Deck 9: Transportation, Assignment, and Network Models

Question 1

The objective of a transportation problem solution is to schedule shipments from sources to destinations while minimizing total transportation and production costs.

Answer 1

True

Question 2

A transportation problem with intermediate points is called a transshipment problem.

Answer 2

True

Question 3

The maximal-flow technique would be helpful to city planners in determining how freeways should be expanded.

Answer 3

True

Question 4

The minimal-spanning tree technique determines the path through the network that connects all the points while minimizing total distance.

Question 5

A typical transportation problem may ask the question, "How many of X should be shipped to point E from source A?"

Question 6

Transportation companies would definitely be interested in the shortest-route technique to optimize travel.

Question 7

The shortest-route technique might be used by someone planning a vacation in order to minimize the required amount of driving.

Question 8

The points on the network are referred to as nodes.

Question 9

Lines connecting nodes on a network are called links.

Question 10

The shortest-route technique is the same as the minimal-spanning tree technique.

Question 11

In a transportation problem, each destination must be supplied by one and only one source.

Question 12

Busy highways are often analyzed with the maximal-flow technique.

Question 13

The minimal-spanning tree technique finds the shortest route to a series of destinations.

Question 14

Cable television companies would employ the shortest-route technique to lay out the cables connecting individual houses.

Question 15

In the minimal-spanning tree technique, it is necessary to start at the last node in the network.

Question 16

The transshipment problem is a maximization problem.

Question 17

In a transportation problem, a single source may supply something to all destinations.

Question 18

We may begin the maximal-flow technique by picking an arbitrary path through the network.

Question 19

Transportation models may be used when a firm is trying to decide where to locate a new facility.

Question 20

The maximal-flow technique might be used by the U.S.Army Corps of Engineers to study water run-off in an attempt to minimize the danger from floods.

Question 21

A point in the network, that is at the beginning or end of a route is called a(n)

A)arc.
B)branch.
C)line.
D)node.

Question 22

The maximal-flow model assumes that there is a net flow from "source" to "sink."

Question 23

When using a general LP model for transportation problems, if there are 4 sources and 3 destinations, which of the following statements is true?

A)There are typically 4 decision variables and 3 constraints.
B)There are typically 12 decision variables and 7 constraints.
C)There are typically 7 decision variables and 7 constraints.
D)There are typically 12 decision variables and 12 constraints.

Question 24

A line in a network that may represent a path or a route is called a(n)

A)arc.
B)branch.
C)line.
D)fork.

Question 25

The two most common objectives for the assignment problem are the minimization of

A)uncertainty or inexperience.
B)total costs or inexperience.
C)total costs or total time.
D)total time or inexperience.

Question 26

The shortest-route model assumes that one is trying to connect two end points in the shortest manner possible, rather than attempting to connect all the nodes in the model.

Question 27

Which of the following problems can be solved as a linear program using binary decision variables?

A)maximal-flow problem
B)shortest-route problem
C)minimal-spanning tree problem
D)product mix problem

Question 28

If your goal was to construct a network in which all points were connected and the distance between them was as short as possible, the technique that you would use is

A)shortest-route.
B)maximal-flow.
C)minimal-flow.
D)minimal-spanning tree.

Question 29

What is said to exist when total demand equals total supply in a transportation problem?

A)an equalized problem
B)an equilibrialized problem
C)a harmonized problem
D)a balanced problem

Question 30

All the nodes must be connected in which of the following techniques?

A)minimal-flow
B)shortest-route
C)maximal-flow
D)minimal-spanning tree

Question 31

In the minimal-spanning tree technique, if there is a tie for the nearest node, that suggests that there may be more than one optimal solution.

Question 32

A traveling salesperson might use the shortest route technique to minimize the distance traveled to reach one of his/her customers.

Question 33

When using the shortest-route technique, the second step is to

A)find the next-nearest node to the origin and put the distance in a box by the node.
B)trace the path from the warehouse to the plant.
C)determine the average distance traveled from source to end.
D)find the nearest node to the origin and put a distance box by the node.

Question 34

Which of the following statements concerning the transshipment problem is false?

A)There can be constraints on the number of units shipped out of an origin point.
B)There can be constraints on the number of units shipped into a destination point.
C)The transshipment problem can be solved with linear programming.
D)Any units shipped from one origin point must all go to the same destination point.

Question 35

A technique that allows a researcher to determine the greatest amount of material that can move through a network is called

A)maximal-flow.
B)maximal-spanning.
C)shortest-route.
D)maximal-tree.

Question 36

Transportation models can be used for which of the following decisions?

A)facility location
B)production mix
C)media selection
D)portfolio selection

Question 37

In the maximal-flow technique, a zero (0)means no flow or a one-way arc.

Question 38

The minimal-spanning tree technique would best be used

A)by a forest ranger seeking to minimize the risk of forest fires.
B)by a telephone company attempting to lay out wires in a new housing development.
C)by an airline laying out flight routes.
D)by an airline assigning crews to work specific flights.

Question 39

The maximal-flow model might be of use to an engineer looking for spare capacity in an oil pipeline system.

Question 40

When using the shortest-route technique, the first step is to

A)connect the nearest node that minimizes the total distance to the origin.
B)trace the path from the warehouse to the plant.
C)determine the average distance traveled from source to end.
D)find the nearest node to the origin and put a distance box by the node.

Question 41

Pipeline fluid flows are indicated below.Determine the maximum flow from Node 1 to Node 3.

A)100
B)400
C)500
D)700

Question 42

Find the shortest route from Node 1 to Node 6.

A)300
B)450
C)550
D)650

Question 43

Given the following distances between destination nodes, what is the minimum distance that connects all the nodes?

A)900
B)650
C)400
D)1200

Question 44

Given the following distances between destination nodes, what is the minimum distance that connects all the nodes?

A)100
B)150
C)550
D)1225

Question 45

Given the following distances between destination nodes, what is the minimum distance that connects all the nodes?

A)900
B)1200
C)1100
D)700

Question 46

Solve the minimal-spanning tree problem defined below:

A)total cost = 13
B)total cost = 15
C)total cost = 17
D)total cost = 11

Question 47

Pipeline fluid flows are indicated below.Determine the maximum flow from Node 1 to Node 4.

A)100
B)150
C)200
D)50

Question 48

Given the following distances between destination nodes, what is the minimum distance that connects all the nodes?

A)1000
B)800
C)700
D)1100

Question 49

Find the shortest route from Node 1 to Node 6.

A)300
B)450
C)550
D)650

Question 50

Find the shortest route from Node 1 to Node 4.

A)750
B)500
C)550
D)600

Question 51

Find the shortest route from Node 1 to Node 5.

A)200
B)350
C)250
D)450

Question 52

Pipeline fluid flows are indicated below.Determine the maximum flow from Node 1 to Node 5.

A)300
B)400
C)600
D)500

Question 53

Given the following distances between destination nodes, what is the minimum distance that connects all the nodes?

A)100
B)750
C)850
D)900

Question 54

Given the following distances between destination nodes, what is the minimum distance that connects all the nodes?

A)450
B)150
C)350
D)650

Question 55

Given the following distances between destination nodes, what is the minimum distance that connects all the nodes?

A)300
B)525
C)675
D)1925

Question 56

Given the following traffic flows, in hundreds of cars per hour, what is the maximum traffic flow from City 1 to City 7?

A)1200
B)1400
C)900
D)800

Question 57

Find the shortest route from Node 1 to Node 4 using the shortest-route technique.

A)650
B)450
C)550
D)500

Question 58

Find the shortest route from Node 1 to Node 5 using the shortest-route technique.

A)350
B)400
C)450
D)600

Question 59

Given the following distances between destination nodes, what is the minimum distance that connects all the nodes?

A)290
B)310
C)620
D)460

Question 60

Pipeline fluid flows are indicated below.Determine the maximum flow from Node 1 to Node 4.

A)200
B)300
C)600
D)700

Question 61

Find the shortest route from Node 6 to Node 1.

A)branches 9, 7, and 2
B)branches 8, 6, and 2
C)branches 8, 6, 7, and 1
D)branches 9, 5, and 1

Question 62

Given the following nodes and distances, determine the minimal length of cable necessary to connect all nodes, using Node 2 as the starting point.

A)1200
B)1100
C)900
D)700

Question 63

Find the least amount of cable that will allow Jack's Cable Company to connect the following nodes (houses).

A)250
B)400
C)350
D)300

Question 64

The Pointy-haired boss has five projects to assign and decides to go against all convention and assign them to individuals rather than project teams.He has the Elbonians estimate the labor cost in dollars of each possible assignment and that information is summarized in the table. What is the LP constraint associated with Project 1?

A)DiP1 + WaP1 + AlP1 + AsP1 + DoP1 ≥ 0
B)DiP1 + WaP1 + AlP1 + AsP1 + DoP1 ≥ 1
C)DiP1 + WaP1 + AlP1 + AsP1 + DoP1 = 1
D)DiP1 + WaP1 + AlP1 + AsP1 + DoP1 ≤ 1

Question 65

The Pointy-haired boss has five projects to assign and decides to go against all convention and assign them to individuals rather than project teams.He has the Elbonians estimate the labor cost in dollars of each possible assignment and that information is summarized in the table.Use Solver to determine which of these assignments is correct.

A)Project 3 = Dogbert
B)Project 2 = Alice
C)Project 3 = Alice
D)Project 4 = Wally

Question 66

The Pointy-haired boss has five projects to assign and decides to go against all convention and assign them to individuals rather than project teams.He has the Elbonians estimate the labor cost in dollars of each possible assignment and that information is summarized in the table. How many constraints are in an LP formulation of this problem?

A)25
B)11
C)10
D)5

Question 67

Table 9-3
To demonstrate the personal touch that is part of the Apple experience, Tim Cook decides to personally deliver the first iCar produced in San Jose to the customer's home in Nashville.In order to minimize the carbon footprint, he decides to push the car rather than actually driving it, and since his time is valuable, he wants to choose the shortest route possible.Fortunately, the first genius he talks to at The Genius Bar is able to determine the drive times between cities Tim might pass through along the way to Nashville.The cities and drive times are shown in the table - the push time is assumed to be a direct multiple of the drive time, which will act as a surrogate to keep the numbers low.

What is the duration of the shortest route for the scenario described in Table 9-3?

A)33 hours
B)34.8 hours
C)40.5 hours
D)41.3 hours

Question 68

Find the shortest route from Node 1 to Node 6.

A)total distance = 350
B)total distance = 410
C)total distance = 270
D)total distance = 520

Question 69

Given the pipeline fluid flows indicated below, determine the maximum flow from Node 1 to Node 5.

A)300
B)350
C)450
D)500

Question 70

Table 9-3
To demonstrate the personal touch that is part of the Apple experience, Tim Cook decides to personally deliver the first iCar produced in San Jose to the customer's home in Nashville.In order to minimize the carbon footprint, he decides to push the car rather than actually driving it, and since his time is valuable, he wants to choose the shortest route possible.Fortunately, the first genius he talks to at The Genius Bar is able to determine the drive times between cities Tim might pass through along the way to Nashville.The cities and drive times are shown in the table - the push time is assumed to be a direct multiple of the drive time, which will act as a surrogate to keep the numbers low.

Write the elements of the objective function relating to the city of Oklahoma City based on the information given in Table 9-3.

A)23SO + 7.83AO + 14.3PO + 11.6OC + 10.3ONo + 10ONa
B)23SO + 7.83AO + 14.3PO - 11.6OC - 10.3ONo - 10ONa
C)-23SO - 7.83AO - 14.3PO - 11.6OC - 10.3ONo - 10ONa
D)-23SO - 7.83AO - 14.3PO + 11.6OC + 10.3ONo + 10ONa

Question 71

The Pointy-haired boss has five projects to assign and decides to go against all convention and assign them to individuals rather than project teams.He has the Elbonians estimate the labor cost in dollars of each possible assignment and that information is summarized in the table.Use Solver to determine which worker is assigned Project 1.

A)Alice
B)Asok
C)Dilbert
D)Wally

Question 72

Table 9-3
To demonstrate the personal touch that is part of the Apple experience, Tim Cook decides to personally deliver the first iCar produced in San Jose to the customer's home in Nashville.In order to minimize the carbon footprint, he decides to push the car rather than actually driving it, and since his time is valuable, he wants to choose the shortest route possible.Fortunately, the first genius he talks to at The Genius Bar is able to determine the drive times between cities Tim might pass through along the way to Nashville.The cities and drive times are shown in the table - the push time is assumed to be a direct multiple of the drive time, which will act as a surrogate to keep the numbers low.

How many constraints including the nonnegativity constraint are needed to model the scenario described in Table 9-3 using LP?

A)6
B)7
C)8
D)9

Question 73

The Pointy-haired boss has five projects to assign and decides to go against all convention and assign them to individuals rather than project teams.He has the Elbonians estimate the labor cost in dollars of each possible assignment and that information is summarized in the table. How many decision variables are in an LP formulation of this problem?

A)25
B)10
C)9
D)5

Question 74

Table 9-3
To demonstrate the personal touch that is part of the Apple experience, Tim Cook decides to personally deliver the first iCar produced in San Jose to the customer's home in Nashville.In order to minimize the carbon footprint, he decides to push the car rather than actually driving it, and since his time is valuable, he wants to choose the shortest route possible.Fortunately, the first genius he talks to at The Genius Bar is able to determine the drive times between cities Tim might pass through along the way to Nashville.The cities and drive times are shown in the table - the push time is assumed to be a direct multiple of the drive time, which will act as a surrogate to keep the numbers low.

Tim Cook wasn't being observant and mistakenly went to The Evil Genius Bar.The evil genius there, distinguishable from his counterpart only by his neatly trimmed goatee, decides to determine the longest route through the network described in Table 9-3.How many hours will Tim's trip take?

A)40.5
B)41.3
C)42.55
D)43.65

Question 75

Given the following traffic flows, in hundreds of cars per hour, what is the maximum traffic flow from Town 1 to Town 7?

A)max flow = 4 units
B)max flow = 6 units
C)max flow = 3 units
D)max flow = 9 units

Question 76

Table 9-3
To demonstrate the personal touch that is part of the Apple experience, Tim Cook decides to personally deliver the first iCar produced in San Jose to the customer's home in Nashville.In order to minimize the carbon footprint, he decides to push the car rather than actually driving it, and since his time is valuable, he wants to choose the shortest route possible.Fortunately, the first genius he talks to at The Genius Bar is able to determine the drive times between cities Tim might pass through along the way to Nashville.The cities and drive times are shown in the table - the push time is assumed to be a direct multiple of the drive time, which will act as a surrogate to keep the numbers low.

How many decision variables are needed to model the scenario described in Table 9-3 using LP?

A)11
B)12
C)13
D)14

Question 77

Table 9-3
To demonstrate the personal touch that is part of the Apple experience, Tim Cook decides to personally deliver the first iCar produced in San Jose to the customer's home in Nashville.In order to minimize the carbon footprint, he decides to push the car rather than actually driving it, and since his time is valuable, he wants to choose the shortest route possible.Fortunately, the first genius he talks to at The Genius Bar is able to determine the drive times between cities Tim might pass through along the way to Nashville.The cities and drive times are shown in the table - the push time is assumed to be a direct multiple of the drive time, which will act as a surrogate to keep the numbers low.

What are the elements of the constraint related to the Nashville node based on the information given in Table 9-3?

A)ONa + CNa + NoNa = 0
B)ONa + CNa + NoNa = 1
C)ONa + CNa + NoNa = 2
D)ONa + CNa + NoNa = 3

Question 78

Given the following nodes and distances, determine the minimum length of cable necessary to connect all six nodes.

A)200
B)300
C)400
D)500

Question 79

The Pointy-haired boss has five projects to assign and decides to go against all convention and assign them to individuals rather than project teams.He has the Elbonians estimate the labor cost in dollars of each possible assignment and that information is summarized in the table. What are the components of the objective function associated with Project 3?

A)29DiP3 + 25WaP3 + 22AlP3 + 34AsP3 + 20DoP3 = 1
B)29DiP3 + 25WaP3 + 22AlP3 + 34AsP3 + 20DoP3 ≤ 1
C)DiP1 + WaP1 + AlP1 + AsP1 + DoP1 = 1
D)29DiP3 + 25WaP3 + 22AlP3 + 34AsP3 + 20DoP3

Question 80

Which of these statements is best?

A)Assignment problems involve determining the most efficient assignment of people to projects, salesmen to territories, contracts to bidders, and so on.
B)The objective of an assignment problem solution most often is to maximize the total costs or time of performing the assigned tasks.
C)In the assignment problem, the costs for a dummy row will be equal to the lowest cost of the column for each respective cell in that row.
D)The objective of an assignment problem solution most often is to minimize the number of assigned tasks.