{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Ch12_167-183

# Ch12_167-183 - 72106 CH12 GGS 2:24 PM Page 167 C H A P T E...

This preview shows pages 1–2. Sign up to view the full content.

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-flow technique can be used to solve a number of in- teresting types of problems. Have students develop and solve max- imal-flow problems different from the ones in the chapter and at the end of the chapter. Teaching Suggestion 12.4: The maximal-flow technique involves subtracting capacity along the path that is picked with some flow. This can be confusing to some students. The capacity is subtracted in the opposite direction of the flow 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 find the solution. The distance placed in the box repre- sents the shortest path from the origin to that node in the network. For 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. Finally, 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 figure shows the results. Alternative Example 12.2: Given the network in the figure on the next page, determine the maximum amount that can flow through the network.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.
• Spring '11
• MichaelHanna
• Flow network, Maximum flow problem, branch branch branch, Branch Branch Branch Branch Branch Branch Branch Branch Branch Branch Branch Branch Branch Branch Branch Branch Branch Branch Branch Branch Branch Branch Branch Branch Branch Branch Branch Branch Branch Branch Branch Branch Branch Branch Branch Branch Bra

{[ snackBarMessage ]}

### Page1 / 17

Ch12_167-183 - 72106 CH12 GGS 2:24 PM Page 167 C H A P T E...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online