Question 1

In the shortest route problem, nodes represent locations, and arcs represent the distance between locations.

Accepted Answer

A) True 
 B)False

Question 2

Minimal spanning tree problem can be applied to find

Accepted Answer

A) minimum distance between nodes 
B)  minimum length to connect all the nodes 
C)  maximal flow in a network 
D)  minimal capacity of a network 
A) minimum distance between nodes 
B)  minimum length to connect all the nodes 
C)  maximal flow in a network 
D)  minimal capacity of a network

Question 3

In the shortest route problem, the algorithm (the final result, that is, the shortest path found from origin to destination) can best be described by the nodes on the shortest path in the order in which they should be traversed to get from origin to destination.

Accepted Answer

A) True 
 B)False

Question 4

[ ] in the labels of the shortest path algorithm given in the text indicates that the node has having a permanent label.

Accepted Answer

A) True 
 B)False

Question 5

The symbol $\mathrm{S}$ in the labeling algorithm for shortest path represents stationary node.

Accepted Answer

A) True 
 B)False

Question 6

In the shortest route problem, the objective is to find the shortest route from an origin to a destination through a network.

Accepted Answer

A) True 
 B)False

Question 7

In the spanning tree algorithm, suppose that nodes 1,2 , and 3 are in the connected component at some point in the algorithm; this implies that all arcs between nodes 1,2 , and 3 , if they exist, will have to be in the connected component.

Accepted Answer

A) True 
 B)False

Question 8

In the linear programming formulation of the shortest path problem, the constraint corresponding to the origin will have 1 on its RHS.

Accepted Answer

A) True 
 B)False

Question 9

Using the data on a network of oil pipelines from Baku in Azerbaijan to a refinery in Turkey, if we solve the network flow problem with Baku as the source node and the Turkish refinery as the sink node, using the shortest route problem, the algorithm will find all shortest paths from any node to any node.

Accepted Answer

A) True 
 B)False

Question 10

If cost per foot length of pipe is $\$ 10$, the minimal total cost of connecting all nodes of a network with this piping is given by the total value of the minimum spanning tree $* 10$.

Accepted Answer

A) True 
 B)False

Question 11

Find the minimal spanning tree of the network given in Figure 6a.

Accepted Answer

Using the minimal spanning tree algorith

Question 12

-In Figure 2b, using backtracking step of the shortest route algorithm, the shortest route from node 1 to node 3 is

Accepted Answer

A)  $1-3$ 
B)  $1-3-2$ 
C)  $1-2-3$ 
D)  $1-2-4-6-3$ 
A)  $1-3$ 
B)  $1-3-2$ 
C)  $1-2-3$ 
D)  $1-2-4-6-3$

Question 13

-What is the total distance corresponding to the minimal spanning tree of Figure 3a?

Accepted Answer

A)  25 
B)  12 
C)  15 
D)  24 
A)  25 
B)  12 
C)  15 
D)  24

Question 14

In a minimal spanning tree solution, which of the following is not true?

Accepted Answer

A)  If you add one more arc to it, it will no longer be a minimal spanning tree 
B)  If you remove an arc, it will no longer be a spanning tree 
C)  You can find the shortest route by picking from the minimum spanning tree judiciously 
D)  There may be alternate minimal spanning trees in a problem 
A)  If you add one more arc to it, it will no longer be a minimal spanning tree 
B)  If you remove an arc, it will no longer be a spanning tree 
C)  You can find the shortest route by picking from the minimum spanning tree judiciously 
D)  There may be alternate minimal spanning trees in a problem

Question 15

-In Figure 3a, bold arc and all nodes attached to it is the connected node. Using the algorithm in the text for finding the minimal spanning tree, which will be the next node added to the set of connected nodes?

Accepted Answer

A)  3 
B)  6 
C)  4 
D)  5 
A)  3 
B)  6 
C)  4 
D)  5

Question 16

Network models are important because of their application potential and ease of solution procedures.

Accepted Answer

A) True 
 B)False

Question 17

In the minimal spanning tree algorithm given in the text, the final result, that is the minimum spanning tree, can best be described by the nodes in the minimal spanning tree.

Accepted Answer

A) True 
 B)False

Question 18

In flows in network, the optimal solution to the maximal flow problem cannot have simultaneous flows in both directions of an arc.

Accepted Answer

A) True 
 B)False

Question 19

The arcs in the shortest path problem represent

Accepted Answer

A)  quantities that can be shipped 
B)  direction of shipping 
C)  flow rate capacity 
D)  travel time from node to node 
A)  quantities that can be shipped 
B)  direction of shipping 
C)  flow rate capacity 
D)  travel time from node to node

Question 20

-In Figure 3b, what is the length of the minimum spanning tree using the algorithm presented in the text and continuing to add nodes to the connected components shown by thick arcs?

Accepted Answer

A) 16 
B)  17 
C)  12 
D)  26 
A) 16 
B)  17 
C)  12 
D)  26

In the shortest route problem, nodes represent locations, and arcs represent the distance between locations.

Minimal spanning tree problem can be applied to find

In the shortest route problem, the algorithm (the final result, that is, the shortest path found from origin to destination) can best be described by the nodes on the shortest path in the order in which they should be traversed to get from origin to destination.

[ ] in the labels of the shortest path algorithm given in the text indicates that the node has having a permanent label.

The symbol $\mathrm{S}$ in the labeling algorithm for shortest path represents stationary node.

In the shortest route problem, the objective is to find the shortest route from an origin to a destination through a network.

In the spanning tree algorithm, suppose that nodes 1,2 , and 3 are in the connected component at some point in the algorithm; this implies that all arcs between nodes 1,2 , and 3 , if they exist, will have to be in the connected component.

In the linear programming formulation of the shortest path problem, the constraint corresponding to the origin will have 1 on its RHS.

If cost per foot length of pipe is $\$ 10$ , the minimal total cost of connecting all nodes of a network with this piping is given by the total value of the minimum spanning tree $* 10$ .

Find the minimal spanning tree of the network given in Figure 6a.

-In Figure 2b, using backtracking step of the shortest route algorithm, the shortest route from node 1 to node 3 is

-What is the total distance corresponding to the minimal spanning tree of Figure 3a?

In a minimal spanning tree solution, which of the following is not true?

-In Figure 3a, bold arc and all nodes attached to it is the connected node. Using the algorithm in the text for finding the minimal spanning tree, which will be the next node added to the set of connected nodes?

Network models are important because of their application potential and ease of solution procedures.

In the minimal spanning tree algorithm given in the text, the final result, that is the minimum spanning tree, can best be described by the nodes in the minimal spanning tree.

In flows in network, the optimal solution to the maximal flow problem cannot have simultaneous flows in both directions of an arc.

The arcs in the shortest path problem represent

-In Figure 3b, what is the length of the minimum spanning tree using the algorithm presented in the text and continuing to add nodes to the connected components shown by thick arcs?

Introduction to Management Science, Modeling, and Excel Spreadsheets

Forecasting

Linear Programming: Basic Concepts and Graphical Solutions

Linear Programming: Applications and Solutions

Linear Programming: Sensitivity Analysis, Duality, and Specialized Models

Transportation, Assignment, and Transshipment Problems

Integer Programming

Nonlinear Optimization Models

Multi-Criteria Models

Decision Theory

Markov Analysis

Waiting Line Models

Simulation Cdrom Modules

Filters

Exam 8: Network Optimization Models

In the shortest route problem, nodes represent locations, and arcs represent the distance between locations.

Minimal spanning tree problem can be applied to find

In the shortest route problem, the algorithm (the final result, that is, the shortest path found from origin to destination) can best be described by the nodes on the shortest path in the order in which they should be traversed to get from origin to destination.

[ ] in the labels of the shortest path algorithm given in the text indicates that the node has having a permanent label.

The symbol S\mathrm{S}S in the labeling algorithm for shortest path represents stationary node.

In the shortest route problem, the objective is to find the shortest route from an origin to a destination through a network.

In the spanning tree algorithm, suppose that nodes 1,2 , and 3 are in the connected component at some point in the algorithm; this implies that all arcs between nodes 1,2 , and 3 , if they exist, will have to be in the connected component.

In the linear programming formulation of the shortest path problem, the constraint corresponding to the origin will have 1 on its RHS.

If cost per foot length of pipe is $10\$ 10$10 , the minimal total cost of connecting all nodes of a network with this piping is given by the total value of the minimum spanning tree ∗10* 10∗10 .

Find the minimal spanning tree of the network given in Figure 6a.

-In Figure 2b, using backtracking step of the shortest route algorithm, the shortest route from node 1 to node 3 is

-What is the total distance corresponding to the minimal spanning tree of Figure 3a?

In a minimal spanning tree solution, which of the following is not true?

-In Figure 3a, bold arc and all nodes attached to it is the connected node. Using the algorithm in the text for finding the minimal spanning tree, which will be the next node added to the set of connected nodes?

Network models are important because of their application potential and ease of solution procedures.

In the minimal spanning tree algorithm given in the text, the final result, that is the minimum spanning tree, can best be described by the nodes in the minimal spanning tree.

In flows in network, the optimal solution to the maximal flow problem cannot have simultaneous flows in both directions of an arc.

The arcs in the shortest path problem represent

-In Figure 3b, what is the length of the minimum spanning tree using the algorithm presented in the text and continuing to add nodes to the connected components shown by thick arcs?

Introduction to Management Science, Modeling, and Excel Spreadsheets

Forecasting

Linear Programming: Basic Concepts and Graphical Solutions

Linear Programming: Applications and Solutions

Linear Programming: Sensitivity Analysis, Duality, and Specialized Models

Transportation, Assignment, and Transshipment Problems

Integer Programming

Nonlinear Optimization Models

Multi-Criteria Models

Decision Theory

Markov Analysis

Waiting Line Models

Simulation Cdrom Modules

Filters

The symbol $\mathrm{S}$ in the labeling algorithm for shortest path represents stationary node.

If cost per foot length of pipe is $\$ 10$ , the minimal total cost of connecting all nodes of a network with this piping is given by the total value of the minimum spanning tree $* 10$ .