Friday, 29 March 2013

Scottish footpaths - an amazing fact

In the magazine, "Scotland in Trust", for Spring 2013, there is an entry:

"Fact File: 1,283,380 people use footpaths on the National Trust for Scotland's outdoor sires each year."

A challenge: how would you measure the number of people using footpaths in one year given that the National Trust for Scotland has 400 miles of footpaths across its properties and managed areas?  And how would you do it to the same accuracy as this statistic - i.e. an accuracy of +/- 0.0004%

Monday, 11 March 2013

Magazine readership statistics

For publishers of newspapers and magazines, circulation is vital.  So, every time a fresh set of circulation statistics is released, the data is sliced and analysed in scores of different ways.  Trends are discovered where statisticians see noise.  And because there is so much competition between titles, the PR teams for each one have to be called in to find the slightest sign of hope, even where the realistic observer would despair of there being any hope.

However, the twenty-first century has brought a fresh problem about the measurement of circulation.  How do you recognise electronic subscriptions?  Publishers who sell them know how many there are, just as they know how many print subscriptions they have.  And they can measure the casual sales of print copies.  And they can count the number of interactive subscriptions there are (where applicable).  And they can count hits on public sections of the content.  But ... how should one combine these disparate numbers, these multidimensional data?  What do changes in each one mean? 

For some titles, print remains the principal form of distribution.  There is a monthly magazine in the UK called Country Life.  Copies can be found in stately homes, and its contents major on life in the country, the pursuits of country life, matters related to land ownership and management.  The advertising pages are full of houses for graceful living, ideal for those with a few million pounds to spend.  Do you think that such a magazine will sell many electronic copies?  At the last count, it sold 38,395 print copies per issue, and a mere 149 digital.subscriptions. 

On the other hand, a magazine for gadget-minded males, CQ, sees nearly 10% of its circulation in a digital form, sent to 11,779 iPads across the world. 

These are perhaps extremes.  But, even the most biassed PR staff will acknowledge that digital subscriptions will continue to grow, and print will shrink, albeit at different rates.  The real problem for publishers is to detect when the overall popularity of their product is declining too fast.  And I suggest that Operational Research can play a part in the analysis of the multidimensional data by constructing models of human behaviour which describe the data that is available, and which can be used to forecast the future - with suitable "What happens if?" questions. 

Two examples of successful O.R. models in related spheres.  (1) In the U.K., for two decades after the end of WW2, the UK crisp market was dominated by one brand.  Then a competitor muscled in on the act.  The competitor knew the size of its sales, but when customers were asked to name the brand that they had eaten most recently, nearly everyone named the original, now less dominant, brand.  O.R. workers produced a valuable model which explained this phenomenon of a discrepancy between sales and responses, how it was changing over time, and which suggested a marketing strategy to make the competitor's name much better known.  (2) The model in case (1) was specific to the problem.  More frequently, sales of new products over time follow a common form.  A slow start, followed by an acceleration, followed by a slowing down of growth as saturation is reached.  The graph of sales per unit time looks like the letter "S".  Over the years, O.R. people and statisticians have developed ways of identifying the parameters of this curve from sales data, making it possible to gear up for changes in the demand and hence in the rate of production.  (The Apple company doesn't need such analysis - every new product seems to sell at a rapid rate from Day 1, missing out the slow start section of the "S")

Saturday, 9 March 2013

Public toilets and queues

My apologies to anyone who finds this blog unsavoury.

In the United Kingdom, and I imagine it is true in other countries, there are building regulations which specify how many staff toilets there should be in office and commercial buildings.  The rules are in the form of tables which give the number of units for different numbers of employees.  The first table is for unisex facilities, and specifies the number of washbasins as well - one per WC, possibly because for unisex use, the washbasin is generally in the same room as the WC. 

Staff at the UK Building Research Establishment published a paper in the 1970s (Davidson P J and Courtney R G (1976) A study of the use of cloakrooms in office buildings, Operational. Research. Quarterly. 27, 789-800, see also D McNickle, Queueing for Toilets in OR Insight in 1998) describing their experiments to find appropriate provision of toilets in an office building, and explaining how some of the statistics were collected without intrusion on privacy and without alerting the subjects that their "cubicle time" was being measured - because they feared that such an alert would affect the data.  The provision was then modelled as a queue. 

Providing the general public with toilets in public buildings, shops and restaurants is a different matter.  Apart from laws which state that where customers may sit for food, there must be provision, there are few guidelines.  And so there are many variations in provision.  Perhaps the best known problem is that found in theatres and concert venues, where the use peaks during the interval.  But generally, it seems as if each architect is free to make their own decision about what to provide, and the layout.  At a church meeting today, the gentlemen had one WC, two urinals, two washbasins and two dispensers of paper towels.  Where is the bottleneck likely to be?  Which facilities will be underused?  [Tina tells me that the ladies had three WCs, two basins and one dispenser.]  One local supermarket has four WCs, one adult urinal, one child urinal, three basins and three hot-air dryers.  Where is the bottleneck likely to be?   Which facilities will be underused?  If I had nothing better to do with my time, it might be interesting to collect data from across the city and beyond to reflect on the variety of solutions - and the lack of thought about what is needed.  And at the same time, to look at the layout of the rooms, because in many cases the natural movement of users leads to people crossing one another's paths. 

That last point leads to another aspect of O.R. which formed part of my postgraduate taught course - which I hated.  We looked at Work Study, plotting the movements of people doing repetitive tasks, and considering how the tasks could be organised to be "More efficient".  I hated it because it reduced the people to machines, dehumanising them.  But there is still scope for O.R. people to advise on the layout of facilities to prevent congestion and facilitate smooth movements of people and equipment.  Ergonomics should be something that O.R. people know about, work study - perhaps not.