A transportation problem

One of the hard lessons of Operational Research is the definition of the system that is being studied.  If you are taught the subject well, then you learn that there are times when optimising a part of the system degrades the whole of the system.  This may be illustrated with a simple, and silly example.  Optimising the storage cost of an inventory will mean that the amount in stock is minimal; but the economic order quantity formula balances this cost with the cost of supply and procurement, so that a larger stock will be held with consequent reduction in the frequency of placing orders.

On a larger scale, the limits of the system being studied are often too difficult to completely include.  But one needs to be aware of them.

Not so long ago, we drove north and east up the motorway form Exeter and then took a main road to a nearby town that we have rarely visited.  (Up means in the direction of London, at least if you live in Devon.) About 400 metres from the motorway junction, there was a lay-by, filled nose-to-tail with cars, all empty.  When we returned, in the early evening, some of the cars had left.  As we watched, cars stopped in the lay-by, one or more passengers got out, and collected cars which had been parked in the lay-by.  Quite clearly, the lay-by was being used as a transport hub by people who shared cars for commuting.  And, one suspects, it was not designed as such.  We have observed similar use of lay-bys, and patches of waste ground, near other junctions of major roads and motorways.  It is a regular phenomenon at park-and-ride car-parks on the outskirts of UK cities, where a large car-park is provided with a bus service into the centre -- and the car park is also used by those sharing a car.  In some countries, but rarely in Britain, road junctions are actually designed to have provision of parking for car-sharing.   Actually, in Britain, there are some service areas for refreshments and fuel at junctions, and these actually deter long-term parking of this nature. 

Now, an O.R. problem would be to determine the optimum size of such a car-park.  The trouble is, at present, the users pay nothing.  Therefore, in terms of revenue to the provider, there is no incentive to provide the space at all.  But if you are thinking of the larger system, and actually encouraging car-sharing, because it is good for the environment and reduces congestion, then you need the space.  And you hope that someone recognises that it is a good use of public money to offer such space.  Once the system is recognised as being "provide enough space for the people who want to car-share from this hub" you can start to assess the size of the provision, using observation of demand, forecasts of traffic, and perhaps surveys of users and potential users.  Of the three lay-bys that I have observed, all are full during the working day, so must be too small.  And so I wonder where any extra cars are parked if a driver arrives too late to find space in the convenient lay-by?.


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