Ch12_167-183

# Ch12_167-183 - 72106 CH12 GGS 3/30/05 2:24 PM Page 167 C H...

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167 T EACHING S UGGESTIONS Teaching Suggestion 12.1: The solution techniques for this chapter are easy and straightfor- ward. Although they obtain an optimal solution, students should be told that other optimal solutions (alternate optimal solutions) may exist. Unlike linear programming, however, these techniques do not alert students to this possibility. (QM for Windows soft- ware, does, however.) Teaching Suggestion 12.2: Have students solve the same minimal-spanning tree problem using different starting nodes. This will show students that they will get optimal solutions regardless of the starting point. In most cases, there will be alternate optimal solutions. Ask how students would recognize alternate optimal solutions for the minimal- spanning tree problem. Teaching Suggestion 12.3: The maximal-Fow technique can be used to solve a number of in- teresting types of problems. Have students develop and solve max- imal-Fow problems different from the ones in the chapter and at the end of the chapter. Teaching Suggestion 12.4: The maximal-Fow technique involves subtracting capacity along the path that is picked with some Fow. This can be confusing to some students. The capacity is subtracted in the opposite direction of the Fow to maintain correct network relationships. Teaching Suggestion 12.5: Students may wonder why we put the distance in a box by the node that is the closest to the origin. This is done to make it easier for us to ±nd the solution. The distance placed in the box repre- sents the shortest path from the origin to that node in the network. ²or larger problems, this is useful to help us keep track of interme- diate results. Teaching Suggestion 12.6: The shortest-route problem can be solved using several tech- niques, including dynamic programming. This can lead to a dis- cussion about selecting the best technique to solve a management science problem. A LTERNATIVE E XAMPLES Alternative Example 12.1: Given the following network, per- form the minimum spanning tree technique to determine the best way to connect nodes on the network, while minimizing total distance. We begin with node 1. Node 4 is the nearest node, and thus we connect node 1 to node 4. Given nodes 1 and 4, node 6 is the nearest, and we connect it to node 4. Now considering nodes 1, 4, and 6, we see that node 7 is the nearest to node 6 and we connect it. Node 5 is connected to node 7, and node 3 is connected to node 5 in the same way. ²inally, node 2 is connected to node 1. Using the minimum spanning tree technique, we can see that the total distance required to connect all nodes is 18. The follow- ing ±gure shows the results. Alternative Example 12.2: Given the network in the ±gure on the next page, determine the maximum amount that can Fow through the network. 12 CHAPTER Network Models 3 1 2 5 4 6 7 5 6 6 6 2 3 2 4 5 2 6 3 3 1 2 5 4 6 7 5 6 6 6 2 3 2 4 5 2 6 3 72106 CH12 GGS 3/30/05 2:24 PM Page 167

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168 CHAPTER 12 N ETWORK M ODELS We begin this problem by putting the maximum fow oF 4 through nodes 1, 2, and 6. This is shown in the Following ±gure.
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## This note was uploaded on 02/06/2012 for the course DSCI 3331 taught by Professor Michaelhanna during the Spring '11 term at UH Clear Lake.

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Ch12_167-183 - 72106 CH12 GGS 3/30/05 2:24 PM Page 167 C H...

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