1 use the ”distance_matrix_calculation.mos” model (1) 3 1 1 1 1 1 (2) (3) (4)(5) (6)(7)...
TRANSCRIPT
1
Use the ”distance_matrix_calculation.mos” model
(1)
3
1
11
11
(2)
(3)
(4) (5)
(6) (7)
Structure of data file:
number_nodes:7
edges:[(1,2) 3(2,3) 1(2,4) 1(2,5) 1(3,6) 1(3,7) 1]
2
Calculate the shortest distance matrix for this network:
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3 4
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26
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16
26
10
121012
14
1012
1020
3
We want to distribute milk(in bottles) and cakes. Milk is produced in the node 1 and cakes are produced in the node 4. Customers are in all nodes. Customers 1,3,5,7,9 need 100 bottles of milk and 20 cakes each, other customers need 50 bottles of milk and 15 cakes each. Warehouses can be located at nodes 1,2,3,4 and each customer must be served exactly from one warehouse (for both commodities). Cost per building a warehouse is 5000 crowns. Handling cost gi is 0,5 crown.
Cost e0 per transport of one bottle of milk to the customers is 1 crown.
Cost e1 per transport of one bottle of milk to the warehouse is 0,5 crown.
Cost e0 per transport of one cake to the customers is 2 crown.
Cost e1per transport of one cake to the warehouse is 1 crown.
1 2
3 4
5
6
7
8
9
10
22
26
10
12
10
16
2610
121012
14
1012
1020
4
We want to distribute milk(in bottles) and cakes. Milk is produced in the node 1 and cakes are produced in the node 4. Customers are in all nodes. Customers 1,3,5,7,9 need 100 bottles of milk and 20 cakes each, other customers need 50 bottles of milk and 15 cakes each. Warehouses can be located at nodes 1,2,3,4 and each customer can be served from different warehouse for each commodity. Cost per building a warehouse is 5000 crowns. Handling cost gi is 0,5 crown.
Cost e0 per transport of one bottle of milk to the customers is 1 crown.
Cost e1 per transport of one bottle of milk to the warehouse is 0,5 crown.
Cost e0 per transport of one cake to the customers is 2 crown.
Cost e1per transport of one cake to the warehouse is 1 crown.
1 2
3 4
5
6
7
8
9
10
22
26
10
12
10
16
2610
121012
14
1012
1020
5
We want to distribute milk(in bottles). Milk can be produced in the nodes 1 and 2. Customers are in all nodes. Customers 1,3,5,7,9 need 100 bottles of milk, other customers need 50 bottles of milk. Warehouses can be located at nodes 1,2,3,4 and each customer must be served exactly from one warehouse.Cost per building a primary source is 9000 crowns. Cost per building a warehouse is 5000 crowns. Handling cost gi is 0,5 crown.
Cost e0 per transport of one bottle of milk to the customers is 1 crown.
Cost e1 per transport of one bottle of milk to the warehouse is 0,5 crown.
1 2
3 4
5
6
7
8
9
10
22
26
10
12
10
16
2610
121012
14
1012
1020
6
Let us consider that local authorities want to locate p=2 facilities at some places from the set 1, 2, 3 and 4 so that an average distance between customer and the nearest facility should be minimized.
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3 4
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22
26
10
12
10
16
2610
121012
14
1012
1020
7
JjIiforz
Iifory
py
JjIiforyz
JjforztoSubject
zdMinimize
ij
i
Iii
iij
Iiij
Ii Jjijij
,}1,0{
}1,0{
,
1
8
Let us consider that local authorities want to locate p=2 fire brigades at some places from the set 1, 2, 3 and 4 so that a distance from the worst located dwelling place from set {1, 2, …, 10} to a fire brigade be minimal.
1 2
3 4
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10
22
26
10
12
10
16
2610
121012
14
1012
1020
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The 2-Centre Problem consists in minimizing the maximum distance between customer and the nearest located facility:
}10,...,1:},max{min{ jdd sjrj
dij 1 2 3 4 5 6 7 8 9 10
1 0 12 24 38 22 10 10 26 22 34
2 12 0 12 26 34 10 20 26 22 22
3 24 12 0 14 48 22 22 20 10 10
4 38 26 14 0 62 36 36 22 24 12
Distancematrix
10
10,..,1,4,..,1}1,0{
4,..,1}1,0{
10,..,1,4,..,1
10,..,1,4,..,1
10,..,11
4
1
4
1
jiforz
ifory
jifortzd
py
jiforyz
jforztoSubject
tMinimize
ij
i
ijij
ii
iij
iij