The Alianz Arena is a football stadium in Munich home to Bayern Munich a German football club. The club have identified 12 potential camera locations within the stadium. They have also identified 25 stadium areas which may require camera coverage during the pre-game, game and post-game activities. The following table indicates each camera location and the stadium areas the camera can cover: Camera Location 1 2 3 4 5 6 7 8 9 10 11 12 Stadium Areas 1,3,4,6,7 8,4,7,12 2,5,9,11,13 1,2,18,19,21 3,6,10,12,14 8,14,15,16,17 18,21,24,25 2,10,16,23 1,6,11 20,22,24,25 2,4,6,8 1,6,12,17 Bayern Munich executives are concerned about the costs for the production. Consequently, they have set an objective of minimizing the number of camera locations. In seeking this objective they want at least one camera to be available to cover each stadium area. Camera location 9 is the "blimp," and executives have decided that the blimp will be used because of viewer expectation and fascination with the shots from this location. Stadium areas 1 and 2 are locker room locations. The viewer interest in football personalities has led the executives to request that at least two camera locations be available to cover each of these areas. Furthermore, one of the following configurations has to happen: at least 2 cameras in locations 1, 2, 3 or at least 1 camera in location 4 and 5. Also due to space limitations if a camera at location 5 is installed then a camera at location 6 cannot be installed. Formulate an ILP model to determine the minimum number of cameras needed for the desired coverage.
The Alianz Arena is a football stadium in Munich home to Bayern Munich a German football club. The club have identified 12 potential camera locations within the stadium. They have also identified 25 stadium areas which may require camera coverage during the pre-game, game and post-game activities. The following table indicates each camera location and the stadium areas the camera can cover: Camera Location 1 2 3 4 5 6 7 8 9 10 11 12 Stadium Areas 1,3,4,6,7 8,4,7,12 2,5,9,11,13 1,2,18,19,21 3,6,10,12,14 8,14,15,16,17 18,21,24,25 2,10,16,23 1,6,11 20,22,24,25 2,4,6,8 1,6,12,17 Bayern Munich executives are concerned about the costs for the production. Consequently, they have set an objective of minimizing the number of camera locations. In seeking this objective they want at least one camera to be available to cover each stadium area. Camera location 9 is the "blimp," and executives have decided that the blimp will be used because of viewer expectation and fascination with the shots from this location. Stadium areas 1 and 2 are locker room locations. The viewer interest in football personalities has led the executives to request that at least two camera locations be available to cover each of these areas. Furthermore, one of the following configurations has to happen: at least 2 cameras in locations 1, 2, 3 or at least 1 camera in location 4 and 5. Also due to space limitations if a camera at location 5 is installed then a camera at location 6 cannot be installed. Formulate an ILP model to determine the minimum number of cameras needed for the desired coverage.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Transcribed Image Text:The Alianz Arena is a football stadium in Munich home to Bayern Munich a German football club. The
club have identified 12 potential camera locations within the stadium. They have also identified 25
stadium areas which may require camera coverage during the pre-game, game and post-game activities.
The following table indicates each camera location and the stadium areas the camera can cover:
Camera Location
1
2
3
4
5
6
7
8
9
10
11
12
Stadium Areas
1,3,4,6,7
8,4,7,12
2,5,9,11,13
1,2,18,19,21
3,6,10,12,14
8,14,15,16,17
18,21,24,25
2,10,16,23
1,6,11
20,22,24,25
2,4,6,8
1,6,12,17
Bayern Munich executives are concerned about the costs for the production. Consequently, they have
set an objective of minimizing the number of camera locations. In seeking this objective they want at
least one camera to be available to cover each stadium area. Camera location 9 is the "blimp," and
executives have decided that the blimp will be used because of viewer expectation and fascination with
the shots from this location.
Stadium areas 1 and 2 are locker room locations. The viewer interest in football personalities has led the
executives to request that at least two camera locations be available to cover each of these areas.
Furthermore, one of the following configurations has to happen: at least 2 cameras in locations 1, 2, 3 or
at least 1 camera in location 4 and 5.
Also due to space limitations if a camera at location 5 is installed then a camera at location 6 cannot be
installed.
Formulate an ILP model to determine the minimum number of cameras needed for the desired
coverage.
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