Deck 7: Network Flow Models

Question 1

The choice of the initial node in the minimal spanning tree technique must be the first node.

Answer 1

False

Question 2

Flows in a network can only be in one direction.

Answer 2

False

Question 3

Regardless of the number of nodes in a network, the minimal spanning tree always contains the two nodes with the shortest distance between them.

Answer 3

True

Question 4

The first step of the minimal spanning tree solution to compute the distance of any path through the network.

Question 5

The shipping company manager wants to determine the best routes for the trucks to take to reach their destinations. This problem can be solved using the minimal spanning tree.

Question 6

The goal of the maximal flow problem is to maximize the amount of flow of items from an origin to a destination.

Question 7

Regardless of the number of nodes in a network, the minimal spanning tree never contains the two nodes with the greatest distance between them.

Question 8

The minimal spanning tree problem is to connect all nodes in a network so that the total branch lengths are minimized.

Question 9

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

Question 10

Branches connect nodes and show flow from one point to another.

Question 11

The shortest route problem is to find the shortest distance between an origin and various destination points.

Question 12

The minimal spanning tree allows the visitation of each node without backtracking.

Question 13

The last step of the minimal spanning tree solution method is to make sure all nodes have joined the spanning tree.

Question 14

A network is an arrangement of paths connected at various points through which items move.

Question 15

The values assigned to branches typically represent distance, time, or cost.

Question 16

Networks are popular because they provide a picture of a system and because a large number of systems can be easily modeled as networks.

Question 17

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

Question 18

Once the shortest route to a particular node has been determined, that node becomes part of the permanent set.

Question 19

The shortest route network problem could help identify the best route for pizza delivery drivers from the pizza parlor to a specific customer.

Question 20

Nodes represent junction points connecting branches.

Question 21

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

Question 22

The source node is the input node in a maximal flow problem.

Question 23

The ________ connects all nodes in a network so that the total branch lengths are minimized.

Question 24

In a network flow problem, the values assigned to ________ typically represent distance, time, or cost.

Question 25

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 ________.

Question 26

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

Question 27

To determine the maximum possible flow of railroad cars through the rail system, they should first select the longest path from origin to destination and ship as much as possible on that path.

Question 28

The shipping company manager wants to determine the best routes for the trucks to take to reach their destinations. This problem can be solved using the ________ solution technique.

Question 29

A company plans to use an automatic guided vehicle for delivering mail to ten departments. The vehicle will begin from its docking area, visit each department, and return to the docking area. Cost is proportional to distance traveled. The type of network model that best represent this situation is ________.

Question 30

In networks with fewer than five nodes, the minimal spanning tree algorithm will yield answers identical to the maximal flow solution approach.

Question 31

The maximal flow solution algorithm allows the user to choose a path through the network from the origin to the destination by any criteria.

Question 32

The maximal flow algorithm may end with capacity remaining at the source.

Question 33

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

Question 34

The direction of the flow is not critical in the maximal flow problem.

Question 35

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

Question 36

The goal of the ________ problem is to maximize the amount of flow of items from an origin to a destination.

Question 37

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

Question 38

A courier service located at the south edge of downtown dispatches three bicycle couriers with identical sets of architectural renderings that must go to three different downtown law offices as quickly as possible. This problem is a likely candidate for analysis using ________.

Question 39

A traffic system could be represented as a network in order to determine bottlenecks using the maximal flow network algorithm.

Question 40

For a directed branch, flow is possible in only one direction.

Question 41

Figure 1. Delivery Routes
Consider the network diagram given in Figure 1. Assume that the amount on each branch is the distance in miles between the respective nodes. Also assume that it is not possible to travel from a node with a higher number to a node with a lower number. Write the constraint associated with the second node (node 2) for the 0-1 integer linear programming formulation of the shortest route problem.

Question 42

Consider the following network, which shows the location of various facilities within a youth camp and the distances (in tens of yards) between each facility. There is a swampy area between facilities A and E.

A clean-up crew is stationed at facility D and wants to take the shortest route to each site. They usually clean up facilities C, E, A and F on the same day and therefore want the shortest route from D to each facility. Recommend a route for the crew to leave from D, clean up each facility one after the other, and return to facility D. (Assume all paths are accessible.)

Question 43

In a typical network flow problem, the branches show flow from one node to the next. The nodes themselves are ________ points.

Question 44

Once a decision maker has determined the shortest route to any node in the network, that node becomes a member of the ________.

Question 45

Consider the following network, which shows the location of various facilities within a youth camp and the distances (in tens of yards) between each facility. There is a swampy area between facilities A and E.

A clean-up crew is stationed at facility F and wants to take the shortest route to each site. They usually clean up facilities B and A on the same day and therefore want the shortest route from F to each facility. Recommend a route for the crew to leave from F, clean up each facility A and B, and then return to facility F. (Assume all paths are accessible.)

Question 46

Pro-Carpet company manufactures carpets in Northwest Indiana and delivers them to warehouses and retail outlets. The network diagram given in the figure below shows the possible routes and travel times (in minutes) from the carpet plant to the various warehouses or retail outlets.
V = Valparaiso, P=Portage, G=Gary, Ha=Hammond, Hi=Highland, M = Merillville, L = Lansing
Determine the shortest route for a carpet delivery truck from the carpet plant in Valparaiso, Indiana, to warehouses in Hammond, Gary, and Merillville. State the total completion time in minutes or each route

Question 47

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?

Question 48

Consider the following network, which shows the location of various facilities within a youth camp and the distances (in tens of yards) between each facility. There is a swampy area between facilities A and E.

Walking trails will be constructed to connect all the facilities. In order to preserve the natural beauty of the camp (and to minimize the construction time and cost), the directors want to determine which paths should be constructed. Use this network to determine which paths should be built.

Question 49

A one-way street in a downtown area should be modeled as a(n) ________ branch in a maximal flow model.

Question 50

Determining where capacity needs to be added within a series of one-way roads within a park represents a ________ model.

Question 51

Pro-Carpet company manufactures carpets in Northwest Indiana and delivers them to warehouses and retail outlets. The network diagram given in the figure below shows the possible routes and travel times (in minutes) from the carpet plant to the various warehouses or retail outlets.
V = Valparaiso, P=Portage, G=Gary, Ha=Hammond, Hi=Highland, M = Merillville, L = Lansing
Determine the shortest route for a carpet delivery truck from the carpet plant in Valparaiso, Indiana, to retail outlets in Portage, Highland, and Lansing. State the total completion time in minutes or each route

Question 52

Determining where to build one way roads at the least cost within a park that takes visitors to every popular sight and returns them to the entrance represents a ________ network model.

Question 53

Figure 1. Delivery Routes
Consider the network diagram given in Figure 1. Assume that the amount on each branch is the distance in miles between the respective nodes. Also assume that it is not possible to travel from a node with a higher number to a node with a lower number. Write the constraint associated with the fifth node (node 5) for the 0-1 integer linear programming formulation of the shortest route problem.

Question 54

Consider the following network, which shows the location of various facilities within a youth camp and the distances (in tens of yards) between each facility.

The camp nurse is stationed at Facility B. What is the shortest route from B to C?

Question 55

Figure 1. Delivery Routes
Consider the network diagram given in Figure 1. Assume that the amount on each branch is the distance in miles between the respective nodes. What is the shortest route from the source node (node 1) to nodes 5 and 6? Indicate the total distance for each route.

Question 56

Write the constraint associated with the Valparasio (source) node for the 0-1 integer linear programming formulation of the shortest route problem.

Question 57

Consider the following network, which shows the location of various facilities within a youth camp and the distances (in tens of yards) between each facility.

Walking trails will be constructed to connect all the facilities. In order to preserve the natural beauty of the camp (and to minimize the construction time and cost), the directors want to determine which paths should be constructed. Use this network to determine which paths should be built.

Question 58

Draw the network associated with the following constraints for a shortest route problem.
X12 + X13 = 1
X12 - X24 = 0
X13 - X34 = 0
X24 + X34 - X45 = 0
X45 = 1

Question 59

Figure 1. Delivery Routes
Consider the network diagram given in Figure 1. Assume that the amount on each branch is the distance in miles between the respective nodes. What is the shortest route from the source node (node 1) to nodes 2, 3, and 4? Indicate the total distance for each route.

Question 60

Write the constraint associated with the Lansing (destination) node for the 0-1 integer linear programming formulation of the shortest route problem.

Question 61

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

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

Question 62

Consider the network shown in the figure. The architect decides to remove a few of the (undirected) arcs but still have each node connected to at least one other node within a single network. Which arcs should be removed and what is the total arc length that is removed?

Question 63

The origin node for this network is node number 1 and flow proceeds from node 1 to node 6. If each of the three longest branches is reduced in length by 10, what is the change in the shortest route through the network?

Question 64

Refer to the figure below to answer the following questions.
Figure 3
Consider the network diagram given in Figure 3 with the indicated flow capacities along each branch. What is the input-output constraint associated with the fifth node of the network diagram for the 0-1 integer linear programming formulation of the maximal flow problem?

Question 65

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

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

Question 66

Refer to the figure below to answer the following questions.
Figure 3
Consider the network diagram given in Figure 3 with the indicated flow capacities along each branch. Determine the maximal flow on the following path: node 1 to node 2 to node 7 to destination node 9.

Question 67

In a network flow model, a directed branch

A) is a branch with a positive distance value.
B) is a branch in which flow is possible in only one direction.
C) is a branch on which the flow capacity is exhausted.
D) is a branch in which flow is not possible in either direction.

Question 68

If we wanted to represent water resources as a network flow problem, which of the following would be represented as nodes?

A) canals
B) pumping stations
C) rivers
D) pipelines

Question 69

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

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

Question 70

Refer to the figure below to answer the following questions.
Figure 3
Consider the network diagram given in Figure 3 with the indicated flow capacities along each branch. What is the input-output constraint associated with the ninth node of the network diagram for the 0-1 integer linear programming formulation of the maximal flow problem?

Question 71

Refer to the figure below to answer the following questions.
Figure 3
Consider the network diagram given in Figure 3 with the indicated flow capacities along each branch. Determine the maximal flow from source node 1 to destination node 9.

Question 72

If the origin node for this network is node number 1 and flow proceeds from node 1 to node 6, what is the shortest route through the network?

Question 73

A branch where flow is permissible in either direction is a(n)

A) directed branch.
B) undirected branch .
C) labeled branch.
D) unlabeled branch.

Question 74

The shipping company manager wants to determine the best routes for the trucks to take to reach their destinations. This problem can be solved using the

A) shortest route solution technique.
B) minimal spanning tree solution method.
C) maximal flow solution method.
D) minimal flow solution method.

Question 75

Refer to the figure below to answer the following questions.
Figure 3
Consider the network diagram given in Figure 3 with the indicated flow capacities along each branch. What is the input- output constraint associated with the first node of the network diagram for the 0-1 integer linear programming formulation of the maximal flow problem?

Question 76

Refer to the figure below to answer the following questions.
Figure 3
Consider the network diagram given in Figure 3 with the indicated flow capacities along each branch. What is the capacity constraint associated with the branch from node 7 to node 9 of the network diagram for the 0-1 integer linear programming formulation of the maximal flow problem?

Question 77

Refer to the figure below to answer the following questions.
Figure 3
Consider the network diagram given in Figure 3 with the indicated flow capacities along each branch. What is the objective function for the 0-1 integer linear programming formulation of the maximal flow problem?

Question 78

If we wanted to represent an office layout as a network flow problem, which of the following would be represented as a branch?

A) offices
B) waiting areas
C) heating and ventilation systems
D) computer rooms

Question 79

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?

Question 80

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?