Monday, 20 December 2010
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)"
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.
Monday, 13 December 2010
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.
Thursday, 9 December 2010
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.
Friday, 3 December 2010
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.
Monday, 29 November 2010
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!
Monday, 15 November 2010
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.
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!
Friday, 5 November 2010
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?
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?
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".
Monday, 25 October 2010
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.
Monday, 13 September 2010
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
Tuesday, 31 August 2010
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.
Monday, 23 August 2010
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?
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.
Thursday, 12 August 2010
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.
Wednesday, 11 August 2010
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?
Friday, 30 July 2010
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.
Wednesday, 21 July 2010
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.
Friday, 16 July 2010
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.
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!
Tuesday, 1 June 2010
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.
Wednesday, 26 May 2010
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!
Monday, 17 May 2010
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.
Wednesday, 28 April 2010
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.
Monday, 19 April 2010
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.
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.
Saturday, 17 April 2010
"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!
Monday, 15 March 2010
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.
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
Wednesday, 17 February 2010
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.
Tuesday, 12 January 2010
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.
Friday, 8 January 2010
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.