06quiz1 - Logistical and Transportation Planning Methods

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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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Problem 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 right-angle 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 right-angle 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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06quiz1 - Logistical and Transportation Planning Methods

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