Sunday, 19 March 2017

The utility value of a towel

Sooner or later, students of operational research encounter the economic concept of utility.  It can lead to an interactive lecture, when one offers a volunteer from the class a fair bet of either £0 or £10, and then offers to exchange that bet for a certain amount £X.  What value of X do you select?  (I found it helped to actually have a £10 note in my hand when I did this.)  With suitable repetitions it is possible to select a few points on that volunteer's utility for money curve, and then sketch the general shape of it.  Most students are risk-averse and this is the typical concave-downwards curve, so X will be less than 5.
 In general, a risk-averse person offered a fair bet between £S1 and £S2 will exchange that bet for an assured amount < 0.5(S1+S2)
This discussion - when I taught it - following the example of the text books - leads on to assessing the utility of non-monetary outcomes, as a way of looking at the results of management decisions.  There was a story, often quoted, of the student who assessed the choice between his status quo for the next academic year and a free ticket to every campus event for the next twelve months.  He preferred the status quo, on the basis that he would not have the numerous temptations of missing classes and essays.
One morning earlier this year, Tina and I arrived at the city swimming pool to find two damp towels in the rubbish bin, and two damp swimming costumes, and a receipt from a (low cost) city centre shop for these four items, dated the previous day.  We recovered the items, put them in the next domestic washing machine load, and gave them to a charity shop later on.
We tried to reconstruct the back story for this purchase and disposal.  One credible account for it was:
Two people were visiting the city and staying in a hotel; they wanted a swim, so made the purchase, and then had the damp towels and costumes to cope with.  Because they were visiting, they had no way of drying them, or wish to take them away, so they chose to dump them.  
Now consider the choice these two had made.
Either:
(Plan A) Don't swim - cost zero
Or
(Plan B) Swim: cost of a towel, costume and one pool entry each - about £15 each
Not everyone would consider the utility of Plan B to exceed that of Plan A; would you?
Meanwhile, Tina and I had the choice:
Either
(Plan Y) Leave these wet items where they were
Or
(Plan Z) Carry them home and spend a little time dealing with them
... and you can work out which had the greater utility for us.


Saturday, 18 March 2017

Where does operational research fit into a community plan?




It is generally assumed that O.R. people are attached to the management pyramid, and the alternative title of “Management science” for the discipline is a reminder of that.  I am grateful that those who taught me to think like an O.R. person included a few reminders that operational research can be used to help any area of business or commerce where decisions are being made.  These areas are generally, but not exclusively, in the area of management and control.  But O.R. can be used for personal decision problems.  It can be used to clarify issues for anyone (or any group) facing choices.  Hence the development of the topic of “Community O.R.” and the increased prominence of pro bono work, not for managers, but for less structured groups of clients. 

A local development (Atmos Totnes) reminded me of this.  Totnes is a very interesting town in Devon, in the South Hams, about thirty miles from Exeter.  It is an ancient town, with a history going back over a thousand years.  It is associated with the family of the computer pioneer Charles Babbage, and the museum’s Babbage Room pays tribute to his contribution to O.R. – a century before the term was invented.  The community there is independent by nature – it used to be known as a centre for alternative lifestyle. 

In Totnes, the milk depot closed down 10 years ago, leading to the loss of over 150 jobs, and leaving an 8-acre brownfield site close to the railway station.  What should be done with this site?  Should it be sold to the highest bidder?  In which case, O.R. would be used to schedule the redevelopment of a plan that met the corporate goals of that purchaser.  Or, could the community of Totnes do something innovative?  That was what happened.

The community chose to write a brief for the regeneration of the brownfield site.  Meetings were held, structured in ways that we in O.R. would recognise, despite not being given that name in the meetings.  Yes, there had to be a group of organisers, but they endeavoured to involve as many people from Totnes as possible, in those structured meetings – all with a goal of reaching an appropriate and socially optimal plan for the site.  They used common sense, and that is sometimes the best kind of O.R. – but they coupled that with sound economic models (good numerate O.R.!)


British legislation has recently been changed to allow community support to back a large planning application.  So the former depot is going to be renewed, over the next five to seven years.  One building – Brunel’s atmospheric pumping station from his ill-fated experimental railway in the 1840s – will be retained.  

The site will have 99 new houses, two thirds being genuinely affordable, and one third for older people (A numerical decision – what criteria led to that?)  There will be employment space, a school for entrepreneurs in food industries, a bakery, hotel, health and well-being centre. 

Hydro power will come from the nearby river, there will be PV panels on roofs and a biomass boiler – which together should make the new site self-sufficient, and may produce an excess.  (Again, someone has done some O.R. related calculations.)

This development is seen as a model for other community schemes; I hope that the lessons in decision-making from Totnes will be learnt by others.