DMOR-02-04 - UF-ESI-6314 DMOR-02-04.xmcd page 1 of 2 02-04....

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Unformatted text preview: UF-ESI-6314 DMOR-02-04.xmcd page 1 of 2 02-04. Model the following problem and display the optimal solution you obtain from Solver. You do not need to turn in your Excel files. Consider the following network, and suppose that we must find two paths from the origin (node 1) to the destination (node 9). Each path represents telephone line that we lay to connect one customer to another (in one direction). However, we need two paths for redundancy in case any one arc breaks. Therefore, the paths must not use any arcs in common. (They can use nodes in common.) Formulate this problem as a network flow problem (use the nodes and arcs below, with their associated costs, and tell me what the capacities and surplus/demand values are). The objective is to minimize the total cost of installing telephone lines. 11 8 1 6 3 3 5 2 7 4 5 5 7 8 9 7 2 9 8 10 8 3 6 i := 1 .. 9 Per Schaum's Outline of Operations Research Chapter 13: "A minimum-span problem involves a set of nodes and a set of proposed branches, none of them oriented. [...] It is not hard to see that a minimum-span problem is always solved by a tree." This means that to solve this problem requires solving the most optimal solution as a tree, removing those arcs from the diagram, then solving the most optimal solution again, thus revealing the two most optimal solutions. Using the Shaum's cheapest-path method to get started. Luther Setzer 1 NASA Pkwy E Stop NEM3, Kennedy Space Center, FL 32899 (321) 544-7435 UF-ESI-6314 DMOR-02-04.xmcd page 2 of 2 Input 123 4567 89 83 1 11 7 2 65 3 7 Output 4 5 38 9 5 10 6 2 7 8 8 9 Input 123 4567 89 3 1 2 5 3 Output 4 5 10 6 7 8 8 9 SUM = 26 Input 123 4567 89 3 1 2 6 3 7 Output 4 5 5 10 6 2 7 8 9 SUM = 28 Luther Setzer 1 NASA Pkwy E Stop NEM3, Kennedy Space Center, FL 32899 (321) 544-7435 ...
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This note was uploaded on 02/02/2010 for the course ESI 6314 taught by Professor Vladimirlboginski during the Fall '09 term at University of Florida.

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