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.


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