Models for thinking with - right or wrong?
The first encounter that I ever had with Operational Research was an article with the title "Models for thinking with". It was a very simple introduction to the science of O.R. Despite its simplicity, it brought out some of the features of an O.R. study, especially the idea of using a model to represent the underlying reality of a business situation or problem.
And I suppose that one of the characteristics of good O.R. is the ability to look at "the problem" and devise ways of modelling it, to include data and decisions. In other contexts, one might call it analysis, but that has other meanings to mathematicians and computer scientists, so I use the term with caution.
There are times when there are several ways of constructing a model. I forget which leading O.R. academic, back in the late 1940s or early 1950s, attended a lecture on the simplex method for solving linear programming models. He remarked afterwards that he doubted if the technique would be of great value, because "the world is nonlinear". His models of the world reflected that nonlinearity; linear programming models give a different model of the world. Which is correct? There are other lessons from history where there have been two (or more) models of a real world situation, and with the passage of time, one has been shown to be incorrect or inadequate. There was a computer engineer who predicted that the US would need four or five computers, back in the 1950s. (So now we have three computers and a smartphone in our study.)
I have blogged in the past about when two models come into conflict, and from time to time, I come across further examples. So here are a few from Devon and Exeter, though most can be replicated in many other places.
(1) How far apart should houses be built? Many semi-detached houses in the city, built in the 1930s to 1950s, were constructed with a shared drive between the houses, leading to a Y-fork and two garages. The width of the shared drive was designed for the cars of that era, and modern cars are too wide to fit. The architect's model of the need was based on current observations (of the size of cars), and did not consider the consequences of any change in the data. Surprisingly, older houses in the city are better equipped for garages, as they were built with a service road at the rear of the property which can give access to cars.
(2) What places should be on signposts? Most signs are put up by people who are local and know the area. Their models of the needs reflect their knowledge. On the other hand, those who are strangers to the area need different information. Sometimes the two are in conflict. A few years ago, a lot of signs went up around here, pointing to "Torbay", as a generic term, known to locals (and thus part of their model of the area) for Torquay, Paignton and Brixham. When it was realised that people heading for Torquay did not identify Torbay with Torquay, the signs were changed. Within the city, one of the car parks has been renamed "John Lewis car park" and there is some confusion as the name does not appear on older street maps, and has only just started to feature on satnavs. The model for signage is a local one, not one aimed at the general user.
(3) Following on from (2) are the signs on long distance routes. There are many examples of signs which indicate a distant town, and the next sign that the traveller passes on the way there has no mention of that distant town. The signs mayhave been designed and erected by two people with different models of the need of the motorist.
(4) The book and film and play "War Horse" (written by Devon author Michael Morpurgo) draws attention to two models of warfare that existed at the start of the first World War. Some army staff believed in the persistence of cavalry, but the cavalry charge was defeated by a model of warfare that used machine guns.
So, lessons -- what assumptions are you making about your models? Are they reasonable?
And I suppose that one of the characteristics of good O.R. is the ability to look at "the problem" and devise ways of modelling it, to include data and decisions. In other contexts, one might call it analysis, but that has other meanings to mathematicians and computer scientists, so I use the term with caution.
There are times when there are several ways of constructing a model. I forget which leading O.R. academic, back in the late 1940s or early 1950s, attended a lecture on the simplex method for solving linear programming models. He remarked afterwards that he doubted if the technique would be of great value, because "the world is nonlinear". His models of the world reflected that nonlinearity; linear programming models give a different model of the world. Which is correct? There are other lessons from history where there have been two (or more) models of a real world situation, and with the passage of time, one has been shown to be incorrect or inadequate. There was a computer engineer who predicted that the US would need four or five computers, back in the 1950s. (So now we have three computers and a smartphone in our study.)
I have blogged in the past about when two models come into conflict, and from time to time, I come across further examples. So here are a few from Devon and Exeter, though most can be replicated in many other places.
(1) How far apart should houses be built? Many semi-detached houses in the city, built in the 1930s to 1950s, were constructed with a shared drive between the houses, leading to a Y-fork and two garages. The width of the shared drive was designed for the cars of that era, and modern cars are too wide to fit. The architect's model of the need was based on current observations (of the size of cars), and did not consider the consequences of any change in the data. Surprisingly, older houses in the city are better equipped for garages, as they were built with a service road at the rear of the property which can give access to cars.
(2) What places should be on signposts? Most signs are put up by people who are local and know the area. Their models of the needs reflect their knowledge. On the other hand, those who are strangers to the area need different information. Sometimes the two are in conflict. A few years ago, a lot of signs went up around here, pointing to "Torbay", as a generic term, known to locals (and thus part of their model of the area) for Torquay, Paignton and Brixham. When it was realised that people heading for Torquay did not identify Torbay with Torquay, the signs were changed. Within the city, one of the car parks has been renamed "John Lewis car park" and there is some confusion as the name does not appear on older street maps, and has only just started to feature on satnavs. The model for signage is a local one, not one aimed at the general user.
(3) Following on from (2) are the signs on long distance routes. There are many examples of signs which indicate a distant town, and the next sign that the traveller passes on the way there has no mention of that distant town. The signs mayhave been designed and erected by two people with different models of the need of the motorist.
(4) The book and film and play "War Horse" (written by Devon author Michael Morpurgo) draws attention to two models of warfare that existed at the start of the first World War. Some army staff believed in the persistence of cavalry, but the cavalry charge was defeated by a model of warfare that used machine guns.
So, lessons -- what assumptions are you making about your models? Are they reasonable?
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