Marshmallow towers

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

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

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?

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

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

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.

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.