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 minimalspanning 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 maximalflow technique can be used to solve a number of in
teresting types of problems. Have students develop and solve max
imalflow problems different from the ones in the chapter and at
the end of the chapter.
Teaching Suggestion 12.4:
The maximalflow 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 shortestroute 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

Click to edit the document details