Question 1

If we wanted to represent an urban transportation system as a network flow problem, which of the following would be represented as nodes?

Accepted Answer

A)  streets 
B)  railway lines 
C)  street intersections 
D)  pedestrian right of ways 
A)  streets 
B)  railway lines 
C)  street intersections 
D)  pedestrian right of ways C

Question 2

In the linear programming formulation of the shortest route problem, the constraint for each node represents

Accepted Answer

A)  capacity on each path. 
B)  conservation of flow. 
C)  capacity on each branch. 
D)  minimum flow. 
A)  capacity on each path. 
B)  conservation of flow. 
C)  capacity on each branch. 
D)  minimum flow. B

Question 3

-Using the network shown and the conventional method discussed in your textbook, what are the first two nodes in the network and why? Now avoid convention and pick the first two nodes that must be part of the correct solution. Why is this the case?

Accepted Answer

Convention dictates that a solution begins with node 1 and proceeds to the nearest node, which is node 3 at a distance of 11. Tossing convention out, one should pick the two closest nodes, which in this network are nodes 4 and 5, separated by only 6 units.

Question 4

In a network modeling problem, the linear programming decision variables are given by

Accepted Answer

A)  source node. 
B)  sink node. 
C)  network branches. 
D)  network nodes. 
A)  source node. 
B)  sink node. 
C)  network branches. 
D)  network nodes.

Question 5

Flows in a network can only be in one direction.

Accepted Answer

A) True 
 B)False

Question 6

Figure 4
-Determine the maximal flow through the network in Figure 4. Assume that all branches are directed branches.

Accepted Answer

A)  10 
B)  11 
C)  13 
D)  16 
A)  10 
B)  11 
C)  13 
D)  16

Question 7

In a network flow problem, ________ connect nodes and show flow from one point to another.

Accepted Answer

The answer of In a network flow problem, ________ connect...

Question 8

A ________ network model could be used to represent the capacity of a series of dams for flood control.

Accepted Answer

The answer of A ________ network model could be used...

Question 9

-Use the network pictured and assume all labeled flows are forward flows. Suppose the reverse flows for each path are exactly half of the forward flows. What is the maximum flow through this network?

Accepted Answer

A)  18 
B)  28 
C)  10 
D)  8 
A)  18 
B)  28 
C)  10 
D)  8

Question 10

Determining where to build roads at the least cost within a park that reaches every popular sight represents a ________ network model.

Accepted Answer

minimal sp

Question 11

The shortest route problem requires that there be a branch from each destination to every other destination.

Accepted Answer

A) True 
 B)False

Question 12

The maximal flow algorithm

Accepted Answer

A)  does not require flow on every branch for the final solution. 
B)  may end with capacity remaining at the source. 
C)  may end with capacity at those nodes leading immediately to the destination. 
D)  all of the above 
A)  does not require flow on every branch for the final solution. 
B)  may end with capacity remaining at the source. 
C)  may end with capacity at those nodes leading immediately to the destination. 
D)  all of the above

Question 13

In a network flow problem, ________ represent junction points connecting branches.

Accepted Answer

The answer of In a network flow problem, ________ represent...

Question 14

The shortest route network problem could help identify the best plan for running cables for televisions throughout a building.

Accepted Answer

A) True 
 B)False

Question 15

The shortest route problem formulation requires a statement that mandates that what goes in to a node must equal what comes out of that node. This is referred to as ________.

Accepted Answer

conservati

Question 16

Figure 2
-Consider the network diagram given in Figure 2. Assume that the numbers on the branches indicate the length of cable (in miles) six nodes on a telecommunication network. What is the minimum number of miles of cable to be used to connect all six nodes?

Accepted Answer

A)  16 miles 
B)  17 miles 
C)  18 miles 
D)  19 miles 
A)  16 miles 
B)  17 miles 
C)  18 miles 
D)  19 miles

Question 17

Figure 1. Delivery Routes
-Consider the network diagram given in Figure 1. Assume that the numbers on the branches indicate the length of cable (in miles) between each pair of the six nodes on a telecommunication network. What is the minimum number of miles of cable to be used to connect all six nodes?

Accepted Answer

The answer of   Figure 1. Delivery Routes
-Consider the...

Question 18

The first step of the minimal spanning tree solution method is to

Accepted Answer

A)  select any starting node. 
B)  select the node closest to the starting node to join the spanning tree. 
C)  select the closest node not presently in the spanning tree. 
D)  arbitrarily select any path in the network from origin to destination. 
A)  select any starting node. 
B)  select the node closest to the starting node to join the spanning tree. 
C)  select the closest node not presently in the spanning tree. 
D)  arbitrarily select any path in the network from origin to destination.

Question 19

The origin node for this network is node number 1 and flow proceeds from node 1 to node 6. If the distance from node three to node six doubles , what is the change in the shortest route through the network?

Accepted Answer

The shortest route c

Question 20

In a minimal spanning tree, the source and destination nodes must be connected along a single path.

Accepted Answer

A) True 
 B)False

Exam 7: Network Flow Models

If we wanted to represent an urban transportation system as a network flow problem, which of the following would be represented as nodes?

In the linear programming formulation of the shortest route problem, the constraint for each node represents

-Using the network shown and the conventional method discussed in your textbook, what are the first two nodes in the network and why? Now avoid convention and pick the first two nodes that must be part of the correct solution. Why is this the case?

In a network modeling problem, the linear programming decision variables are given by

Flows in a network can only be in one direction.

Figure 4 -Determine the maximal flow through the network in Figure 4. Assume that all branches are directed branches.

In a network flow problem, ________ connect nodes and show flow from one point to another.

A ________ network model could be used to represent the capacity of a series of dams for flood control.

-Use the network pictured and assume all labeled flows are forward flows. Suppose the reverse flows for each path are exactly half of the forward flows. What is the maximum flow through this network?

Determining where to build roads at the least cost within a park that reaches every popular sight represents a ________ network model.

The shortest route problem requires that there be a branch from each destination to every other destination.

The maximal flow algorithm

In a network flow problem, ________ represent junction points connecting branches.

The shortest route network problem could help identify the best plan for running cables for televisions throughout a building.

The shortest route problem formulation requires a statement that mandates that what goes in to a node must equal what comes out of that node. This is referred to as ________.

Figure 2 -Consider the network diagram given in Figure 2. Assume that the numbers on the branches indicate the length of cable (in miles) six nodes on a telecommunication network. What is the minimum number of miles of cable to be used to connect all six nodes?

The first step of the minimal spanning tree solution method is to

The origin node for this network is node number 1 and flow proceeds from node 1 to node 6. If the distance from node three to node six doubles , what is the change in the shortest route through the network?

In a minimal spanning tree, the source and destination nodes must be connected along a single path.

Management Science

Linear Programming: Model Formulation and Graphical Solution

Linear Programming: Computer Solution and Sensitivity Analysis

Linear Programming: Modeling Examples

Integer Programming

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Project Management

Multicriteria Decision Making

Nonlinear Programming

Probability and Statistics

Decision Analysis

Queuing Analysis

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the Simplex Solution Method

Transportation and Assignment Solution Methods

Integer Programming: the Branch and Bound Method

Nonlinear Programming: Solution Techniques

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