1. 1 Use the ”distance_matrix_calculation.mos” model (1) 3 1 1 1 1 1 (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. 2 Calculate the shortest distance matrix for this network: 12 34 5 6 7 8 9 10 22 26 10 12 10 16 26 10 1210 12 14 10 12 10 20

3. 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 g i is 0,5 crown. Cost e 0 per transport of one bottle of milk to the customers is 1 crown. Cost e 1 per transport of one bottle of milk to the warehouse is 0,5 crown. Cost e 0 per transport of one cake to the customers is 2 crown. Cost e 1 per transport of one cake to the warehouse is 1 crown. 12 34 5 6 7 8 9 10 22 26 10 12 10 16 26 10 1210 12 14 10 12 10 20

4. 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 g i is 0,5 crown. Cost e 0 per transport of one bottle of milk to the customers is 1 crown. Cost e 1 per transport of one bottle of milk to the warehouse is 0,5 crown. Cost e 0 per transport of one cake to the customers is 2 crown. Cost e 1 per transport of one cake to the warehouse is 1 crown. 12 34 5 6 7 8 9 10 22 26 10 12 10 16 26 10 1210 12 14 10 12 10 20

5. 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 g i is 0,5 crown. Cost e 0 per transport of one bottle of milk to the customers is 1 crown. Cost e 1 per transport of one bottle of milk to the warehouse is 0,5 crown. 12 34 5 6 7 8 9 10 22 26 10 12 10 16 26 10 1210 12 14 10 12 10 20

6. 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. 12 34 5 6 7 8 9 10 22 26 10 12 10 16 26 10 1210 12 14 10 12 10 20

7. 7

8. 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. 12 34 5 6 7 8 9 10 22 26 10 12 10 16 26 10 1210 12 14 10 12 10 20

9. 9  The 2-Centre Problem consists in minimizing the maximum distance between customer and the nearest located facility: d ij 12345678910 101224382210 262234 2120 26341020202622 32412014484822 2010 43826140626236 222412 Distance matrix

10. 10