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Logistical and Transportation Planning Methods
1.203J/6.281J/13.665J/15.073J/16.76J/ESD.216J
Massachusetts Institute of Technology
Cambridge, Massachusetts
Quiz #1
October 25, 2006
OPEN BOOK
TWO HOURS
4 PAGES, 3 PROBLEMS
PLEASE SHOW ALL YOUR WORK!
1
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View Full DocumentProblem 1:
Patrolling Police Car (40 points)
A patrolling police car is assigned to the rectangular sector shown in the figure.
The
sector is bounded on all four sides by a roadway that requires 50% of the police car’s
patrolling time.
The other 50% of the time, the car patrols the inner rectangular part of
the sector.
Thus, at a random time when the police car is available for dispatch, the
police car’s location is equally likely to be drawn from a uniform distribution over the
bounding roadway or by a uniform distribution over the rectangular part of the sector
inside the bounding roadway.
Travel is rightangle or the Manhattan metric, with
directions of travel parallel to the sides of the rectangle.
911 calls for service are also
distributed randomly over the rectangular sector, in the same way as the police car and
independently of the location of the police car.
That is, 50% of the 911 calls are
uniformly distributed over the bounding roadway and 50% uniformly distributed over the
inner rectangular part of the sector.
Given a random call for service at a give location,
the police car will follow a minimum distance rightangle path from its current location to
the location of the call.
Thus, we assume that the police car can exit the bounding
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 Fall '06
 hansman

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