Monday, 15 December 2008
The stories were short on detail about the "computer system" except that it had details of 27 million addresses and came from Canada with the name of Pegasus Europe. It seems to have been around for several years, but evidently there have been recent changes in the system which have led to the unhappiness.
Reading the story, it was obvious that there was a mathematical model behind Pegasus of a familiar kind -- optimal (or efficient) route planning for vehicles (postpersons) with constraints (loads, time). Someone, somewhere had been using operational research to help the postal service. And as an operational researcher, I ought to feel proud.
But I don't. The news reports showed that something was lacking in the O.R. process. I can recognise several possibilities for what was wrong, but without further information I can't give a full diagnosis. Maybe someone from the post office can help. So, in no particular order, here are my observations and questions:
(1) Was this system tested and developed for the UK postal service, or was it an off-the-shelf system into which British data was inserted? If it was the latter, then did anyone verify the assumptions that had been made by the designers?
(2) Given the size of the database, it seems likely that the system is largely, if not wholly, deterministic. If so, what sensitivity analysis was carried out? And if so, what changes were made to the data and the model as a result? If not, why not?
(3) How much communication was there before, during and after the development of the system? Who with? Did the creators/users of the system discuss what they were doing with staff at all levels of the system?
(4) Was the objective simply cost-based? Or were there other criteria?
(5) Did anyone concerned with the data collection, input, modelling and recommendations actually go out and test the results? Or, to put it bluntly, would the modeller trust the model's output if they were asked to do a postperson's job?
(6) Did the modellers collect feedback from the postal service about the implementation?
For years, I have taught that an essential part of O.R. is a feedback loop, that an O.R. project is not properly implemented until it has been accepted (and possibly welcomed) into the practice of the organisation. It seems, from the press, that this project lacked this.
We are often reminded of places in companies where there is "OR inside". I feel that this is a story of "OR Inside" which omitted the essential, friendly face of OR outside.
Where was Genchi Genbutsu?
Last week, I was invited to take part in an eBay survey and said yes. I am not sure what behaviour of mine had prompted this particular survey; it may have been another action that was outside their forecast limits, when I bought in a "Buy it now" sale; I invariably use auctions for my collecting.
There was something familiar about the structure of the questions, but I confess that I didn't recognise what it was until after I had answered the last questions and submitted the online survey. eBay was using the AHP (Analytic Hierarchy Process) to find out what I felt about some of the factors that vary from vendor to vendor. I was asked to imagine that I was considering an item at a particular price (30 British pounds) in a Buy it Now sale. That fixed one variable. Then I was asked to consider variations of delivery cost, photo and description quality, speed of communication, first in a ranking, and then by a succession of "Which do you prefer?" comparisons where two sales with differing profiles were offered. I think that I was reasonably consistent in my answers, although the example sales that were offered did not fit into my profile of eBay use. (For stamps, postage is seldom more than GBP1 within the UK and usually less than USD3 internationally; the examples offered had postage figures of up to GBP6.)
Wanting to find out more, I Googled for "eBay analytic hierarchy process" and came up with the answer that eBay does use AHP and ANP (network) and its use is mentioned in the citation of an INFORMS award to Thomas Saaty and in a publicity release put out by Decision Lens, the consultancy used by eBay for their AHP work.
It is strange to contribute to an OR study and only realise that you are doing so afterwards!
Monday, 1 December 2008
Genchi Genbutsu (現地現物) means "go and see for yourself" and it is an integral part of the Toyota Production System. It refers to the fact that any information about a process will be simplified and abstracted from its context when reported. This has often been one of the key reasons why solutions designed away from the process seem inappropriate.
I don't know why there is so little literature drawing on the parallels between Genchi Genbutsu and practical O.R.; good O.R. requires the modeller to understand what is happening in practice, and you do not learn that by sitting in an office. I suppose that there are eqivalent expressions in English -- "go and see for yourself", "management by walking around", "walk the line". But too many managers (and a few O.R. people) rely on second-hand information.
Tuesday, 25 November 2008
So what rules to follow? I have several. There are about 40 journals which are abstracted cover-to-cover. These are the journals published by one or more national O.R. societies, such as Operations Research, Management Science, Journal of the Operational Research Society, 4OR and ORiON. There are others which are clearly primary journals in O.R. such as Omega and Health Care Management Science Dealing with these is, so to speak, easy. Then there are about a hundred which regularly include O.R. related papers. Then, I have a long list of journals which have, at one time or another, provided one or more abstracts for IAOR. Some of these abstracts have been found by serendipity, others by researchers citing them in papers in the principal journals. But I need to decide that binary question in each case; is this O.R.? I look at the content (as described in the title and the abstract). As I do, I ask myself what the paper is about. If it is a paper about theory, is the theory directly concerned with a modelling tool (not, I stress, necessarily a mathematical tool) from the suite of techniques used in O.R.. If so, I say yes. If the theory is less directly relevant, I speculate about whether it is close to a technique that is used in O.R.. Practical papers are considered with the question: is this about a decision-making problem? Is there something that a decision-maker could learn from? Is this paper about a problem in practice where I would expect an O.R. person to be involved?
These may appear naive heuristics, but they work. And in my reading, I can add further questions. When I taught in a unit devoted to statistics and operational research, I often used the (crude) distinction that statistics was concerned with looking at what had happened, and O.R. with modelling what might happen, to answer the questions "What if?" and/or "What's best?"
There are still fuzzy edges, at the interfaces with other disciplines. Engineering problems, economic models, psychology of decision-making ... all pose classification uncertainties. But all of these point to the universality of O.R. in the world today.
Two stories from my experience this week illustrate this:
(1) (and this is horrifying) A radio interview with a debt-counselling service in my home city of Exeter. The speaker described how a door-to-door salesman offered a loan "with 100% interest", which the borrower thought was a very good deal.
(2) My national newspaper headlined a column chart showing the "U.K. Government borrowing" for this year and the previous two. Each column was below the axis, and the amount was clearly marked as being negative, becoming increasingly negative as time progressed. Obviously nobody had realised that borrowing a negative amount meant the opposite of what was intended.
Those of us involved in education can take these as reminders that when we have numerical results to communicate, we need to explain them as clearly as possible.
To end on a lighter note, on the same theme. Another newspaper story concerned with the current credit crunch had obviously been hastily sent through a spell-checker. There were two references to £100bun loans.
Monday, 17 November 2008
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)
Throughout my working life, I have worked alongside some excellent statisticians, and been part of some wonderful data collection exercises. Randy R's comment sums up an important aspect of the work of O.R. people -- taking data which has been collected and making sense of that data for other people to use intelligently.
Over the past week, Google's work on modelling influenza epidemics has been made public. Essentially, the company is monitoring the fraction of search queries that they judge to be related to flu, week by week, and region by region in the USA. The results so far show that the fraction of queries that are related to flu increases during an epidemic, and the change can be seen more quickly than is possible by conventional means of epidemiological monitoring. So here is "really useful information" for "management and decision-making". Google's work can be read here.
Monday, 10 November 2008
"On the first day of operation alone, 36,584 passengers were frustrated by the 'Heathrow hassle' that Terminal 5 had been designed to eliminate." More than 600 flights were cancelled in the first 11 days, and "23,205 bags required manual sorting before being returned to their owners". The causes: "Insufficient communication between owner (BAA) and operator (British Airways, or BA), and poor staff training and system testing".
All this sounds strange, because the airline BA has one of the most efficient O.R. teams in the United Kingdom. (Yes I mean it, and am not hoping for freebies.) But the word "communication" is at the core of the problem, as a short extract from what Iggy Vaid (a shop steward for staff working on T5) said in an appraisal of the mess:
"I hate to say that about my own airline, but culturally the existing management structure is one where you cannot tell the emperor that he has no clothes; you have to say his clothes are beautiful. No supervisor or person can tell his or her boss that the system will not work. If you do you are not a team player; you are sidelined, so for that reason you say that it works and the emperor has beautiful clothes."
Even the most efficient O.R. work will not be successful if there is no way to communicate it.
Later in the report from which I am quoting (The Independent, Saturday 10th November 2008) another area of potential (inevitable) breakdown was highlighted:
"Should there be a failure in the system at any point it will not self-rectify."
Hidden in these words is a warning for every large O.R. project
There is little evidence of large increases in income or employment associated with the introduction of professional sports or the construction of new stadiums.
Monday, 3 November 2008
It contrasts with a visit that I paid to a similar rescue centre, where stroking selected animals was free as part of the overall "experience". Another model of costing?
It is a colourful edition, with several accounts of the 2008 conference at Sandton in South Africa. My friend, former colleague, and predecessor as editor of IAOR (International Abstracts in Operations Research) has printed his diary and thoughts about the event. That is one of the worthwhile articles in the newsletter, even though Graham is described as one of the "stall warts" of IFORS, and his account is a "dairy account". Spell checkers are wonder full!
Tuesday, 28 October 2008
It is to be hoped that the city will work with the winners and consider using their solutions and models in the network design.
The models suggested that, for a London-based scheme to be successful, 12 large bicycle stations should be placed near railway stations in central London with 250 smaller stations distributed throughout the West End and the City of London. An average of 20 bikes per small station was found to be the most efficient number.
Monday, 20 October 2008
Monday, 6 October 2008
The picture has one entry along the x-axis for each chapter in the Bible and there are coloured arcs between chapters which cross-reference to one another. (This means that there is a word, phrase or idea that occurs in one chapter that also appears in another; "The Lord is my Shepherd" in Psalms links with "I am the Good Shepherd" in the gospels.) There are 63779 such arcs -- the picture is beautiful. Mathematicians and O.R. scientists will recognise that the structure is a graph, with each chapter a vertex, and that leads to assorted questions about the graph. How many components does it have? Are there isolated vertices? What are the properties of the components?
I'd like to hear answers.
Tuesday, 16 September 2008
A part of my education in O.R. was the apocryphal story about the O.R. consultants and the problem of the lifts in the skyscraper. Occupants of the building complained about the time they spent waiting for the lifts to get from the upper floors to the lobby. So the consultants looked at the options, they built models of the consequences of extra lifts, faster lifts, dedicated lifts from the upper floors, etc., etc. The reduction in mean waiting time was always very small. Then the psychologist in the team suggested that the company place mirrors in the waiting areas for each lift shaft. He explained why. Why? (see the end of this blog)
I had the same sort of problem at the weekend. Each year, on the second Saturday in September, I take part in a prayer walk around the churches of the city of Exeter, my home. The idea is that a group will start early in the morning, follow a winding route around the city, stopping to pray in about 25 different churches, praying for the city and its people. I have the responsibility of planning the route; for several years we have used the same route. This is not a TSP, of course, because the walkers don't end at the start point. It is not quite minimal but is quite close to the best.
In 2008, two new churches came into the list of city churches. We decided to include one of them, miss the other, and omit another, because it was linked strongly with these two. But the selected new church would add so much extra mileage to the old route that we needed a new plan. So we made the walk have two starts, with two groups starting at 8am and converging on the cathedral at 10am to walk for the rest of the day together. So I devised such a route; the two initial legs had minimal lengths for the churches that they visited, given the fixed end at 10am. However, I had forgotten the psychology. The second route had a lot of road walking, and went past the main railway station, so there was traffic. The consensus was that it would be better to walk a little further (about 300 to 400 metres) and walk beside the river on a footpath, away from the traffic. So that is what we will probably do next year -- alter the start and route to give more traffic-free paths.
Why the mirrors? The reason was that it was not the actual waiting time that people notices, but the perceived waste of time. Mirrors distracted people; some could admire themselves and tidy their clothes and appearance, others could watch. (In the 1970's there were sexist stereotypes for these activities, which I will not repeat.)
Wednesday, 10 September 2008
Mary Pettibone Poole, A Glass Eye at a Keyhole, 1938
I had not come across this thought-provoking quotation until yesterday; then I was in a meeting and found it inscribed on the wall of the small conference room. Yes, it has O.R. applications. Part of the skill in the O.R. scientist should be (must be?) the ability to recognise where a model developed earlier in a different context might apply to a practical problem. So queue theory is used for call centres and for slow moving inventories. Location theory applies to ATM outlets and airports. But sometimes the obvious is not appropriate -- then the O.R. scientist needs brains to challenge the obvious.
Wikipedia doesn't tell me anything about the author or the book. And I wonder who has used their brains and challenged Mary's words, rather than repeat them?
[Malcolm King, David K. Smith and Alan Mercer "Towards Diocesan Planning" Journal of the Operational Research Society 29 p856-866 (1978); Malcolm King and David K. Smith "Are the Clergy Being Deployed Fairly?" The Churchman 5 p54-60 (1980); Malcolm King and David K. Smith "Planning the Deployment of Clergy" Long Range Planning 5 p104-111 (1982)]
Earlier, Alan had published "The Churching of Urban England" in the proceedings of the 1969 IFORS conference, which looked at the location of places of worship.
So there are two possible areas for fruitful O.R.; manpower planning, and location models.
I wonder if Bishop Davis knows about this work.
Monday, 1 September 2008
Business Week reporter Stephen Baker, has written The Numerati, which describes the superpowered contributions that mathematicians-and operations researchers-are making to businesses and organizations today. Publishers Weekly has given advance praise, calling The Numerati a "captivating exploration" about "a new breed of entrepreneurial mathematicians." Houghton Mifflin is publishing the book this fall (autumn if you live in the United Kingdom).
There is a video of an interview with the author here.
Some of INFORMS' most enthusiastic members are blogging about O.R., operations management, engineering, and science. Have you visited their blogs yet?
Former INFORMS President Michael Trick of Carnegie Mellon University, who currently serves on the INFORMS Public Information Committee (PIC), blogs from conferences and shares fresh news about O.R. Michael Trick's Operations Research Blog.
Fellow PIC member Aurélie Thiele of Lehigh University shares her views at Thoughts on Business, Engineering, and Higher Education.
Wharton Professor Gerard Cachon, the current editor of M&SOM and the incoming editor of Management Science, blogs on operations management at Matching Supply with Demand.
Visit these blogs, catch up on news and views, and share your own O.R. perspectives. Know about more O.R. blogs? Let us know by sending an email to firstname.lastname@example.org.
To which we can add this blog, and that of Laura McLay (Punk Rock Operations Research)
A major cereal company in the U.K. (the name begins with "K") offered vouchers for free swims on its packets. As a promotion, it has been very successful. But the swimming pool in Exeter has had to restrict the hours when the vouchers can be used. It isn't really a rationing of use, simply a way of allowing the fee-paying swimmers time to enjoy their swim and concentrating the use of the vouchers to times when fee-payers can stay away.
This is an interesting solution to a demand problem. It has obvious links to revenue management.
It’s 9:20am on Sunday morning, and I’m going into church. Together with my wife Tina I am in Sandton, South Africa for the triennial IFORS (International Federation of OR Societies) conference, which starts today. Sandton is a strange place – a suburb of Johannesburg – with a strange, artificial air to it. We arrived yesterday and checked into one of the conference hotels. It’s four-star, international, impersonal and totally devoid of character. We are noticing the difference (it is almost culture shock) after a week and a half of holiday. The first week was a safari in an overland truck, staying in game lodges and backpackers’ hostels, in a group from five countries and speaking three languages. The beds were more comfortable than our four-star accommodation here, and the staff of lodges and hostels were friendlier.
Amidst the hotels, offices and shopping malls of Sandton, there is one convenient church; I’ve tried to find somewhere to worship at most of the IFORS conferences that I have been to, with interesting results. Here Tina and I, with conference friends, have arrived to find the church empty except for one man fixing the P.A. “Everyone else will be along shortly” he tells us; sure enough, at 9:28, the church fills up ready for the 9:30 service. We are welcomed, and the service proceeds, with more and more people drifting in over the next half-hour. The sermon – longer than in most U.K. churches, has an O.R. link; some of the New Testament parables stop with a cliff-hanger and seem incomplete; isn’t this a bit like some reports of O.R. work, which leave the reader asking “What happened next?”
My afternoon is spent talking about the International Abstracts in O.R. (IAOR), which I edit, and whose sales provide IFORS with a steady income stream. The conference is the time when we are launching an updated version of the electronic IAOR, so the leaders of IFORS are particularly interested in the report. Then I get involved with a meeting for editorial advisers of another journal, which is filled with statistics about submission rates and publication delays.
IFORS conferences follow a regular pattern: reception on Sunday, two days of papers, one day-long excursion or choice of excursions, and two more days of papers. The evening’s reception has been scheduled for two and a half hours, and by the time Tina and I get there, people are already drifting away. O.R. observation: receptions should be shorter, to allow people to meet one another; what is the optimum length?
Being in Africa, the conference opens with drumming and dancing, followed by a welcome from the minister of science and a plenary speech by Clem Sunter about Scenario Planning “The world and South Africa in the 2010s”. Some of his remarks about planning are clearly particularly pertinent for the minister. Then there are the usual parallel sessions that make up all conferences. I opt for the session on developing countries, to hear the seven papers that have been shortlisted as candidates for an IFORS prize. Like many conference sessions, this one is a curate’s egg.
I skipped out of the sessions for part of Tuesday to accompany my “accompanying person” on the trip to a glass factory – which was ninety percent disastrous. The most interesting bit was meeting the team who had created the key-rings in the conference packs. Made of glass beads, threaded onto wire, each is different. Our guide explained how the random patterns were produced, using a device worthy of Heath Robinson; all the parts used are recycled materials. The following day we have opted for a trip to a diamond mine. What struck us most forcefully was the ordinariness of the site, apart from the intense security. We didn’t lose touch with O.R.; the mine has monthly performance targets, derived from a forecasting model. Earlier this year, the target was missed because of power cuts; loss of 20% of the power meant a loss of 50% in production.
Sandton is a strange place for a conference. Because of the security, Tina can’t simply go off for a walk, and she spends a good deal of time reading in the hotel garden. There is a wide choice of shopping malls, one linked to our hotel by an underground passage, another attached to the convention centre. Even the winter sales in the shops fail to attract her for very long.
Thursday – another day of parallel sessions. In the evening, the gala conference dinner, enlivened (if that is the right word) by a parade of representatives of the 48 national societies that are members of IFORS, ordered according to when each society joined the federation. There is more dancing, loud jazz music, queues for the buffet, and very few speeches. Years ago, I read some words of Hermann Bondi: “Little children, from the age of three upwards, ask the question ‘Why?’ The aim of education is to stop such questions. Education has its failures. They are called scientists.” The dinner is a time for me to ask “Why?” and the subsequent question, for me (as an O.R. scientist), is “How?” “Why is the service so poor? How could it be improved?” These two questions have never been far from my mind all week. “Why is the design of the convention centre where the conference is being held so weird and inefficient? How …?” “Why is the hotel service indifferent? How …?” My mentors in my distant O.R. youth emphasised the importance of time spent on site, experiencing the problem that was being studied; managers in service industries often should learn the same way, experiencing the service as a customer and seeing how it could be improved. The hotel has a sort of feedback loop of control, with customer response forms; will any of my comments be dealt with if I were to come back next year?
And then comes Friday, and the closing plenary session. Very interesting, but the presentation is very poor, and the speaker could have said in 20 minutes what took 45. Those delegates who are still around start to disperse, some back home, others to holiday in South Africa. Has it been a successful conference? Yes, I have met a lot of people, some old friends, some new ones. Have there been any outstanding sessions? Not for me, sadly.
Back in the office in Exeter the following Monday, there are my emails to be dealt with, and a meeting with my research student, M, and her project sponsors. She has been trying to make sense of a large mass of historic data; we spend time trying to get something useful out of it for the sponsor. I encourage M to “play with the data” to try and find useful information, though I remind her that this is not an expression to use in our presentations. The meeting with sponsor goes well, as we are joined by one of the U.K.’s experts in the type of data we are looking at, and he has excellent communication skills as he talks about the project and its context. He doesn’t mind when I ask those two questions, over and over “Why?” and “How?”. In terms of information gained, the hour with him has given me as much as the whole conference.
Wednesday, 27 August 2008
But sometimes one wishes that the results of design as the result of a modelling process could be made public. By doing that the benefits of one person's analysis could be usefully shared. I come across such an example regularly. What is the optimal separation between cycle racks? By the swimming pool, there are six racks, at 45cm apart. The outermost racks are therefore 225cm apart, and one can park seven bicycles in the space. Near the office, there are four racks, 100cm apart. Two bikes can be parked in each gap, so in 300cm there are eight bikes. Which is better?
Tuesday, 26 August 2008
I have my own problem in waste management, and have considered it from an O.R. perspective. How should I deal with the clippings from the hedge at home? The hedge is about 50 metres long, nearly two metres tall, and is privet. I use electric trimmers, once or twice a year. Privet branches tend to be long and straight, but there are a lot of them. The options are (1) to load them into the car and take them to the council dump, (2) to buy sacks from the council to be taken away by the garden refuse collection, (3) to burn them on a bonfire, (4) to shred them, (5) to leave them in a heap to rot slowly.
(1) and (2) are expensive options, and I would derive no benefit; (3) I reject on the basis that I do not like polluting the air and have no space for a fire; (5) is unsightly in the garden. So I shred the cuttings. But how? Over the years I have found that I can get a lot of shredding done with the rotary mower, simply by driving the mower over the trimmings as they have fallen on the ground. The method fails if the long straight branches have been raked -- the random alignment of branches is important. Some branches are not shredded by this process, and those go though a electric shredder -- which I do not use for the whole process as it is slower than the mower. Then I have to compost or use the shredded wood and leaves as mulch -- so I benefit from the nutrients; the garden is not totally organic, but I feel that I have done a little for the planet, and found my personal optimal solution. Now how can this process be written up as a journal paper?
Wednesday, 20 August 2008
Wednesday, 13 August 2008
This week I watched the first episode in a new BBC TV series, Britain from Above. The opening programme focused on the infrastructure which lies behind life during a typical day in Britain. So there were mentions of transport, electricity supply, water supply and treatment, communications and so on. The filming was of a very high quality, and there were some good computer graphics, although quite often there was too little time to appreciate the message. The programme tended to move from topic to topic, trying to hold the viewer's attention -- and assumed a limited attention span.
I very much enjoyed reading Infrastructure: The Book of Everything for the Industrial Landscape which looks at the engineering behind a nation's infrastructure, and the BBC programme touched on this. But it also looked at aspects of control, and I wondered what would have happened if the presenter had been familiar with the work of O.R. scientists. For those who know how ubiquitous O.R. is, the programme emphasised that O.R. is the hidden science behind many things.
Sadly, for commercial reasons, much of the practical work of O.R. professionals in practice is never published. Why should you tell the world what you have done, and how you have done it, when your results could be exploited by your competitor?
To take one example from the programme, one that caught the attention of several commentators. At the end of the programme "Eastenders", there is a great surge in demand for electricity as well over a million kettles are switched on across Britain. The electricity industry has to cater for this demand, and we saw the man with the responsibility watching the demand rise, and bringing hydroelectric power stations "online" to cope with the demand. More power was bought from France. The same electricity industry uses O.R. to deal with the varying demand, with models (some of which are as simple as large linear programs) that show when diferent means of generating power should be used. When I talked about this with a researher in the industry, he spoke about the sudden demands for power during and at the end of TV programmes, and also of the difficulties that are created by having a cheap night-time tariff for electricity. Many users have timers which switch on appliances at the start of this tariff.
Tuesday, 12 August 2008
But, how far have I actually swum in that pool this year? I keep a spreadsheet for these swims, and that is updated every time I swim, so the number of swims in the city pool is reliable. I have swum once elsewhere, and we are discounting that five minute splash in a cold, open air pool. There are three obvious sources of error.
First, I may have miscounted. There is no mechanism for recording the lengths except my head, and I know that sometimes I lose track. But to counter this source of error, I usually swim with my wife, and she also counts lengths and we can generally verify the number of lengths each has swum (she is a little faster); I also know how fast I swim, so the clock on the wall of the pool gives a safeguard against gross error. As I swim an even number of lengths, my count is likely to be in error by \plusminus 2 if at all. I would hazard that I have made an error on at most 5 occasions. So the count of the lengths is 8300 \plusminus 10
Second, I do not always stay in the same lane of the pool, so I don't swim exactly the length of the pool. But simple geometry tells me that even if I swim slightly off straight, the difference between what I swim and the length of the pool is very small. We are talking about a variation of \plus 0.05% at most, say 4 lengths.
Third, I trust the pool builders to have measured correctly. But here is the most intriguing source of error. The pool is not exactly 25 metres. There is a tolerance because it was surveyed with measuring line when it was built. Everyone believes that it is exactly 25 metres, but the tolerance is probably \plusminus 150cm (6 inches) -- about 0.5%
So, all in all, I have not swum exactly 207.50 kilometres this year. The extreme range is
8294 * 0.024850 to 8314 * 0.025150 kilometres, i.e. (206.1 to 209.1) But that is the extreme range, and the confidence interval is smaller -- an exercise for the reader.
Why does this matter?
One, the Olympic Games are currently happening. How accurately are lengths of tracks and pools measured? The times of races are recorded very accurately, because we are very good at recording time. But how much tolerance is there in the distances?
Secondly, for O.R. professionals, how often do we believe in spurious accuracy of data? When I learnt about L.P. in the oil industry, we were told a cautionary tale, of the analysts who checked their data; one measurement of viscosity of crude oil was always given as an integer, a small integer. This was then processed through the L.P. model. Where did this value come from, they asked. As one should, they checked. The data was supplied by an experienced worker, who dipped his thumb and forefinger into the crude oil, rubbed them together, and pronounced the measurement. Now, far too often, I see papers submitted for journals where there are tables of results quoted to six or more significant figures. Where did these come from? Usually from the analysis of a few dozen observations that were each measured to two or three significant figures. The best models in the world cannot conjure more accuracy from the model than was in the source data; but all too often we forget that, at our peril.
The results are only as good as the data.
Wednesday, 23 July 2008
Mike Trick was there and he is also creating a blog (http://mat.tepper.cmu.edu/blog/?p=297) so I won't repeat what he has already written.
The conference facilities were pretty good; one new feature for me was that the computers for presentations were set up with folders for each session and speaker, so the team of students who were "go-fers" could download your presentation from a memory stick in advance and you would know where to find it. (How different from the days when one travelled with a wallet of overhead transparencies! Mind you, when I went to one conference in Jerusalem, the airport security inspector demanded that I produce my slides to him before I went to the aircraft to demonstrate that I was genuine; I wonder what would he do now?)
But I often tend to look at things with an OR professional's eye, and the convention centre had room for improvement ("Science of better")
(1) The design was weird -- access to upper floors was generally by escalators, and these were at the xtreme sides of the ground floor foyer -- not very convenient.
(2) There wasn't an obvious channel for feedback when things went wrong for participants -- if a light-bulb needs to be replaced, who do you tell? There were numerous staff around, but they did not have identifiable roles.
(3) We had a splendid banquet, but the main course and dessert were buffet style, even though there was a surfeit of waiting staff. 600 people had to negotiate their way around the tables to the buffet ... not easy.
(4) The conference organisers had a desk for queries during the conference -- a classicly designed bad queue led to this; the number of servers was uncertain, as some people came to the desk and then went away again, and the users (Customers) formed an indeterminate number of lines to the desk, and jockeyed. Service times were extremely variable -- a rope barrier and one line of users would have been much better.
More another day!
Tuesday, 17 June 2008
Guesstimation: Solving the World's Problems on the Back of a Cocktail Napkin by Lawrence Weinstein & John A. Adam
The authors encourage their readers (and their students) to have a feel for the size of numbers, and developing the skill of estimating reasonably accurately the scale or size of some measurable event or situation. The publisher's website for the book gives some examples, as well as a pdf of the first chapter. Something in the latter intrigued me. Suppose that there is a lottery with a hundred million tickets. If all those tickets were piled high, what would the height be?
In the UK, there is a National Lottery with about fourteen million different entry tickets. Like many university lecturers, I have used it for examples of simple (and not so simple) probability and statistics. So I started to wonder how high the pile of cards would be for the UK National Lottery. Following Weinstein and Adam, you start by thinking how thick a ticket would be, and conclude it is somewhere between 0.1 mm and 0.2 mm (a pack of 500 sheets of paper for the computer printer is 5cm thick, and lottery tickets are thicker). If we work with the smaller figure, we are talking of a stack 1,400,000 mm high, or 1,400 metres, or 1.4 kilometres. The figure is more than this, but less than twice, so we may as well call it 2km. Now we have a sense of the small probability of winning. 2km is higher than the highest mountain in the UK. Put that stack down, along a straight road; now it will take 20 minutes to walk from one end to the other, with just one card being the winner.
Guesstimating the size of things has more serious applications than this, but I am pleased to see that a publisher thinks it is worth putting a book like this in the marketplace. O.R. people use guesstimates quite often, to get a feel for the rightness of an answer, or a feel for the problem. In the early days of O.R., in the UK in the second world war, Winston Churchill heard of a ship crossing the Atlantic with a load of dried egg and asked one of his scientific advisers to estimate from the tonnage of the ship how many eggs were in the ship. The serious business of war was held up while the adviser worked it out, on the back of an envelope. Weinstein and Adam would be proud!
Monday, 16 June 2008
Operational researchers are familiar with problems of multiple criteria measurement. The cynical O.R. person will mutter about adding apples to oranges and trying to work out what the result is. Everyone will have their views on the best place to live, and what makes it so good. And that list will almost certainly not coincide exactly with the criteria used by the magazine. Let me admit that I like Copenhagen, perhaps because my late friend Ellen had a flat which was ten minutes walk from the gates of Tivoli Gardens, and so could hardly have been more convenient for visiting the place. Even without that personal experience, it is a very pleasant city, but my criteria would not have included (for instance) Monocle's number of international flights from the city airport, nor the ease of buying drinks at 1a.m..
So, seeing such analysis of multiple criteria optimisation, the O.R. person ought to reflect on how difficult it is to measure the "hard to measure" and on how to work with clients and decision-makers when some of the consequences of choice are determined by aesthetic and qualitative scales.
Tuesday, 10 June 2008
Now I enjoy swimming, and go to the pool several times each week. When I started work at the university, one of the free perks of the job was being able to stroll to the open-air pool that was five minutes walk away from my office, and swim. The pool was free for staff and students. Now there is a charge, and I have moved my regular swimming to the public pool managed by Exeter city council. But, even though the pool was free, it didn't mean that everyone used it. Removing the charge for some goods or service doesn't automatically bring in more customers.
So I wonder what kind of modelling has been done by the UK government in advance of this announcement. The claim is that it will bring two million more people into regular exercise. As an O.R. person, I wonder what model yielded that figure, about 3% of the UK population. And how do you really measure "regular"? If the figure is accurate, what does it mean for the numbers of people using a typical swimming pool on a typical day? Most pools have lane swimming for serious swimming. Before 9am, Exeter's pool has two "fast" lanes, one "medium" and one "slow". The fast lanes are crowded when there are six or seven people in each, the medium one can take a few more, and swimming in the slow one is awkward when there are 20 in it. Can you recognise a queueing problem here? When does the congestion in a service system get so bad that arrivals turn away?
Swimming pools provide several further O.R. related questions. I used to ask one of my modelling classes how big the hot water tank that feeds the showers should be for a set of public showers. For simplicity, these showers often have no control over temperature, simply an on-off button or tap. So the water temperature cannot fluctuate too much. Therefore, the heating system must be able to maintain the water temperature within a small range, putting design limitations on it.
Another problem comes with lane swimming. There is a heuristic which says that it is safer if alternate lanes go in opposite senses, clockwise, anti-clockwise, clockwise ... across the pool. Why? Because adjacent lanes are swimming together, and a swimmer only needs to avoid those coming towards themselves on one side, not two. But overtaking in lane swimming is an art, which leads to models of congestion. Assuming that I am two metres tall, then if I make a turn after the person in front of me, then to overtake them, I need to swim an extra two metres in the time that it takes for us both to complete a length -- unless they give way. So you need to be in the region of 10% faster than the person ahead to complete overtaking in a normal pool. And if there is a third person behind, then that person will see congestion. It is rather like two similar speed trucks overtaking on a two or three lane road -- it takes time and there are people held up behind. Swimming has the complication of turning at the ends of the pool. But there's a research possibility: "The similarities and differences of lane swimming and overtaking trucks." You read it here first!
Tuesday, 27 May 2008
It was a pioneering time in Exeter, setting up an undergraduate programme in "Mathematical Statistics and OR" (MSOR for short) and we had some stimulating years with annual cohorts of 20 to 30 students, who wanted to "do something with their mathematical skills, but not a mathematics degree".
We developed links with industry and ran some fascinating projects; maybe more of these later, when I have time.
My postgraduate work centred on the water supply industry, and we encountered a problem which (like the supermarket cashiers problem) is simple to state, but leads to more complexity as one gets into it. A water supply reservoir has many purposes. First, to store water to supply the users. For that it ought to be full. Second, to restrain floods. For that it needs to have space in it, and not be full. Third, to provide recreation. For that, the level should not fluctuate much, under normal circumstances. So what should the reservoir manager's policy be about releasing water, both in the short term (when floods are imminent) and in the long term, when the weather is calm. How can forecasts help? The problem was nicknamed the "Noah and Joseph" problem, by reference to Noah who encountered floods (a short-term phenomenon) and Joseph who dealt with droughts (long-term).
From time to time, people ask me what I do.
First answer: "I work at the university".
Some people change the subject; others ask: "What subject?"
Second answer: "I teach a branch of mathematics."
More people change the subject, or admit that they did not get on with mathematics; however, some ask a little more.
So I explain that OR is not really a branch of mathematics, but a subject in its own right, which uses mathematics and other ideas to answer questions for business and commerce, either "What's best?" or "What happens if ...?" And my standard, simple illustration is the local supermarket, and the number of cashiers on duty. The best number is somewhere between too small and too many; too few, and the queues get big, and the customers start to go to another store; too many, and there are no queues, but the cashiers are not working fully. So there must be a "Right number" -- the problem is mathematical. But the number depends on the time of day, day of the week, month of the year. So you need to forecast the number of customers who will shop on different days at different times. More mathematics. And you need to devise a shift system for the staff of the store so that the full-time and part-time employees have regular work patterns. More mathematics (or OR!) So what started as a simple question, "How many?", has become a much larger problem for the company.
Having explained that, my audience starts to realise that OR is useful in their world, and I can recount other applications that often surprise and fascinate them.
I meant to introduce myself, but it has turned into an introduction to explaining OR to my dinner guests.