;
2) the supply of large taxis in Exeter is limited;
3) there is heavy demand from other users on a Friday evening, so a supplier may not have enough vehicles; should you order taxis from several taxi companies;

It was a good party, though I ate too much. And the Christmas ale ("Raisins to be Cheerful" from St Austell Brewery) was very good.

More about queues

2010-12-13T02:21:00.000-08:00

This is simply a link to a wonderful account of how Disney and other theme parks in the USA manage their queues.
How do you disguise the fact that you are in a queue which zigzags in a snake? You make it zigzag through something that is part of the attaraction. Read about it here.

You can’t have a system if there is no line on it

2010-12-09T03:41:00.000-08:00

Do you believe that "You can’t have a system if there is no line on it"? If you go to this site there's a rap song about numbers, with the refrain above.

What do you think?

Queues, psychology, and collapsing websites

2010-12-09T03:21:00.000-08:00

One of the problems of queues which involve people is to forecast when and at what rate the customers will arrive. Recently, the UK supermarket giant, Tesco, made a spectacular mistake in the run up to the Christmas rush and the holidays. Here's the story:
---------------
The Tesco Big Christmas Exchange
Back in November 2010, Tesco announced it was launching a Big Clubcard Voucher Exchange. Lasting four weeks, it gave collectors of Clubcard points the opportunity to double the value of their vouchers on a large range of non-food items, ranging from wine and computers to Christmas decorations.

A similar scheme was launched earlier in the year. However, Tesco trumpeted the fact that this time the scheme had been revamped, so now customers would be able to exchange their vouchers online.

But it went wrong

The scheme was launched around the time that most customers received their November points statement, early in November. If you wanted to double up your vouchers, the closing date was Sunday 5 December.

Clearly Tesco expected the bulk of interested shoppers to take part once they got their statement through, rather than leave it to the last minute. This was very much a mistake, as news reports and Internet message boards are awash with tales of shoppers facing enormous queues to exchange their vouchers, only to give up and try and do it online. With predictable results, the Tesco website collapsed under the weight of so many users.
------------------
Yes, it was bad understanding of psychology, leading to not enough provision of servers for the customers. There is a great deal of literature about call centres and the behaviour of customers, so someone should have been aware of the likely rush at the end. And, I suspect, there should have been some monitoring of the rate of redemption of the vouchers, which might have given advance warning of the changing rate of redemption. If only 10% of the customers redeemed their points in the first half of the offer, then it might be foreseen that there would be a great demand in the second half.

OR and the holidays

2010-12-03T03:05:00.000-08:00

This blog post contributes to the INFORMS monthly blogging theme. Look for the INFORMS blog to summarize the blogs at the end of the month.

I have two younger brothers, and we all have families. Choosing where to meet, when to meet and what to do for a Christmas family get-together is a multi-criteria decision problem, and our conclusions demonstrate that solutions to a repeated problem change with time as circumstances alter.

One brother (Michael) lives near Leicester, one (Andrew) near Gatwick, and we live in Exeter. For simplicity, these may be regarded as the vertices of a triangle, sides 4 hours, 5 hours and 3 to 4 hours (depending on the traffic around London).

In the old days it was easy. We all met at my parents' home, which was reasonably central. All that was needed was to schedule who travelled when, and help mum with the catering, cleaning and beds. It wasn't too hard to plan what to do.

Even when mum died, we continued to gather at the same place, but we needed to plan a great deal more for the catering.

Then dad came and lived with us, and people came here; with a smaller house than the parents' home, we needed to arrange that Andrew and Michael would overlap for lunch on the day that one arrived and the other departed.

But when dad died, we all felt that there were better times of the year to visit one another. Tourist attractions are generally closed in December, and that limits the scope for days out. So the problem became more interesting. Meanwhile, the next generation was growing up, which brought other people's criteria into the decision process.

We reached a conclusion that we did not need to meet in December, and for several years got together for a Saturday in January, when it was cheaper to travel by public transport, and there were places we could visit together or things we could do together. So that gave a feasible solution, which ticked several boxes for all of us: ease of travel (we each made a train journey with at most one change of trains), a warm place to meet with space for presents to be exchanged, an activity which was pleasant. There was one surprising downside; the presents that we gave had to be compact and portable as we would be carrying them all day.

Then there was a birth and activities which involved theatre or shows in London became infeasible. One year we strolled in London with a toddler, and fortunately the weather wsa good. We all saw parts of the capital which were new, so it was a memorable meeting.

Another birth meant a baby and toddler to be entertained, along with two twenty-somethings who might or might not be around in January, but were more likely to be available in the week between Christmas Day and the New Year. So the weight attached to different criteria changed. We fed our locations into a website (rendeznew) which told us that the meeting point in the centre of the three homes was near Swindon. So we searched for a suitable place to meet and eat there, hopefully with space for the restless children.

And that is the solution at present. Soon after Christmas, three cars (loaded with people and presents) will congregate on a gastropub near Swindon. Each of us will have a two to three hour drive each way, and we have told the staff that it is a family gathering. We are trying out a third pub, for variety.

Could all this be automated? As I have explained, there have been changes in our needs and hence on the emphasis on different criteria. The web site wasn't really needed, as we could see from a map that Swindon was reasonably central, and we had the knowledge of the UK road system to guide us. Once we had found the right locale, we could have searched for places to eat, by specifying criteria (must have car park, serve vegetarian food, be child friendly) but these would be binary constraints (yes/no) and we might want to treat them as slightly soft constraints.

Sometime, I may return to the algorithm used in rendeznew, which has interetsing O.R. aspects.

An astute reader may spot that there is one constraint which we have implicitly included. Nobody wants to stay in a hotel for the family get together.

Supply chain benefits

2010-11-29T07:37:00.000-08:00

Over the last few years, O.R. professionals have given a great deal of attention to supply chains and their behaviour. O.R. people have improved JIT systems, developed algorithms for distribution of goods, and much else. In Saturday's Indepenedent newspaper (27/Nov/2010, page 55) there was an amusing story of the consequences of improving supply chains.

The story reads: "The John Lewis quest for worldwide domination continues with another new initiative designed to ensure shoppers never leave their department stores. Retail Week reports that supply chain improvements have reduced the amount of space John Lewis needs for stockrooms these days, so it plans to turn some of them into beauty spas and hairdressers. It's even promising to install theatrical stages in some of its cafes so you can be entertained while taking a break from spending your money."

Retail Week had the original story in its issue dated 26th November.

The lesson for O.R. models of supply chains is that they need to consider what happens to storeroom space when the needs for buffer stock is reduced. These aspects of the system may not appear automatically in the supply chain model ... but evidently they should!

Parking meter risk

2010-11-15T04:36:00.000-08:00

In the street where I live, there are parking restrictions, so if you park on weekdays between 9:30am and 3:3opm, you must pay. The days and the times are to deter people from parking and catching a bus into Exeter, since the maximum length of stay is 4 hours. This means that there are three parking meters in the street. About once a week, a couple of men in a van come round to collect the cash from the machines.

Come to another city, Portsmouth, where my work has taken me, and there the parking meters in the streets that I use are labelled "No cash is left in this machine overnight". A similar notice applies in the "pay and display" car parks in the city centre of Exeter.

So we have different policies concerning the collection of cash. I doubt whether anyone constructed a model to determine the policy for our street and the different one for the second category. It could be an interesting model to work with. Balance the cost of collection, the amount expected to be collected, with the cost of a machine, the perceived risk of vandalism and robbery from a machine, etc.

Qantas rescheduling

2010-11-15T04:21:00.000-08:00

After a recent "incident" in which an A380 airbus had to abort its flight, all the company's wide-bodied jets have been withdrawn. How does an airline deal with the the knock-on effect of this? They reschedule their flights and passengers. And, we, the public, see the results. Rescheduling has involved the downsizing of aircraft across all Qantas international routes.

Flagship routes to Los Angeles and London from Australia, usually operated by the super-jumbos, will now use older and smaller Boeing 747s, as will all other A380 flights. 100 passengers per flight who were bumped off have been transferred to other airlines.

The downsizing of shorter flights will continue with Boeing 747 flights to Hong Kong and Tokyo now using Airbus 330s, replaced on their normal routes such as Singapore to Perth with even older Boeing 767s. According to the airline, although it is committed to bringing its A380s back into service as early as possible, the new schedules give certainty to those travelling in the near future.

As the Qantas grounding drags on, fares on certain routes have been increased.

That's the public picture; behind this there must have been some complex modelling, which will be kept restricted. Maybe one day, some Qantas O.R. worker will tell us about the models that were hastily built and modified. If you have been involved with a large O.R. problem, then you can imagine what is involved. To replace aircraft A on flight A1 means substituting aircraft B. How many passengers will be lost? What will it cost? But aircraft B was assigned to flight B1 and needs to have a substitute, aircraft C. And so on. Then, the speeds of A, B and C are likely to be different, so there are further consequences.

Which passengers should be bumped? There will be data on the flying habits of the passengers, which can be used to help this. I suspect that the O.R. people at Qantas are busy doing their hidden science!

The greatest invention for queues

2010-11-05T09:21:00.000-07:00

Twice, in the last month, I have been caught in unorganised multiserver queues. In one, long lines formed for each server, and people at the back jockeyed as they watched thelines move. Those in the middle simply were stuck in the queue they had selected.

In the other, people milled around until there was a free server, and by mutual agreement identified the leading person in the line.

Both queues could have been improved by the use of snake barriers, as used in theme parks and at many airports (but not in Madeira, the first place I noted). Surely these are one of the great inventions of queue management?

Perception of value

2010-11-05T09:13:00.001-07:00

The Commissioner for Victims of Crime Louise Casey has called for the right to trial by jury to be stopped for everything other than major crimes such as rape and murder. Casey said: "Defendants should not have the right to choose to be tried by a jury over something such as the theft of a bicycle or stealing from a parking meter."

How valuable is a bicycle? Louise Casey obviously thinks that they are cheap, that cycle crime is minor and trivial. But, has she bought a bike recently? Bikes cost a lot more than the money you can get out of a parking meter, with many worth over £1000, more than some cars. Moreover, organised criminal gangs are responsible for stealing thousands of pounds worth of bikes: for their victims, this is not a trivial matter. According to the British Crime Survey, 480,000 bikes are stolen every year.

(Some of the above has come from the Cyclist's Touring Club (www.ctc.org.uk)). For O.R. scientists, her misconception is a warning; make sure that everyone knows (or agrees) the real value of items in your studies. The classic area is placing a value on the cost of inventory. How much does it cost to store one widget for one time period?

How big a sample? Follow up.

2010-11-05T09:07:00.000-07:00

The results of my sample (blog of October 25 2010) came back this week, and they show no trace of cancer. Thank God!

However, in these days of customised lettters, it was sad to see that the NHS could not use their data in a friendly way. Part of the letter applied to follow-up tests, which happen every two years between the age of 60 and 75 (don't ask how "every two years" fits into a fifteen year period) and then are optional. It is not too difficult to customise the letter to say either "We will invite you to a test in two years time" or "You have reached the age when testing becomes optional".

How big a sample?

2010-10-25T04:43:00.000-07:00

I am always interested in how people reach a decision which involves a numerical answer, because this is often related to O.R.. What follows may be thought to be slightly distasteful -- you have been warned.

One reason for not writing any blogs for several weeks has been travels on holiday, to which I may return later. In the middle of these, I passed a milestone birthday, which was duly celebrated. Soon after that, I received a letter from the National Health Service telling me that they screen all men of my age and over for cancer of the bowel. To do this required me to take samples from material which had passed through that part of my body. (Do I need to say more? No? Good.)

The sample scheme asked for samples from three pieces of material (produced at different times) and two smears from each one, giving six specimens.

So, questions: why two smears? why three pieces? Why not fewer from each and more pieces? I don't know the reasoning, but suspect that the answer is psychological as well as physical. Two eliminates some possibility of contamination. Three is enough for the average person to cope with. Put together, there are enough specimens for the analysts to look at, and reduce the risk of false positives and overlooking the symptoms by accident.

Fair Exchange in 1948

2010-09-13T09:01:00.000-07:00

In 1948, the railways in the United Kingdom were nationalised by the then government. There were four (the "Big Four") railway companies operating in the country, and they acted independently of each other for many purposes. So, after nationalisation, British Railways had a fleet of steam engines from four different stables. Because of the war, many of these locomotives were past their best. Each of the companies had its own locomotive designers, and over the years, each company had developed its own style of locomotive design, to meet the topography of the region, and the objectives of its railway service.

The new management realised that this might be inefficient, so commissioned trials to help find a range of standard steam locomotives. So they mixed and matched, taking locomotives from one stable and running them on the other types of track. The aim was to find the "best".

Now, one of the first questions one asks in O.R. is "What do you mean by best?" According to the history of the 1948 Exchange, nobody really thought of this. Obviously it is a multi-criteria problem, and there are several types of locomotive to be identified and designed. But, even for one type, such as hauling express trains, there are various criteria to consider. The Wikipedia article about the exchange comments:
the testing had little scientific rigour, and political influence meant that LMS practice was largely followed by the new standard designs regardless.

So the optimum was found, not so much by scientific analysis, but by politics. O.R. scientists, beware!

And a little footnote from the book which started me on this story, Amazing and Extraordinary Railway Facts by Julian Holland:
One eminent railway historian was shocked that the Stanier Black 5 type had performed badly; it appeared that the driver and fireman had tried to minimise the fuel consumption during the trial.

So, of course if your staff don't understand the aim of the experiment, they may interpret it in the wrong way. Beware!

A Stanier Black 5

The abuse of forecasting

2010-08-31T04:29:00.000-07:00

Mention the name "Gene Woolsey" to operational research scientists of the 1970s and 1980s, and you will probably get the reaction that he spoke and wrote great deal of common sense, mostly in "Interfaces". One of his stories is how he did a study in a particular factory, and a couple of years later returned on a visit. He said that he wanted to creep away quietly; the solution that he had proposed had been pinned on a board, and was being followed to the last detail. In the intervening years, the environment had changed, so all the external parameters of the model were different, making the solution totally inappropriate.

I thought of Gene last week, when our gas company sent us "Your Annual Gas Statement". It reads
"We've tried to make it as easy as possible to understand."

"Your usage: From 25 Aug 2009 to 24 Aug 2010, you used 15396.49 KWh of gas.
If you continue to use energy at the same rate over the next 12 months, we forecast your cost will be £568.21"

What wonderful precision! Especially as the power consumption is based on reading a meter which is accurate to +/-1 metric unit, and one of those is between 11 and 12 KWh. So, the meter can't determine whether we used 15390 or 15400 KWh, so the last three significant figures of their record are unnecessary. That translates to making the pence in the forecast unnecessary. But these errors are tiny in comparison with the assumptions that we will continue to use energy at the same rate.

It worries me that somebody has thought that this information is intended to be useful. If it was someone from the O.R. department, then I suggest that they creep away quietly now.

If you are from, or know someone from, the O.R. department of British Gas, do let them know of the abuse of forecasts.

Cutting your hedge

2010-08-23T13:29:00.000-07:00

When I taught a course on multiple-criteria decisions, I used the frequency of hedge cutting as an example of conflicting objectives. Should you cut the farm hedges each year, or every two years, or every three years? The more often you cut, the more it costs, but each cut costs less. And hedge-cutting around a farm happens close to harvest time, so there are other annual tasks to schedule. The location of the hedge also matters. Those by tracks need more frequent trimming than others.

Visiting Old Walls Hydro reminded me of these, because the site has just achieved a high standard of conservation, and one requirement is that hedges are trimmed every three years. But there is a complication which I had overlooked in my course. In three years, some hedgerow trees get so large that a sapling in year 0 is a substantial tree in year 3. Should you trim that tree? Or allow it to grow to be a tree?

Models for hydroelectricity

2010-08-23T13:13:00.000-07:00

Last week Tina and I visited the Old Walls Hydro site in Ponsworthy on Dartmoor. Water is taken from the West Webburn river and diverted along a leat to give a 16 metre head of water for two turbines. As a piece of engineering it is fascinating.

Various aspects of the design reminded me of some operational research principles. For parts of the design, the owners were told that what they proposed was impossible. How many times does an O.R. scientist or team meet such prejudice? Too often. Sometimes the problem is posed with a feasible region that is too small, simply because nobody has pushed the limits. Beware of incorrect definitions of feasibility!

Then, there were matters of feedback. One of these concerned filtering the water before it entered the pipes to the turbines. Leaves and other vegetation falls into the leat and is trapped on a wire mesh conveyor belt. Once sensors detect that there is a difference in the level of water before and after this screen, a motor starts and removes a "belt-load" of debris. How should this be powered? The simple answer would be to take the power from the turbines ... but that can be affected by the presence of the debris and could cause the system to collapse. So, the motor is isolated from the hydro power. It runs on a small battery, which of course is then trickle charged from the turbines. The O.R. lesson is that feedback needs to be controlled, so that it gives useful control at all times, and not in ideal conditions.

Rubik's cube

2010-08-12T14:14:00.000-07:00

Rubik's cube is not mainstream O.R., but news about it has made the news today, with the proof that every scrambled position can be solved in 20 moves or less. The announcement is here. It is good when mathematics is covered in the press.

There is a slight link with O.R., but I won't exaggerate it. In theory, you could create a dynamic programming formulation of the problem of solving a scrambled cube. The state would be the description of the cube; the decision would be which of the possible moves to make next; the single stage cost would be one; and the objective would be the minimum number of moves needed to solve the cube from its present state. Stages would be identified with the objective value. But before anyone tries this, note that the researchers looked at 55,882,296 cases (states).

And for the last two years, I have shared an office with Peter Vamos, one of Erno Rubik's cousins.

Farewell to all that

2010-08-11T13:23:00.000-07:00

Today I removed my last possessions from the university campus. Since I retired, I have had the privilege of a little working space on campus, in an office shared with several other active retired staff. I have used it for writing and editorial work, and valued the chance to see and talk with former colleagues.

Alas, that has now come to an end. The office is no longer to be free for the honorary staff, and so I decided to move my last few things home. As I did so, I thought back over the 35 years since I came to Exeter. It is unusual to have spent so much of one's entire working life in one place.

I have had six different offices, in three different buildings.

When I came, the data and programs for my research came with me in two card cabinets, each holding 10000 punched cards. When I left, I needed a USB stick to carry far more data and material. I regret that one of the datasets that was on punched cards has been lost; it can never be replaced, and there was scope for some more statistical analysis to be done on it. Some of the research publications that I had used for my PhD research were on microfiche; that is a medium which has practically disappeared. When I came, I already had a small collection of books and journals that filled about 12ft of shelf space. Even with pruning, I have three times that space for professional material.

When I started, the language of choice for programming was Fortran. That was my fifth language (after Algol 60, Titan Autocode, Basic, CSL). We progressed through Simula, Pascal, C and C++. The first desktop computer we used was a PET, but we never did any research on it. A research grant provided a more substantial machine in 1981 or 82, which used 8inch floppy discs, and compiled a Pascal program in about 20 minutes! Olivetti PCs arrived in 1986, and thereafter most of my computing was based on PCs.

What changes will there be in the next 35 years?

Algorithms for better public transport

2010-07-30T05:31:00.001-07:00

It is always pleasant when an operational research project is commented on in the media. I spotted this in Boing Boing, an online blog which I find fascinating and also frustrating. The story is about a research project into better algorithms for timetabling public transport, and has the acronym ARRIVAL, meaning
Algorithms for Robust and online Railway optimization: Improving the Validity and reliAbility of Large scale systems.

ARRIVAL is hosted in Greece (here), but has been an international research project, sadly without UK involvement. It has produced several published research papers, as well as practical solutions to transport problems.

EURO XXIV (EURO24) in Lisbon, part 2

2010-07-21T06:02:00.000-07:00

I realise that my first blog about the conference was a little negative. Let's look at the good things about conferences.

I met a great number of people, renewing old friendships, and in a few cases, starting new ones. Conferences are great for this, especially if most of the time, you are beavering away in one place, not meeting like-minded people. I have several friends who I have only met at conferences. It is even a good place to see friends from other parts of the U.K.. Of course, one shouldn't really admit that one goes to conferences to meet people; as far as our paymasters are concerned, we go to present our research work and to listen to other people present their research work.

That's the theory. In practice, many of the presenters are there to "Tick the box" of conference presentation. There is not enough time to discuss the material in depth in the sessions. And people work in tight little niches. So the chances are that you won't get many questions that stir new ideas.

But it was good to be part of this conference. Jim Cochran gave an excellent plenary session about teaching O.R. and making it interesting. The best attended session that I went to was on financial optimization and had some good papers. The worst for attendance was on sustainable development ("we are working on sustainable development for developing countries. To calibrate our model, we are using Luxembourg.") A good number turned up to a session on graphs and networks, but fewer were interested in water systems. And in all these, there were interesting models being discussed.

The conference organisers had excellent catering, apart from the reception. Endless coffee, chilled bottled water, fruit juice or squash, and biscuits to eat. Lunch was one of the easiest conference lunches I have known -- huge buffet tables, so very little queueing.

Springer had a demonstration of their touch-screen library, with 200 books available. All could be read and re-read on screen, though I wonder how long before their text books are on an electronic book?

The sun shone; Lisbon is beautiful, though the university campus could do with more effort clearing rubbish and repairing pavements. I wondered why there were so many police on the campus.

Locating emergency ambulances

2010-07-16T14:39:00.000-07:00

The ambulance station in Exeter is on the east side of the city. The city is divided by the river Exe, and the bridges across the river form a bottleneck for traffic. Quite often there is gridlock on the roads approaching the bridges.

So the ambulances are deployed away from the station at times of peak traffic. Yesterday, Tina and I were walking by the river and we spotted such a redeployed ambulance parked by the footpath. It made me wonder ... about the policy for deploying ambulances. This one was placed so that it could cross the river, or leave the city to the north and west. In either direction, the response time would be about ten minutes less than if it started from the base station. My wondering focussed on what conditions prompt such deployment. Is it when the traffic is reported to be at a particular state? Or simply at particular times of day? Has anyone worked on this?

I was reminded of the policy of French traffic police that I saw on holiday; they were deployed to busy roads and junctions and set up tables to deal with on-the-spot fines.

EURO XXIV (EURO24) in Lisbon

2010-07-16T13:59:00.000-07:00

I spent some time in Lisbon this week for the 24th EURO conference. EURO is the association of national OR societies from Europe (plus those in Israel and Africa). It was based on the university campus, running from the evening of Sunday 11th July and ending late on Wednesday 14th July. For various reasons I couldn't stay for the last day.

As usual, I have come away from the conference with mixed feelings. It was a huge event, with about 2,700 delegates from the European nations and beyond. Many of them were research students presenting their work in a forum related to Operational Research.

As usual, when things went wrong, I stopped to wonder how things could be improved. So here are some general suggestions for any conference ....

1) Learn from the mistakes of other people. Some things go wrong every time, in different details. One of the disadvantages of EURO is that there is insufficient corporate memory. Each conference is arranged without much having beenlearnt from earlier ones.

2) Consider all the bottlenecks in the queues and points of service associated with a conference. Delegates need service with their registration and need to be able to use the conference website to answer a range of questions quickly and without having to go thorugh too many hoops. So the website should be simple to use and comprehensive. Registration on site is the first queue most people encounter and it should be as simple and quick as possible, which means that efforts should be made in advance to make service times as short as possible OR to have lots of people to give service. To complete my registration I needed to join three queues (for my badge, for my confernece bag and papers, for my banquet ticket). If I had gone on the excursion, there would have been another queue. At other events, these queues could be replaced by one. Similarly, catering queues need to be minimised. It doesn't take advanced use of queue theory to work out that 2,000 people gathering for a buffet meal need a lot of service points. 100 servers perhaps?

3) Help the delegates to find their way around. The home team knows its way around the buildings, but everyone from elsewhere doesn't so they need signs that can be found easily and read quickly.

4) Make sure that the rooms are suitable for the meetings. I spent an afternoon in a room directly underneath the waste pipes of the ladies' toilets, so there were regular sounds of flushing. Another session was in a warm room, and the window opened in such a way that the screen was obscured by the frame.

5) For presenters. Do think about what you should put in your presentation. Nobody will take in your equations and constraints with a hundred variables -- my record was seven different subscripts in the equations on one screen. And large tables are too much to take in during a fifteen minute presentation. There is only time for two or three main points, and then these need to be put simply and clearly.

6) Also for presenters. Do rehearse the presentation, and do it with an audience who will be honest with you. Because the presenters come from all over the place, some of them are less fluent in English than the Brits and other English-speaking countries. Going through the presentation several times before will deal with nervousness, and keep the talk to its time slot.

7) For session chairs. Keep strictly to the timetable and follow your instructions carefully. At EURO the majority of sessions lasted 80 minutes with four papers. They were supposed to keep to 15 minutes presentation, and 5 minutes discussion. Chairs were to keep an eye on the time and stop the speaker. That allowed delegates to move between sessions at those 20 minute intervals. And if presenters didn't show up, then there should be a gap, because there could be people switching sessions to hear the talks at their scheduled times. Did this happen? No ... talks over-ran, chairs failed to stop them, and if there were no-shows, they just went on with the next paper.

8) For everyone, especially those with major responsibilities; there is a time and place for everything, and some plenary sessions are not the times for unnecessary announcements and speeches. For many EURO delegates, a lasting memory of the conference will be the description of how to adjust the conference souvenir bag that was given after the conference banquet!

Revenue management in the news

2010-06-01T03:00:00.000-07:00

Two stories about revenue management have been in the news recently. As I heard about them, I wondered what data had been used within the companies concerned to inform the decisions.

Ryanair, the budget airline, has announced that the cost per item for checked baggage will be higher in July and August than at other times. (£15 per item normally, £20 in July/August; those are the online fees; in person at the airport costs more, and so does the second item). Ryanair reckons that the introduction of fees for checked baggage has reduced the number of passengers with hold baggage from 80% to about 25%. Presumably the company expects that there will be an increase during the holiday months, which will mean that they will need more ground staff, more fuel and possibly fewer passengers.

The other story concerns telephone charges. For many years in the UK, phone calls between 6pm and 8am during the week have been cheaper. Earlier this year, BT (British Telecom, phone provider) changed this period to be 7pm to 7am, and recently another supplier, TalkTalk, has followed suit. It is suggested that the motive is more concerned with profits than regulating peak demand, since the hour 6pm to 7pm is not generally used for business calls, more for domestic. It may be that there is high demand for domestic internet services in the early evening, and therefore this is an attempt to shift telephone demand away from that period. But the companies are not saying.

One of the speakers on this subject was described as working in "Pricing consulting" and I thought to look up such businesses on the internet. I really should know better! "Pricing consulting" led to numerous pages advising how much to charge for consultancy! The perennial problem of words which can be nouns or verbs.

Genetic algorithms

2010-05-26T05:59:00.000-07:00

I am ashamed to admit that I was slow to appreciate the possibilities of genetic algorithms. Way back in the 1980's, pre-internet, my colleague Keith and I were visited by a group of researchers from a local compnay who wanted to set up a project with our OR staff at the university. One of them asked if I had thought of using GAs. At that time, I had never heard of them; it was two or three years later that I next encountered them, and I suspect that if we had known even a little about GAs when the project proposal was being put together, we might have been able to contribute some applications in the literature. Since then, some of my work has used GAs and other meta-heuristics.

I was amused to discover the cartoon in xkcd, which imagines what might happen if food recipes were created using GAs.

It reminded me of other examples of cross-over from GAs to everyday life. Ian Stewart imagined evolution of crosses between cats and birds, with an imaginary landscape of various combinations of cats with wings and birds with paws. There have been several research projects for creating abstract art by GAs, and some of these projects have linked the concept to abstract music as well. Somehow, even if we had caught on to the idea of GAs after that casual conversation, I don't think that I would have gone into computer art!

Snow, cold and outlying data

2010-05-17T05:11:00.001-07:00

One of the recurrent problems of production monitoring is to try and determine if a process is out of control. Observations are made at various times, and from these, one is supposed to determine whether or not there are problems.

An article on the website of KNMI (the Dutch Meteorological Institute) asks whether the winter of 2009-2010 was unusual. It is here. The author asks whether the weather was unusual, by looking at various statistics from different parts of the world. What makes the page so interesting is the way that the statistics are considered with and without a model that incorporates global warming. It is a reminder for O.R. workers doing control modelling to make sure that observations are related to the correct underlying model.

Marshmallow towers

2010-04-28T04:40:00.000-07:00

I wish that I had more time to look at some of the amazing/fascinating talks at TED (www.ted.com). I came across Tom Wujec's short talk about his "Build a marshmallow tower" this week (Thank you to Boing Boing.)
http://www.ted.com/talks/tom_wujec_build_a_tower.html
Among the lessons from the research are that successful projects need organising, they need specialist expertise, and that there is great value in iteration, testing and improving. (Note the success of groups with someone with organisational skills, the work of architects, the kindergarten students.)

These lessons apply to O.R. projects as well.
(1) Time spent planning is seldom wasted;
(2) O.R. is not just about techniques; there needs to be experience of project work provided by a broad exposure to O.R. work
(3) the process of O.R. model-building ought to be iterative, with feedback from simple models feeding the refinement of the next development of that model.

O.R. on a trip to London

2010-04-19T05:57:00.000-07:00

We went to London for a two-day break last week, and, inevitably, I looked at some of the experience with a pair of O.R.-problem-seeker's spectacles. Two of the things I saw are worth recording.

We went to the theatre (Phantom of the Opera); earlier in the year we had booked online and bought the cheapest tickets on sale ... even for a treat like this, we couldn't face paying some of the prices. The cheapest seats are £25; in Exeter and Taunton, where we generally go to the theatre, the most expensive seats are less than £20. When we got to the theatre, we discovered that the section in which our seats were located was closed for the evening, and we were bumped up to higher quality seats ... in fact the most expensive ones, at £59 each. At no charge, of course. So here is the cheapskate's optimal policy for theatre-going. Book well in advance, for a midweek (less popular) evening, in the cheapest section fof the theatre. Then wait and see what happens when you arrive. At worst, you have your seats. But you may get an upgrade instead. (Oh, and take your own chocolates ... theatre prices are high!)

We bought Oyster cards to pay for the trips around London on the bus and tube. The cost of fares is deducted from the balance on the card, up to a daily maximum, which depends on where you travel and when. So, off-peak, in zones 1-2, the cap is £5.60, which is also the price of a day card. We didn't save much except time with that. We did save when we used the tube in the morning rush-hour. Even then, the scheme has a cap on the day's deduction. Looking at the calculation of caps, we spotted an anomaly. For someone whose use of the system consists of one journay in the morning rush-hour and a number of journeys in the off-peak season, the cap may be more than the combined rush-hour fare and the cost of the day card. So it is better not to use the same Oyster card for the rush-hour and the rest of the day. So here's the optimal strategy for anyone doing this type of day's travelling very often. Have two cards. Use one for the rush-hour, and the other for the wandering about. It depends on what zones you are using, so I am not going to spell out what to do ... an exercise for the reader.

Queues in Nationwide Building Society

2010-04-19T05:43:00.000-07:00

I suspect that the problem of queue control is the most obvious area where O.R. has made impacts on everyday life. Certainly, it is the example that I use in my "cocktail-party" explanation of what O.R. models.

Last week, the U.K.'s largest building society, the Nationwide, announced that any of its card customers wishing to withdraw less than £100 would have to use a cash machine (ATM = Automatic Teller Machine). This was an attempt to cut queues. The building society, like most others, offers numerous financial services, such as mortgages, savings accounts and insurance. Already, there are attempts to reduce the queues at the tellers, by filtering the customers according to the type of transaction. In Exeter's branch, there are four tellers, and a single queue, with several assistants on the customer side of the tellers who ask people who are queueing whether their transaction could be handled in some other way.

But the latest move has attracted criticism, as the customers who are most affected are thought to be those who are least comfortable with the ATMs -- the elderly, the disabled .... Maybe those customers could be encouraged to sabotage the scheme by carrying (say) £80, queueing to deposit it, and then withdrawing £100 at once. That way they will get the £20 they need, and without facing the (to them dreaded) ATMs.

Where does this quotation come from?

2010-04-17T12:25:00.000-07:00

We were in a seminar today about God's work in mission and this quotation was thrown into the discussion. It doesn't feature (yet) on Google, so I am putting it here for Google to find!

"If the impossible is not part of our plans, then God is not one of our partners".

What does that have to do with O.R.? Not much, but it is a reminder that O.R. cannot be applied to Christian work because of God's role in it!

Marriage as an optimisation problem

2010-03-15T04:06:00.000-07:00

I do not read the UK national newspaper "Daily Mail" very often, but I bought a copy on Thursday 4th March 2010 to read on a rail journey. To my astonishment, there was a whole page based on a research paper in the European Journal Of O.R.

The paper was never cited, so I had to use the journal's webpage to find the item concerned. Details are below.

The author of the newspaper's article, Mark Barrowcliffe, used his marriage as a counter-example to the conclusions of the EJOR article. He concludes:

"The elements of love are nothing more complicated than passion, companionship and mutual respect. And if you've got those in abundance, who really gives a spud what the European Journal of Operational Research thinks anyway?"

Personally, I remember the question which was asked by modellers in O.R. during the second world war. The model in question was about the optimal size of convoys, to minimise losses. Before the solution was put into practice, the team were asked "Would you trust your children to cross the Atlantic in such a convoy?" Maybe the researchers should have asked "Would you like your marriage to be organised on the basis of a mathematical model?"

European Journal of Operational Research, Volume 202, Issue 2, 16 April 2010, Pages 547-553
Innovative Applications of O.R.
Optimizing the marriage market: An application of the linear assignment model

Nguyen Vi Cao, Emmanuel Fragnière, Jacques-Antoine Gauthier, Marlène Sapin, and Eric D. Widmer

aHaute Ecole de Gestion de Genève, 7, rte de Drize, 1227 Carouge, Switzerland

bUniversité de Lausanne, Institut des trajectoires biographiques/Centre, PaVie Bâtiment Provence, 1015 Lausanne, Switzerland

cUniversité de Genève, Département de sociologie, Uni Mail, 40, Bd. Pont-d’Arve, 1211 Genève 4, Switzerland

dSwiss Foundation for Research in Social Sciences, c/o Université de Lausanne, Bâtiment Vidy, 1015 Lausanne, Switzerland

eUniversité de Lausanne, Centre de recherche Méthodologie, inégalités et changement social (MISC), Bâtiment de Vidy, 1015 Lausanne, Switzerland

fUniversity of Bath, School of Management, BA2 7AY, UK
Received 23 January 2008;
accepted 3 June 2009.
Available online 18 June 2009.

Abstract

Research shows that the success of marriages and other intimate partnerships depends on objective attributes such as differences in age, cultural background, and educational level. This article proposes a mathematical approach to optimizing marriage by allocating spouses in such a way as to reduce the likelihood of divorce or separation. To produce our optimization model, we use the assumption of a central “agency” that would coordinate the matching of couples. Based on a representative and longitudinal sample of 1074 cohabiting and married couples living in Switzerland, we estimate various objective functions corresponding to age, education, ethnicity, and prior divorce concerning every possible combination of men and women. Our results show that the current state of previous termmarriagesnext term or partnerships is well below the social optimum. We reallocate approximately 68% of individuals (7 out of 10) to a new couple that we posit has a higher likelihood of survival. From this selection of new partners, we obtain our final “optimal” solutions, with a 21% reduction in the objective function.

Keywords: Couples matching; Divorce; Linear assignment model; Marriage market; OR in societal problem analysis

http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VCT-4WJHB57-1&_user=122866&_coverDate=04%2F16%2F2010&_alid=1249518507&_rdoc=1&_fmt=high&_orig=search&_cdi=5963&_sort=r&_docanchor=&view=c&_ct=65&_acct=C000010082&_version=1&_urlVersion=0&_userid=122866&md5=4dc338c24d645e812002a3284a3d0b99

Small schools and multiple criteria

2010-02-17T02:47:00.000-08:00

The county of Devon, where I live, has many areas where there are small villages and few towns. The population is concentrated in the towns and cities, but a significant number of people live in the villages and commute, or work locally. Today there has been some discussion about the provision of education for children and a report about Devon has identified several primary schools with fewer than 30 children in the whole school (age 5 to 11) and one secondary school with less than 500 children. The report raises the question about the viability of such schools, based on the cost per capita. Fairly obviously, education is an area where there are economies of scale -- you need a couple of teachers at least in each school, you need buildings and these must be heated and lit whther there are 10 children or 50.

So should small schools be closed and the pupils transferred to larger ones, where the cost per child will be smaller? I suggest that this would make an interesting question for an examination on multiple criteria optimisation or soft systems. There are other factors than the cost per capita to consider. Schools in small communities are a social focus for those communities. Families and children belong to them. What are the effects on children if they have to spend an extra hour at each end of the school day in travel?

Listening to the radio discussion this morning reminded me, once again, that operational research needs to be multidisciplinary. The figures matter, but behind those figures are people with needs and aspirations that cannot be measured.

The Bishop and Wartime O.R.

2010-01-12T05:25:00.000-08:00

Earlier this year, Bishop Graham Leonard died. He had been Bishop of Truro (next door to Devon) and then a very distinguished Bishop of London. In his obituary in the "Church Times" there was a one-sentence reference to the fact that during 1944-1945 he had been seconded to the Army O.R. group. No further explanation, and I wondered how many of the readers of the paper would know what O.R. was. A further search led to a national newspaper recording that he had worked on fuses. That led to yet another search using the keywords "Operational Research" and "fuses" which didn't turn up any more about the late bishop.

However, the search turned up a reference that in 1944-45 the Army O.R. group had been working on fuses used against the V2 "flying bombs". And that reference was also fascinating, as Dorothy Hughes one of the first four lady "Chelsea Pensioners" had been involved with that section.

Automated attendants

2010-01-08T07:55:00.001-08:00

I learnt a new technical term today: "automated attendant". It describes the telephone systems that are familiar (and often infuriating) in the 21st century. The caller dials the number, and an automatic service directs the caller to select a service using the buttons on the telephone. There are all sorts of jokes about this and I found a You-Tube video of the song "Press one for English".

My curiosity was aroused when I rang the offices of a national club in the UK. The club advertises that it has 60,000 members. When an automated attendant answered, I wondered what the economies of such a system might be. At what size of organisation does it become worthwhile to install one? Has anyone done an O.R. study of this? There needs to be a measure of the number of calls that come to the office per day, both on average and -- for a club -- the peak times for renewals. And there's questions of the number of people in the office whose job includes answering the phone. It could be an interesting study. The model would be straightforward, the data collection more challenging. However, I have discovered that the systems are so cheap, that they are probably worthwhile for more offices than currently use them.

Operational Research in Iran

2009-12-14T04:47:00.000-08:00

A new journal of O.R. has been launched, and has now published two issues. This is the Iranian Journal of Operations Research, published from Tehran. On first glance, its contents are generally theoretical, but that is true of many other O.R. related journals. The first abstracts from it will appear in IAOR in early 2010.

What is not clear is hows strong the fledgling O.R. socety is in Iran. The web address suggests that there may be plans for it to develop, but the English version is limited at present.

The best statistic I have heard for a long time

2009-11-30T02:30:00.000-08:00

BBC Radio 4 has a flagship news and current affairs programme every weekday morning called "Today". Following one interviewer's comment, the presenter commented "The best statistic I have heard for a long time". He then paused and added words to the effect that the statistic was not good news, but had been presented in a clear way so that the meaning was easy to understand. It strikes me that those of us who work with mathematical models could learn from this example.

The interview had been about the social deprivation of parts of the east of London, and the comment was made: "for every tube stop on the Jubilee line [on London Underground] going east, from Westminster to Canning Town, life expectancy decreases by one year". It is not good news. But the information is conveyed in a way that is clear, simple and easy to assimilate. It is not cause and effect. Underground stations do not affect life expectancy. But one has a clear sense that the further you travel along the line, the more social deprivation, leading to lowered life expectancy, you will encounter. And the figure of "one year" is probably a rounded version of the data ... but for the purposes of this graphical illustration, it is precise enough. Someone has found a way to present information, which is of use to planners, in a way that is easy to take in. So we can learn from the example.

But, as usual, the story above is only part of the story. The statistic has been created by using limited information and extending it. The data which had been used said that the life expectancy for residents near Westminster station was seven years more than that for people living near Canning Town. They are eight stations apart. Nobody has written abot the life expectancy at those intermediate stations. All that has been done is to draw a straight line between the two extremes and assume linearity. Even though the method is not rigorous, it is still graphic. How can we learn to strike a balance between rigour and clarity?

Optimising a sound system

2009-11-09T05:23:00.000-08:00

A curious story came my way, which is a piece of optimisation which has never been (and probably never will be) written up as an academic paper. But that's true of much applied O.R. all the time. Even academics who need to publish find that some of their studies are simply unpublishable. The story came from Dustin Curtis' blog.

He described meeting a sound engineer who set up ambient sound systems for Walt Disney World. Here's an extract:

In the mid 1990’s, the park started researching the problem. It would eventually find no existing solution, so the engineers had to design and construct, on their own, one of the most complex and advanced audio systems ever built. The work paid off: today, as you walk through Disney World, the volume of the ambient music does not change. Ever. More than 15,000 speakers have been positioned using complex algorithms to ensure that the sound plays within a range of just a couple decibels throughout the entire park. It is quite a technical feat acoustically, electrically, and mathematically.

Just think what O.R. tools would be needed for that sort of optimisation and design!

Smeaton's Tower

2009-10-19T03:19:00.000-07:00

On 16th October 1759, Smeaton's lighthouse on the Eddystone Rocks (14 miles out of Plymouth) was illuminated for the first time. The original lighthouse has been dismantled and re-erected on Plymouth Hoe.

To mark the anniversary of this pioneering building, it was illuminated by candle-power once again on the evening of 16th October 2009.

The lighthouse featured on British one penny coins until 1970:

Why mention this in a blog about operational research? Logistics. 250 years ago, the lighthouse was illuminated by 24 candles. Three lighthouse keepers had the job of ensuring that these were lit all night, every night. They were dependent on supplies from the mainland, and the lighthouse was notoriously difficult to reach. Sometimes the keepers went for weeks without fresh supplies. So, here's the problem: how did the stock controllers plan for candles, food and supplies for the lighthouse? Apart from fresh fish, there were no other sources of food on the Eddystone Rocks. Sometimes the keepers were starving when boats reached them from the mainland. It makes academic models of inventory management seem ... academic.

And now for something different:

The Keeper of the Eddystone Light

My father was the keeper of the Eddystone light
And he slept with a mermaid one fine night
Out of this union there came three
A porpoise and a porgy and the other was me!
Yo ho ho, the wind blows free,
Oh for the life on the rolling sea!

One night, as I was a-trimming the glim
Singing a verse from the evening hymn
I head a voice cry out an "Ahoy!"
And there was my mother, sitting on a buoy.
Yo ho ho, the wind blows free,
Oh for the life on the rolling sea!

"Oh, what has become of my children three?"
My mother then inquired of me.
One's on exhibit as a talking fish
The other was served in a chafing dish.
Yo ho ho, the wind blows free,
Oh for the life on the rolling sea!

Then the phosphorus flashed in her seaweed hair.
I looked again, and my mother wasn't there
But her voice came angrily out of the night
"To Hell with the keeper of the Eddystone Light!"
Yo ho ho, the wind blows free,
Oh for the life on the rolling sea!

by: Charles Wingate

How many items make a pack? part 3

2009-09-09T02:49:00.000-07:00

Two more odd sized packs for the record.

Tesco supermarket is selling packs of Broccoli with a nominal 335gm ... why? .. so they can sll them at 50p each and display a price of £1.50 per kilo!

A mail order company offered me packs of paper hand wipes (see part 2) with 260 in a pack.

How many items make a pack? part 2

2009-09-01T04:08:00.000-07:00

Today I gave blood (it was, according to the records, my 66th time). The UK blood donation service collects a donation of 470ml. Why 470? I asked, being an Elephant's Child with insatiable curiosity (or "'satiable curtiosity" as Kipling wrote).

The service decided on 470 because it was found to be an amount that a healthy donor of minimum weight can safely give; if it were to be increased, then it would prevent some donors from giving. If it were reduced, then handling it (because each donation is divided into parts) might become difficult. So it is 470ml (or equivalent because it is weighed) for good reasons.

How many items make a pack?

2009-08-24T03:28:00.000-07:00

From time to time, I observe a package or a product in a shop or elsewhere, and wonder why the manufacturers have selected a particular size or number of items.

On my website, there are pictures from the ROCARO conference in Niamey in 2004, including a picture of a beer bottle holding 48cc. Why 48?

The paper towels in the washroom here come in packs of 180 towels. Why 180?

British food packaging is plagued with anomalous sizes. Jam, marmalade and numerous other items are sold in packs weighing 454gm or 340gm (equivalent to 1 pound, or 12 ounces). Flour is sold in bags weighing 1.5kg -- a reminder that it was formerly sold in bags weighing 3 pounds (why 3?)

For the final consumer, these assorted sizes are little more than an irritant; but within a supply chain, they can be more serious.

Now I shall start to collect and report odd-sized packs.

More about psychology

2009-08-24T02:39:00.000-07:00

It is salutary to remember that the second world war, which had such an influence on my childhood, is now studied as "history" at schools. Although I was born several years afterwards, the war was sufficiently recent to affect me in various ways. Added to the change in "distance" is the change in technology and communication.

It was natural for my training in O.R. to begin with a little of the background to O.R. from WW2; we were all peers, in the sense that we had grown up with family experiences from parents and relatives of the horrors of that conflict. And our lecturers on the postgraduate O.R. programme had either experienced the pioneering wartime years of O.R., or had been mentored by those who had been involved. One of the first case-studies we heard about was the classic of "O.R. against the U-boat".

(The O.R. pioneers had been asked to try an improve the success of depth charges used against enemy submarines. The main numerical control in a depth charge is the depth at which the explosive is triggered, by the pressure of water. Until O.R. was brought in, the calculations assumed that a submarine dived immediately at the time it was sighted by the approaching aircraft. Therefore the depth was set at about 150 feet. The O.R. team convinced the military that the deth should be set much less, since submarines did not dive as quickly as had been assumed, and the accuracy of the aircraft was greater for a submarine that remained visible for longer. Suffice it to say that the "success" rate increased. This is pictured on the cover of an out-of-print book.)

I was reminded of this story last week when I noticed a copy of a book about the WW2 battle against U-boats for sale as an unwanted book in the city library. It was written from the point of view of a naval historian, and I spent a few minutes looking to see whether there was any mention of O.R. and its place. Yes, O.R. was mentioned in two places. The first retold the story of the depth charges. The second was non-mathematical. It was the psychology of spotting an aircraft. And the O.R. group were credited with the idea that the underside of the attacking aircraft should be painted white, which would camouflage them against the sky. The O.R. people analysed the results afterwards and demonstrated that this simple measure increased the success rate by a further 30%.

Reflecting on these stories over the last few days, I wondered about two aspects of these stories.

First, how much do we encourage our fellow O.R. scientists to think about psychology and human behaviour?

Second, what are the stories of O.R. success that we can use to enthuse the next generation of O.R. people?

(In the latter context, I have used the success of airline O.R. groups in rescheduling U.S. flights after the atrocities of 9/11, and the role of O.R. in scheduling public transport for the Olympic Games in Beijing.)

Football Statistics

2009-08-17T04:29:00.000-07:00

I confess that I do not follow fotball particularly closely, but a column in the Independent on Saturday 15th August caught my eye. It was headed "The Statistics" and below were two bar charts that showed: (1) Points won by champions; (2) Points required to stay up. The two recorded time series are for the last 17 seasons.

I have just run regressions on these (sad, but there seemed to be a time trend) and discovered that the number of points needed to stay up is getting smaller at a statistically significant rate. Now this is curious, as there would seem to be no real reason for such a trend. It cannot continue for ever. But, of course, there is a simple trap that the data led into. The reason that there appeared to be a time trend was that the first three years were all high, and of course, they influenced the regression line. Remove those three outliers and then there is no trend. A caveat for the careless analyst.

OR Insight

2009-08-17T03:06:00.000-07:00

I have just received the latest (September 2009, 22:3) issue of the journal OR Insight, one of the OR Society's regular publications. I'm interested because it has an article that I wrote, the first which has appeared in this journal.

OR Insight aims to promote Operational Research in action, with a serious emphasis on the application area. Since the start of the year, a new editorial team has been in charge and they have been determined to get good quality reports of the nature of modelling and tackling problems with OR. (So why did my paper get in!)

My paper discusses the phenomenon of "Open Studios" as a means of promoting the creative arts in the UK and elsewhere. I tackled it from an OR perspective, and as such I think it is the first paper in the area. I wrote for OR Insight because I wanted to tell a story, and this seemed the best journal for that type of paper.

But there are three other excellent papers, each telling a story of a study and the modelling which went with it.

The first considers one of the difficulties of modern life - home deliveries from mail order companies and similar. If you are out when the delivery van arrives, what happens to your package? Fraser McLeod and Tom Cherrett model one option, that customers should go to a central collection point; they look at the environmental impact of that scenario.

The second looks at health care provision of transport. The perspective is focussed on the patient (in contrast to the the apparent manager-centred perspctive often met in OR studies). The authors (David Bamford, Helen Thornton and James Bamford) conclude with two penetrating questions: "What went well?"; "What could we have done better?" Maybe those should be asked at the end of more OR studies!

And the third, by Gary Graham and John Hill, looks at the regional newspaper industry in the 21st century, and the relationship between print and electronic media. The internet is creating value for the newspaper industry, even though sales of regional newspapers are falling slowly in the UK.

Go get a copy!

Mathematical language in the news

2009-07-15T07:05:00.000-07:00

When I heard one of the reporters on BBC radio 4's early news programme saying "X will be a subset of Y" today, the words grabbed my attention. Hearing the language of mathematics used in such a context is unusual. The story concerned the UK government's plans to be "Greener" and the reporter actually said:
"UK economic policy will be a subset of green planning".

To mathematicians, subsets are well defined, so all of X will be in Y; there may be items of Y that are not in X, but no items of X will be outside Y. The implication is that all UK financial planning will have to be seen as part of the desire to preserve the environment. As an O.R. person, it is interetsing to see that politicians are recognising that the "System" in which they plan has enormous boundaries. That must be forthe good.

But I don't foresee the Government's chief economist being replaced by an environmentalist for a little while yet.

More on the "Diet Problem"

2009-07-15T07:01:00.000-07:00

I have discovered that my Excel spreadsheets for the diet problem are still online.
The Macdonald's diet problem with UK date is at:
http://www.secamlocal.ex.ac.uk/people/staff/DKSmith/BigMacLP.xls
A similar problem with Fairtrade goods and wholefoods is at:
http://www.secamlocal.ex.ac.uk/people/staff/DKSmith/FairTradeCW2.xls

In each case the prices will need to be checked and updated.

Two sides of the "Diet Problem"

2009-07-14T02:56:00.000-07:00

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.

Railways in the UK

2009-06-22T02:45:00.000-07:00

To people in Britain born before -- say -- 1955, the name "Doctor Beeching" automatically conjures up the story of the drastic curtailing of the UK railway network. Following a study of the financial health of the UK railway system, in the early 1960's, Doctor Beeching recommended the closure of many railway branch lines and many stations on the remaining lines. From a network which connected cities, towns and villages, the network became one which connected cities and large towns. The report envisaged rail users commuting to their nearest station by car or public transport, and continuing their journey by rail. Over the years, the Beeching closures have been condemned by many people. Unfortunately, it is very difficult to reverse them; old tracks have been taken up, and the land has reverted to farmland or used for housing. Some stretches of the network have become footpaths and cycleways.

Last week, proposals were published to try and reverse some changes, by reopening lines and reinstating stations. Intriguingly, the proposals were based on a cost-benefit analysis, and the proposals were those which exceeded a threshold for the ratio of costs to benefits. So O.R. was used, at least in the financial model. Two cheers for the report! It would get three cheers, if there was evidence that the compilers had looked at the feasibility of the proposals, asking questions such as the availibility of car-parks for rail users, and whether or not timetables could be adjusted to include the new stations and lines.

Digital Britain

2009-06-22T02:12:00.000-07:00

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

2009-06-01T02:46:00.000-07:00

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?"

Measuring and comparing risks

2009-05-27T02:20:00.000-07:00

Yesterday's newspaper had a feature about the risks associated with competing in a triathlon. A study presented to the American College of Cardiology Conference had reported that the death rate among competitors in triathlons was about twice that of competitors in marathons. (1.5 per 100,000 competitors compared with 0.8). That news report closed with the comment from one of the staff at my university that the idea that exercise is dangerous should be compared with sedentary life.

O.R. professionals ought to be able to see through the nonsense of the report and the comment. What are you trying to measure? How do you compare one activity with another? The death rate in the U.K. is about 1 per 100 per year, or 1000 per 100,000. Dividing that by 365 and then by 8, we get 0.35 per 100,000 in a three hour period. So the death rate in marathons (which last 3 to 4 hours for the majority of competitors) is about twice the national death rate. But the rate varies with age and gender and lifestyle. However, the national death rate includes deaths from accidents, which generally affect the more mobile sectors of the population. The people who die outside marathons include the terminally ill, the aged, etc. -- not the sort of people who compete in endurance sport. They probably have an extremely small chance of dying of natural causes in the next three hours. But they have that risk of accident. So we can conclude that the person who decides to enter an endurance sport increases their chance of dying during that event. But the actual risk is still very small; the half-marathon that I mentioned earlier has about 2500 competitors. If the figures for marathons and half-marathons are comparable, there will be an avaerage of one death every fifty years.

But, even more seriously, the reports about when the deaths occur in triathlons, as all but one of those recorded were in the swimming sport, should alert organisers to warn the competitors about the risks of not being prepared for a long, frantic swim in water that is colder than in heated swimming pools.

As for me, I shall cycle home today. My risk of an accident is about 1 in 4000 based on an average of 1 accidents per ten thousand person miles (here) and a journey of 2.5 miles home. (This is about my experience -- I have been hospitalised three times in 40 years of cycling, with an average annual mileage of a little over 1000 miles, giving 3 accidents in 40,000 miles.)

Displaying data provocatively

2009-05-18T06:24:00.000-07:00

For many years, I have been interested in the potential for using O.R. in developing countries. By a process of serendipity, I have just discovered Gapminder, where data about the world's nations are shown in original and challenging ways. I wish that I had discovered the site before now!

Spreadsheets and O.R.

2009-05-13T03:26:00.000-07:00

The journal Interfaces from the U.S. O.R. Society (INFORMS) is one that I have always enjoyed reading. It describes itself as the "Journal on the Practice of Operations Research" and has often published detailed descriptions of case studies. Older members of the O.R. community will recall that for many years it was edited by Gene Woolsey, and he contributed anecdotes about his practical experience; it wasn't always the received wisdom of O.R. academics, but it was based on genuine experience of getting ones hands dirty doing our discipline.

The March-April 2009 issue of Interfaces has arrived (it takes time to cross the Atlantic) and includes an article "How Electronic Spreadsheets Changed the World" (Rick Hesse and Deborah Hesse Scerno). There was a great deal to which I could relate, as we ran a spreadsheet modelling course in the degree programme in Mathematical Statistics and O.R. at Exeter University. (From the launch of the programme, we taught students to write simple programs in Fortran, then Pascal, Simula and Smalltalk. I recall telling applicants that we expected them to use computers as a tool to help them solve problems, so we stressed a thoughtful approach to programming, and the willingness to use computer packages sensibly.)

Spreadsheets came on the scene in the 1980's -- and provided many companies and individuals with a reason for buying a personal computer. Then spreadsheets were used in schools, with the result that university entrants and others joining the job market had a basic knowledge, often of Excel. But that basic knowledge did not extend to much model-building. We found that we needed to share ideas from computer programming with students in order to help them build appropriate models. As the article emphasises, spreadsheets are wonderful -- used in the right fashion. And O.R. people need to recognise that their fashion is different from that of other professionals, and so their spreadsheet skill set needs to be honed suitably. And that takes time!

Running a sponge station

2009-05-05T03:34:00.000-07:00

Google can't find the expression "Running a sponge station", so this is a first!

On Sunday 3rd May, our church ran a sponge station for the Great West Run, which is Exeter's half marathon. You can see our church at 1:41 on the video, and just glimpse some of our sponge station roadies in the next two seconds.

Our job was to hand out damp sponges to runners as they passed, and we were equipped with cheap sponges, bins for water, tabards to wear. After that, we were on our own. With experience from 2008, we had buckets and large jars for water as well, and the church tap was running continuously to refill the bins. We needed a team to collect discarded sponges, which were then washed (my job) and returned for reuse as the runners passed the church four times!

There is an assignment problem here, dealing with the varied jobs that need to be done; moving water, collecting sponges, washing, handing out. Unfortunately, it is a messy problem to solve. I don't know the skills of the volunteers, and the demands on the team in fiture will depend on the weather! So, like so many messy problems, it was solved dynamically, as each of us who could transferred between tasks as required.

At the end, we had shown God's love for the community.

Celebrations!

2009-05-05T03:15:00.000-07:00

Not much about O.R. today. It has been the Bank Holiday weekend in the U.K., but for Tina and myself, it has been our wedding anniversary party. We celebrated 33.3333 years since we got married on an overcast day in December 1975. We decided to mark one third of a century for several reasons, but most imporatnat, it moved the anniversary to late spring, and, hoepfully, good weather, and the opportunity for friends to travel to be with us.

On Friday evening, our church hosted a concert by the Exmouth Town Concert Band in aid of charity, and we had requested two items which had been played at our ceremony. The first was the theme from the film "The Dambusters", the second was Grieg's "Morning" from the Peer Gynt Suites. Our ceremony included a hymn written in the early 1970's to be sung to the film tune, but it was not well known then. So John, our organist, included it in the voluntary before the service. We heard later that many in the congregation had expressions on their faces showing their gradual recognition of the tune, and also their surprise at its use in the voluntary. Later, those faces showed even more surprise as our guests realised that they were going to sing to that music. We wish we had had eyes in the backs of our heads to see the congregation. John had also suggested, wisely, that the music before the service should be selected by myself and Tina's mother, as Tina herself would not be there to hear it!

On Saturday we hosted a party in the garden for about 60 friends and family. The sun shone, the food and drink were there in plenty, and everyone seemed to enjoy themselves. Thanks to my brothers, sisters-in-law and nephew, Tina and I were free to circulate. In my welcome, I realised that the most appropriate word to describe the fact that everyone knew us, but nobody else knew everyone else, was the mathematical term intersection -- so I used it! Apart from that, the only O.R. related part of the day was the need to schedule the preparations of garden, food and ourselves, and that had to be done dynamically!

One unexpected aspect of such a gathering was the way that several people had known us very closely at different times in our lives and in different circumstances, and such people had the opportunity to share their memories with others. So a friend from undergraduate days discovered how different I had seemed when I embarked on a postgraduate course at a different university, and friends from Exeter discovered varied aspects of our lives.

Then we had a small, intimate supper for family and one couple whose love and support has meant a great deal to us over more than 33.3333 years.

Nappies, Diapers and decisions

2009-04-28T08:32:00.000-07:00

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!

The secretary problem, and ants

2009-04-22T02:29:00.000-07:00

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.

Psychology and swimming pool management

2009-04-21T05:38:00.000-07:00

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.

Lessons for O.R. from the primary school

2009-04-20T02:26:00.000-07:00

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

2009-04-20T02:13:00.000-07:00

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".

Travels in a mathematical world

2009-04-14T03:13:00.000-07:00

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

2009-04-14T03:01:00.001-07:00

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

decision-making.moshe-online.com

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!

The coin machine problem

2009-03-27T03:38:00.000-07:00

Yesterday I saw inside a new machine and realised that its designers had solved an interesting multicriteria problem.

Many British supermarkets have introduced self-service checkouts; the shopper brings their basket to the machine, scans the items one by one without the need for a cashier, and pays by card or by cash at the end. I use one such supermarket regularly when buying a few items, because it is generally quicker than queueing for a cashier. As I have used it, I have been interested in the algorithm it follows for giving change for cash purchases. The first part of the algorithm is straightforward; if your bill is for P pence, then as soon as you have inserted any sum greater than P, the machine gives change. (So if you want to get rid of small change, then you must put that small change in before the larger coins.) But the second part concerns the coins that are dispensed as change.

British coins have values 1, 2, 5, 10, 20, 50, 100 and 200 (pence). My change has never included coins of value 2, 50 or 200. 9 pence in change is dispensed as four 1s and one 5. 90 pence in change is dispensed as one 10 and four 20s. So when I found staff maintaining one of the machines, I stopped to look (probably being labelled by the CCTV operators as a suspicious character). There were six storage receptacles for coins to be given as change, labelled 1, 5, 10, 20, 100, 100. So there is no way that I could be given a 2, a 50 or a 200.

The designers needed a design that worked with an algorithm. Have a stock of coins to give change in a logical way, and keep that stock inside a small volume. So they eliminated three coins from inclusion. So, objective 1: Be able to give change; objective 2: keep the number of storage bins to a logical minimum. But there was a subtle objective 3: use coins of small volume, to maximise the number of coins in the machine.

2 pence coins are larger in volume than those of value 1, 5, 10 and 20. 50 pence coins are larger than 2 pence. 200 pence (2 pound) coins are very large. So these were the coins to remove from the machine's design.

Now, was this design a multicriteria O.R. problem, or not? I think it was -- even if it has a solution that will not shake the world! But it does make the world a little better.

Precisely how do you measure?

2009-03-24T07:49:00.001-07:00

I am reading a book with an intriguing title. "How round is your circle?" which discusses measurement and engineering mathematics (among much else). The authors point out that experimental science progressed in step with the ability to make accurate measurements. This was especially the case in astronomy, which in turn led to Newton's laws and the law of gravity being demonstrated.

I have mentioned my concern about over-precision in measurement in other blogs. Recently, Exeter, where I live, has erected signposts for the benefit of pedestrians. Distances are measured in time. This is a method often used, but is prone to abuse and error. Jokes abound about the hotel that is "two minutes from the beach" (provided you are an Olympic runner and there is no traffic in the streets), or the house for sale that is "ten minutes drive from the city centre" (when there is no other traffic, you ignore speed limits and stop signs). The problem with some of Exeter's distances is that they are too precise. One reads 19 minutes to the university campus, which is so large that it takes over 20 to cross it. There is a case for defining a set of walking times that can be used, to allow for the variation in pace, and the problem of where do you measure to. What do you think the set should be: 1,2,3,4,5,8,10,15,20,25,30,40?

How did you get started in O.R.?

2009-03-24T07:37:00.000-07:00

For many O.R. scientists in the U.K., the route to that career was a simple one. After a first degree (3 years) with a BSc (Bachelor of Science) or BA (Bachelor of Arts) one took a one year Master's degree as a conversion course. That one year led to an MSc or MA (abbreviations as above). There were several universities offering such conversion courses. Funds for the twelve months often came from a government body, a grant-giving research council. They did for me.

Over the last few years, this funding has declined. And now it is to cease altogether. The research council argues that it should fund research, not training. But the O.R. profession has depended on the conversion courses. What will happen?

It looks as if, in the short term, the courses will continue. There are overseas students who want the British training programmes. There are a few students who will borrow money to follow the course. There may be businesses who will sponsor a recent graduate through the degree, but possibly as a part-time programme.

All in all, the route that I and thousands of other U.K. O.R. profssionals have followed is about to die.

Multicriteria Decision Making

2009-03-16T06:43:00.000-07:00

A great deal is being written in O.R. journals and related publications about the science of multiple criteria decision making (MCDM). A few days ago I experienced one of the ways that MCDM can be especially complex.

I regularly visit a university to examine the undergraduate scripts and attend meetings as part of my duties as external examiner. My hosts book me a hotel for my overnight stay. Up to now, they have booked me into one of two hotels, E and I. I have been indifferent between them.

Both are a few minutes' walk from a railway station. Both are a few minutes' walk from the offices where we meet. Both have all the facilities of a modern impersonal hotel. Both have a good breakfast bar. E is close to a nice place to eat in the evening. I has its own in-house restaurant. I have been content in each one.

But earlier this month, I was booked into a third hotel, H. H is much further from the station and the office. Being concerned for the planet, I don't want to take a taxi for a journey that takes 20 to 25 minutes on foot, so I walk. H has all the facilities of E and I, and there was a very pleasant place for an evening meal close by.

But on the criteria that I had judged E and I by, H would be less attractive. But H has a swimming pool that is large enough to have a "decent" swim. E and I do not. A new dimension has been added to the MCDM problem. And that makes the choice for me more complex. Where shall I ask to stay next time?

Of course, if I took taxis everywhere, there would be no problem. But I do not. And there's the problem of weighing the advantages of convenience against the joy of a swimming pool. No wonder MCDM is challenging!

Mobile telephones and development

2009-03-11T05:47:00.000-07:00

The Independent, the national newspaper that I read daily, had an article yesterday in which Clare Rudebeck explained how the spread of ICT (and especially mobile phones) is improving the quality of life for many people in the Third World.

If you have travelled in a developing country in the last few years, and especially if you have moved from the comfort zone of a hotel, you will have seen vendors of mobile phones and SIM cards. Looking more closely, you may have seen booths where the owner of a phone rents out his phone to members of the public. The article discusses this phenomenon, and quotes Richard Heeks, Professor of Development Informatics at the University of Manchester (UK). Following that lead, I found several items in a newsletter. Operational Research contributes to these, with models of the uncertain future. But had you been forecasting development of telecommunications in sub-Saharan Africa 20 years ago, would you have believed that there would be no need for an infrastructure of fixed telephone lines? I doubt it!

Spot the yield/revenue management! (2)

2009-03-03T04:40:00.000-08:00

Another area of yield/revenue management that wasn't mentioned before is that of green fees at a golf club. High at weekends and holidays, low during the week.

Measuring the difficult

2009-03-03T02:42:00.000-08:00

Sometimes in operational research it becomes necessary to measure something which is difficult. From time to time, the O.R. literature reports on studies which fall in this category, and it is fascinating to see how the profession tackles the problem of measuring the difficult. Statisticians have techniques for surveys which ask extremely sensitive questions.

I have just come across a paper which falls in this "Fascinating how the research measured the difficult". How do you measure people's journeys in an elevator? Here's the citation:

@ARTICLE{Fascinating,
AUTHOR ="Kiyoshi Yoneda",
TITLE ="Elevator Trip Distribution for Inconsistent Passenger Input-Output Data",
JOURNAL ="Decision Making in Manufacturing and Services",
YEAR = "2007",
volume = "1",
number = "1/2",
pages = "175--190",
note = "Fukuoka University, Fukuoka, 814-0180 JAPAN",
abstract = "Accurate traffic data are the basis for group control of elevators and its performance evaluation by trace driven simulation. The present practice estimates a time series of inter-floor passenger traffic based on commonly available elevator sensor data. The method demands that the sensor data be transformed into sets of passenger input-output data which are consistent in the sense that the transportation preserves the number of passengers. Since observation involves various behavioral assumptions, which may actually be violated, as well as measurement errors, it has been necessary to apply data adjustment procedures to secure the consistency. This paper proposes an alternative algorithm which reconstructs elevator passenger origin-destination tables from inconsistent passenger input-output data sets, thus eliminating the ad hoc data adjustment.",
file = F
}

One of my colleagues was involved in a study of what coins people would put into a slot machine that gave change, in order to determine what mix of change the machine should have. He started with a survey of the students we teach, and then asked them to repeat the survey with ten friends.

On the subject of elevators, I liked "10 Clever Elevator Ads".

The curse of the sat-nav system

2009-03-02T03:22:00.000-08:00

In the UK, and I guess in most other countries, satellite navigation systems (sat-navs) are a blessing and a curse. Surprisingly little has been published about the design of the algorithms used in them, though essentially they use modified forms of Dijkstra's method, which is also the dynamic programming approach. A fellow blogger has commented on some of the stories from the UK, Belgium and the Netherlands.

Over a meal on Friday evening, friends were talking about stories which don't reach the national papers. They mentioned the large number of small sites for caravans (there is a club which has private use of fields in many farms) which have the warning "Do not use sat nav" in their guide-book. Another friend mentioned that a passenger ferry across a river, at the end of a lane, is marked as accessible to vehicles.

There are several problems with sat-navs that these stories highlight. Most obvious is that data can be incorrect, and once published, is hard to retract. Next is that data may change; roads can be closed for repair, and even online updates may not help, even if the user chooses to subscribe to such a facility. But from an O.R. point of view, there is the question of the wrong algorithm. Many of the problems could be dealt with if the algorithm took into account the kind of vehicle, which would mean solving a constrained shortest path problem ... and for nearly all cases, that would mean using the normal algorithm on a modified dataset. But that would increase the price of the system.

So we end up with people cursing the system, damage to property thanks to incorrectly routed vehicles, a cost to society with special road signs trying to stop vehicles routed with sat-nav ....

Designing road markings

2009-03-02T03:14:00.000-08:00

I am someone who frequently asks the question "Why?" about the design of everyday objects, because of the interplay between design and operational research. On my way to the office today, I noticed that one of the advanced stop lines for cyclists seemed much larger than others that I encounter. So I asked myself "Why is it that size?" and then speculated about the optimal size for such a road marking.

The wonders of Google led me to a website from the UK Department for Transport, which says that the "cycle reservoir should be between 4m and 5m in depth. If the reservoir is shallower than this cyclists can feel intimidated by the close proximity of the vehicles queuing behind them. If the reservoir is deeper than this, motorists may feel encouraged to encroach into it." So the design is based on psychology, which links to some of my earlier blogs here. It is reassuring that someone has thought about the design and suggested guideline measurements.

So if you see me around Exeter with a 4metre tape measure, you will know that I am checking the roads!

Spot the yield/revenue management!

2009-02-23T03:08:00.000-08:00

When I was a child, there was a very popular series of cheap books called "I spy". In each one there were about 30 to 50 items that one might see in a chosen situation. "I spy in London", "I spy in a hospital", "I spy on the railways" and so on. There were brief explanations of each item, and a point score alongside; common items scored 5 to 20 points, rarer ones might score 40 or 50. (One of the latter, I recall, was seeing a valley with river, road, railway and canal alongside each other.) There was also space to note where and when the item had been seen. The books were educational and fun; some facts were in them which I never encountered elsewhere in my education.

I am thinking that there should be a similar book for yield/revenue management. "I spy RM". Increasingly, RM enters our daily lives. The text books tell us that it was largely a product of the 1980's and airline management, but the roots of it go far further back, to hairdressers who charge different prices on different days of the week, and hotels which have weekend rates. So where can one spot RM today?
(1) Transport especially in the UK on flights and rail journeys, but there are cases of coach and bus travel;
(2) Hotels -- certainly if you Google for the topic, it is RM in hotels that comes out top, possibly because hotel management is diffused compared with the centralised management of airlines.
(3) Restaurants and other food and drink outlets
(4) Theatres and (slightly) cinemas
(5) Delivery of goods -- this encounter was what prompted me to blog today; we decided to order from a supermarket for home delivery and discovered that there were different prices for different two hour delivery slots. (We only decided to use the service because we had a £10 off voucher, which more than covered the deleivery charge at any time.)

Are there other, even rarer cases of RM?

In IAOR, the research papers are indexed under Yield Management, not RM. I have found that the expression Revenue Management is used by accountants to describe budgeting, so I prefer to use Yield.

Can the solution be implemented?

2009-02-16T06:26:00.000-08:00

A story from the press today tells how the Paris Metro (underground rail network) has been forced to change its tickets. For over a hundred years, the Metro has used small tickets, 2inches long by 1inch wide, or probably 50 by 25 mm. Latterly these have had a magnetic stripe which is used in the automatic barriers. But the authorities have noticed that more and more often, the tickets become demagnetised while being carried by members of the public, and tickets carried by women are more likely to suffer than thse carried by men. The problem is the increasing use of magnets as clasps on handbags, magnets which are strong enough to keep the bag closed, and therefore strong enough to demagnetise a ticket. So, sometime soon, the Metro is joining other mass transport systems and using cards with RFID and chips.

There are links between this story and O.R.. First, the general one -- that the solution to an O.R. problem may have been appropriate once, but should be monitored to make sure that the setting remains the same. Hence the title of this blog: can the solution be implemented? Or are there some good reasons why the behaviour of some of the people involved has changed? Second, I hope that the O.R. team who work for the Metro have done some analysis of the time it takes to check a new-style card in order to be sure that the barriers can cope with the passengers using the system at peak times. Turnstiles are servers in a complex queue, and changes in service times affect the characteristics of the queue.

The story is here

Optimising the sub-system or the system?

2009-02-03T03:31:00.000-08:00

There was heavy snow in Southern England yesterday, and there were problems with the transport infrastructure. In London, all the buses were cancelled, flights were cancelled, trains delayed, roads congested and blocked by accidents. Inevitably, some people asked the question "Why?". "Why can other countries cope with heavy snow, while England cannot?"

"Why?" is, of course, the correct question for an O.R. analyst to ask. And, I am pleased to note, there were people prepapred to give an O.R. answer. It comes down to the words of today's title. Should one optimise the system or the sub-system? For the commuter whose journey has been disrupted, the sub-system is non-optimal because he or she believes that the optimal solution is for there to be no problems with the commuter's journey. But the speaker explained that optimising the system means that it is not economic to have expensive equipment and trained staff needed for one or two days every ten years. It was a matter of costs and benefits. Naturally, the speaker didn't use these words, but they were implicit. And then the speaker added that with increasing numbers of people able to work from home, the difference between optimising the system and optimising the sub-system became even greater.

The picture is of my back garden this morning.

Commuting Behaviour

2009-02-02T02:59:00.000-08:00

A further observation from my trip to London is how there is a great difference between the social mix of commuters on public transport between Exeter and London. In Exeter, relatively few male executives use public transport. The rail lines are reasonably busy, but few males use the buses for commuting. But in London, it is quite normal and acceptable to use public transport. Of course, the infrastructure is better, but there is a difference in psychology as well. I wondered what research had appeared about the popularity of public transport commuting in cities of varying sizes.

It is relevant to O.R. because anyone working on transport models needs to remember the acceptability and feasibility of different modes of transport in different places. Behavioural psychology has its place in operational research.

Google turned up some figures for the United States. The comments are interesting. I wonder how much correlation there is between population and these percentages? And is there a similar set of data for other countries? And are there geographical effects to take into account?

RAW DATA: PUBLIC TRANSIT USE

Top 5 Cities for Public Transit Use

54.63% New York, NY
37.72% Washington, D.C.
32.66% San Francisco, CA
31.65% Boston, MA
25.92% Philadelphia, PA

With the exception of Washington , D.C. , every city here grew up in the horse and buggy days, with streetcar rail systems. The District of Columbia is part of the 1960-70s "graduating class" of newly subway-enabled cities, along with Atlanta (MARTA) and San Francisco Bay Area cities San Francisco and Oakland (BART). BART reaches regional airports, commuter rail systems CalTrain, ACE and Amtrak, and someday it may even roll down to suburban San Jose . Atlanta is planning to extend MARTA with its back-to-the-future PeachTree Street Trolley and improved bus service.

Bottom 5 Cities for Public Transit Use

1.07% Fort Worth, TX
1.03% Tulsa, OK
0.97% Oklahoma City, OK
0.54% Virginia Beach, VA
0.40% Arlington, TX

Surprise! These southern cities would benefit from re-installing light rail systems. Adding rail would provide residents relief from high gas prices -- and improve these cities' economic competitiveness. With air-conditioning thrown in, light rail would also provide relief from summer humidity.