Tuesday, 28 May 2013

Silly statistics, family style, Kipling and Bondi

The average UK mother of children aged 2 to 10 is asked 288 questions per day.  An online newspaper article (with comments) is here.

This was the result of a survey of 1000 mothers.  Just imagine how they did it!  How many days' observation? 

Many years ago, the late Sir Hermann Bondi, who had strong links with OR in the UK, told an audience the following.

Little children, up to the age of eight, nine, or ten, are constantly asking the question "Why?".  One aim of education is to stop them asking that question.  Education has its failures.  The resulting failures are called scientists.

One of the comments quoted Rudyard Kipling's poem, "I KEEP six honest serving-men", from the "Just So Stories", which I have heard quoted as being apposite for an Operational Research Scientist.

I KEEP six honest serving-men
(They taught me all I knew);
Their names are What and Why and When
And How and Where and Who.
I send them over land and sea,
I send them east and west;
But after they have worked for me,
I give them all a rest.

I let them rest from nine till five,
For I am busy then,
As well as breakfast, lunch, and tea,
For they are hungry men.
But different folk have different views;
I know a person small—
She keeps ten million serving-men,
Who get no rest at all!

She sends'em abroad on her own affairs,
From the second she opens her eyes—
One million Hows, two million Wheres,
And seven million Whys!

Monday, 27 May 2013

A royal location problem

Last week I came across an interesting location problem.  Location problems are all about deciding where to site one or more facilities or buildings to meet some specific criteria.  There are several mathematical models which are used to help with these problems, and countless books and articles have been written about them.  My PhD student, now Professor, Shams-ur Rahman, modelled the location of health facilities in Bangladesh; one of the constraints was political - each sub-district had to have the same number of health centres, even though this meant that the locations were sub-optimal on other criteria.

The problem that I encountered dates from the second world war.  What would happen to the British royal family if the country was invaded?  Where would they go?  The government had contingency plans for a last ditch conflict on British soil rather than surrender.  And for morale, the king and his family were to stay in the country as long as possible.  So, it was necessary to plan for a relocation of the government and leading civil servants to a new base, away from London.  With the king close by.

The decision had been taken secretly that the new centre of government would be in the West Midlands, specifically Worcestershire and  Warwickshire.  That area satisfied several criteria; it was away from the coast (and one assumed that an invasion would be by sea and land, rather than by air); there were good transport links from London (rail and road) and also to both Liverpool and Bristol, in case a further evacuation was needed; the BBC had a broadcasting centre at Evesham in Worcestershire; and there were no major cities close by which might be targets for bombers; there were RAF airfields and military training camps; the land was not mountainous.  Also, secretly decided, some of the royal family would be evacuated by sea to Canada if the country fell. 

So, where do we send the king?  He would need a mansion or country house.  It must be in the right area, especially for communication and (possibly) further evacuation.

Now come the extra constraints on the location problem.  First, how many alternative houses do we plan for?   It would be unfortunate if the chosen site was rendered unusable, either through a direct attack, or because of the route taken by the invasion.  What if two choices were unusable?  Having several alternatives means that the actual choice can be left to the last minute depending on circumstances.  And second, we assume that the enemy has made the same analysis of where the government of resistance would be based.  So, the chosen home for the royals must be one that is not immediately obvious to the enemy.  Here comes a bit of game theory.  Enemy and UK both think of obvious places.  Both reject these as "Too obvious".  Enemy and UK both think of less obvious places, and reject these.  Enemy and UK think of even less obvious places.  Now we have a list of - perhaps - twenty sites - and the UK makes a selection from these, including some of the obvious and less obvious ones.  It's a bit of bluff and double-bluff.

Croome Court
Tina and I were visiting Croome Court, in Worcestershire, last week.  Records found there show that it was one of five houses (so there is the number of alternatives) surveyed and provided with emergency food supplies in early 1940.  It is a small country house, close to the Bristol-Birmingham road and railway, and also close to the River Severn - which might (at a pinch) be used for a water-borne evacuation.  There was an RAF airfield nearby at Pershore.

The first choice for the alternative royal residence was Madresfield Court, about 5 miles away as the crow flies.  It wasn't necessary to use it for this purpose, but Croome Court was used by the Queen of the Netherlands and her government in exile. 

I wonder what the civil servants thought when they were given the instructions about this location problem?  You are to choose a number of country houses in Worcestershire and Warwickshire for the royal  family.  How many is up to you, but you must justify the cost.  You are to choose ones which are adequate, but not obvious to an enemy.  Then you are to survey them and provision them.   They didn't have the tools for location modelling that we take for granted.

So far, I have been unable to identify the other three possible houses; Google only turns up Madresfield. 

Tuesday, 14 May 2013

Models for customer and consumer behaviour

The first article that I ever read about OR carried the title "Models for thinking with".  It mentioned optimisation, and analysis, but concentrated on the essence of creating a model (mathematical or otherwise) of an enterprise, where decisions had to be made.  This affects design and both OR people and engineers need their models for thinking with.  Experience changes designs, and evidence feeds into the models that are used.  Some early motor-cars had their rear doors hinged at the rear.  If the door opened while the car was moving, then the door would swing open, giving no protection for the rear-seat passenger.  One picture of these that I saw recently labelled them "Suicide doors".  A popular British car of the 1960s had door handles which pointed forwards - there were accidents where these gouged the flesh of pedestrians.  In each case, there had been unforeseen situations in the models used for the design.  Early ATM machines gave customers their cash before returning the debit card - and numerous cards were left in the machines as a consequence. 

Purchasing new household equipment exposes people to changes in routine.  Other writers have commented on the difficulties of changing to a new model of a mobile phone, a DVD recorder, or other electronic item.  Purchasers change these at comparatively long intervals, during which time the manufacturers make steady changes and introduce new features.  What should be in the instruction manual (which was probably written by someone who is familiar with the immediately preceding model!)?

We have just bought a new upright freezer; the problem is that our behaviour (lifestyle) has been developed with the old one.  The new one has drawers and no shelves.  We have grown used to freezing food on a shelf, and, once frozen, either moving it  to a drawer, or to one side of the shelf to make room for further food to be frozen.  So we shall have to start freezing food in the spacious fast freeze drawer.  But that is going to mean
either (a) reserving that drawer for fast freezing (wasted space at other times)
or (b) rearranging items in the fast freeze drawer so that items we put in are not in contact with frozen food (inconvenient because it is so deep)

In due time we will adapt our lifestyle - but the model used by the designer for human behaviour with their freezer didn't include the way we use ours.

We have had to adapt our behaviour to the model used by the oven timer on our cooker.  A long time ago, the earliest cooker timers in the UK allowed you to set the start time and the finish time.  The next generation allowed you to set the start time and the duration of the oven being on.  Both of these needed a simple operation to keep the oven on for a while longer.  Our current model asks for the duration and the time to switch off.  Extending the cooking time requires reprogramming the timer, or switching it to manual.  You can see the reasoning in the designer's model for the use of a timer on an oven.  The oven is being used to prepare a meal, so you set the time of the meal and then the cooking time.  How reasonable!  But, that model presupposes that the oven is being set for one item.  What about the person who wants to cook a joint and to add a hot pudding to the oven before the joint is cooked?  What time should you programme to finish, and how long for?  That behaviour wasn't in the mind of the designer.

All of these are reminders that when we use models for thinking with, we must think of as many aspects of the situation as possible, and not assume that everyone behaves in the same way.