Parking Permit Problems

Exeter, like many cities and towns, has a parking problem.  There are many streets which have no provision for off-street parking for residents and businesses.  Some were built in the 19th century, before cars, others date from the 20th century and the houses were built on false assumptions; either that local people would not have cars, or, in many parts of the city, the houses were planned when cars were smaller.  (The latter is seen in at least two ways; the plots for garages were made the wrong size; houses were built too close together and the garages were built behind the houses.)  And increasingly, households own more than one car.  So many people park their cars on the roads outside their homes.
However, if this parking is not regulated, chaos may follow.  If the streets are close to places of work, then commuters may try to park there.  Often there is not enough space in a street for every house to have one parking space, let alone have space for more than one.
So, residents in many streets obtain parking permits.  These allow the car to be parked anywhere within a zone around the owner's home, generally including the street in front of their home (but not always, because it may be a major traffic route).  Exeter has several zones, and cars may only have a resident's permit for one.  Business users may have permits for some vehicles, and there is a category of "essential visitors" as well. 
The operational research problem is the establishment of the zones.  It is not like the problem of establishing wards for elections, since not all streets need to be allocated to a zone; there may be sufficient parking in a residential area so that no restrictions are needed.  The zones do not overlap, so one could pose the problem as one of dividing the whole city into parking permit zones and the rest.  If you did that, the "rest" might be quite hard to define - it seems better to simply say that the problem is of defining zones for parking.    A zone must be contiguous, have natural boundaries, be easy to define, and must be "fair" to residents and businesses.  And it must not be too large.  (A large zone could lead to people commuting from one side (home) to the other (work or shops or transport hub) especially if the zone touches areas of business or commerce.)    So there are multiple objectives to be satisfied. 
One approach would be to create one zone at a time.  It might not be optimal, but it might give a "good enough" solution.  Heuristic methods can be pretty good!
All over the city, such zones have been set up.  Generally, people are happy with them, even though you have to pay for the privilege of parking outside your own house, or as near as you can find a space.
However, changing the zones can be controversial.  Recently, the city has added new zones where there was unrestricted (read "free for all") in the past.  Not everyone was happy, because it was necessary to draw boundaries where the residents were in the former habit (of necessity) of parking in one of several nearby streets, and these were now in different zones.  But the council does not issue two permits for one vehicle. 
So, here is a practical problem.  I have suggested one solution method.  Is there a better one?


  1. One possible way to mitigate problems with adding zones is to partition zones into smaller chunks. Suppose that zone A consists of chunks A1 and A2, with A2 due east of A1. Later, the city adds zone B, whose western edge abuts the eastern edge of A. Partition B in B1 and B2. A permits let you park in A1 or A2, and B permits let you park in B1 or B2. Now offer permits for zone C, consisting of A2 and B1, to residents living near the A/B boundary.


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