ons existed, and distance in the vertical direction must be at least 50% more the than the horizontal distance for the sector. He explained that laying out sectors in that manner meant that the patrol areas would have a greater tendency to overlap different residential, income, and retail areas than if they ran the other way. He said that these areas were layered from north to south in the city, so if a sector area was laid out east to west, all of it would tend to be in one demographic layer. Angela indicated that she had almost enough informa- tion to develop a model, except that she also needed to know the average travel speed the patrol cars could travel. Joe told her that cars moving vertically traveled an average of 15 miles per hour, whereas cars traveled horizontally an average of 20 miles per hour. He said that the difference was due to different traffic flows. Develop a linear programming model for this problem and sol ve it by using the graphical method.

Understanding Business
12th Edition
ISBN:9781259929434
Author:William Nickels
Publisher:William Nickels
Chapter1: Taking Risks And Making Profits Within The Dynamic Business Environment
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Subject: management science

METROPOLITAN POLICE PATROL
time it took to respond to a call (assuming that a car left
immediately upon receiving the call) is simply the average
distance traveled divided by the average travel speed.
Angela told Joe that now that she understood how aver-
I he Metropolitan Police Department was recently criti-
cized in the local media for not responding to police calls age travel time to a call was determined, she could see that
in the downtown area rapidly enough. In several recent it was closely related to the size of the patrol area. She
cases, alarms had sounded for break-ins, but by the time asked Joe if there were any restrictions on the size of the
the police car arrived, the perpetrators had left, and in one area sectors that cars patrolled. He responded that for their
instance a store owner had been shot. Sergeant Joe Davis city, the department believed that the perimeter of a patrol
was assigned by the chief as head of a task force to find a sector should not be less than 5 miles or exceed 12 miles.
way to determine the optimal patrol area (dimensions) for He noted several policy issues and staffing constraints that
their cars that would minimize the average time it took to required these specifications. Angela wanted to know if any
respond to a call in the downtown area.
Sergeant Davis solicited help from Angela Maris, an distance in the vertical direction must be at least 50% more
analyst in the operations area for the police department. than the horizontal distance for the sector. He explained
Together they began to work through the problem.
Joe noted to Angela that normal patrol sectors are laid areas would have a greater tendency to overlap different
out in rectangles, with each rectangle including a number residential, income, and retail areas than if they ran the
of city blocks. For illustrative purposes he defined the di- other way. He said that these areas were layered from north
mensions of the sector as x in the horizontal direction and to south in the city, so if a sector area was laid out east to
as y in the vertical direction. He explained to Angela that west, all of it would tend to be in one demographic layer.
cars traveled in straight lines either horizontally or verti-
cally and turned at right angles. Travel in a horizontal di- tion to develop a model, except that she also needed to
rection must be accompanied by travel in a vertical know the average travel speed the patrol cars could travel.
direction, and the total distance traveled is the sum of the Joe told her that cars moving vertically traveled an average
horizontal and vertical segments. He further noted that past of 15 miles per hour, whereas cars traveled horizontally an
research on police patrolling in urban areas had shown that average of 20 miles per hour. He said that the difference
the average distance traveled by a patrol car responding to was due to different traffic flows.
a call in either direction was one-third of the dimensions of
the sector, or x/3 and y/3. He also explained that the travel and solve it by using the graphical method.
additional restrictions existed, and Joe indicated that the
that laying out sectors in that manner meant that the patrol
Angela indicated that she had almost enough informa-
Develop a linear programming model for this problem
Transcribed Image Text:METROPOLITAN POLICE PATROL time it took to respond to a call (assuming that a car left immediately upon receiving the call) is simply the average distance traveled divided by the average travel speed. Angela told Joe that now that she understood how aver- I he Metropolitan Police Department was recently criti- cized in the local media for not responding to police calls age travel time to a call was determined, she could see that in the downtown area rapidly enough. In several recent it was closely related to the size of the patrol area. She cases, alarms had sounded for break-ins, but by the time asked Joe if there were any restrictions on the size of the the police car arrived, the perpetrators had left, and in one area sectors that cars patrolled. He responded that for their instance a store owner had been shot. Sergeant Joe Davis city, the department believed that the perimeter of a patrol was assigned by the chief as head of a task force to find a sector should not be less than 5 miles or exceed 12 miles. way to determine the optimal patrol area (dimensions) for He noted several policy issues and staffing constraints that their cars that would minimize the average time it took to required these specifications. Angela wanted to know if any respond to a call in the downtown area. Sergeant Davis solicited help from Angela Maris, an distance in the vertical direction must be at least 50% more analyst in the operations area for the police department. than the horizontal distance for the sector. He explained Together they began to work through the problem. Joe noted to Angela that normal patrol sectors are laid areas would have a greater tendency to overlap different out in rectangles, with each rectangle including a number residential, income, and retail areas than if they ran the of city blocks. For illustrative purposes he defined the di- other way. He said that these areas were layered from north mensions of the sector as x in the horizontal direction and to south in the city, so if a sector area was laid out east to as y in the vertical direction. He explained to Angela that west, all of it would tend to be in one demographic layer. cars traveled in straight lines either horizontally or verti- cally and turned at right angles. Travel in a horizontal di- tion to develop a model, except that she also needed to rection must be accompanied by travel in a vertical know the average travel speed the patrol cars could travel. direction, and the total distance traveled is the sum of the Joe told her that cars moving vertically traveled an average horizontal and vertical segments. He further noted that past of 15 miles per hour, whereas cars traveled horizontally an research on police patrolling in urban areas had shown that average of 20 miles per hour. He said that the difference the average distance traveled by a patrol car responding to was due to different traffic flows. a call in either direction was one-third of the dimensions of the sector, or x/3 and y/3. He also explained that the travel and solve it by using the graphical method. additional restrictions existed, and Joe indicated that the that laying out sectors in that manner meant that the patrol Angela indicated that she had almost enough informa- Develop a linear programming model for this problem
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