Deck 18: Transportation and Assignment Solution Methods

Question 1

In a balanced transportation model where supply equals demand, all constraints are equalities.

Answer 1

True

Question 2

Assignments are made to locations with 0 in the opportunity cost table.

Answer 2

True

Question 3

If the number of unique assignments is less than the number of rows or columns, a line test must be used.

Answer 3

True

Question 4

The transportation model is a special type of linear regression model.

Question 5

It is not possible to solve a transportation problem that has ≤ instead of = signs for the supply constraints.

Question 6

An assignment problem that involves 6 machines to be assigned to 4 workers cannot be solved using the assignment problem solution procedure described.

Question 7

The supply and demand values along the outside rim of a tableau are called rim requirements.

Question 8

Unacceptable (prohibited) routes in a transportation problem are assigned cost values of zero.

Question 9

The linear programming model for a transportation problem has constraints for supply at each source and demand at each destination.

Question 10

An assignment problem is a special form of transportation problem where all supply and demand values equal 0.

Question 11

In a transportation problem, items are allocated from sources to destinations at a minimum cost.

Question 12

An opportunity cost table is developed by first subtracting the minimum value in each row from all other row values and then repeating this process for each column.

Question 13

An opportunity cost table is developed by first subtracting the minimum value in each row from all other row values and then repeating this process for each row.

Question 14

The transportation model assumes that shipping costs are the same, regardless of the number of units shipped.

Question 15

An optimal solution occurs when the number of independent unique assignments equals the number of rows or columns.

Question 16

An assignment problem is a special form of transportation problem where all supply and demand values equal 1.

Question 17

Assignments are made to locations with 1 in the opportunity cost table.

Question 18

In a balanced transportation model where supply equals demand, all constraints are inequalities.

Question 19

Transportation problems can be solved by the simplex method.

Question 20

Transportation problems are solved manually within a tableau format.

Question 21

Generally, ________ problems match people to an equal number of tasks at a minimum cost.

Question 22

A(n) ________ solution occurs when the number of independent unique assignments equals the number of rows or columns.

Question 23

Given the following transportation tableau where the numbers in each cell represent transportation costs from the specific source to the specific destination with supply figures corresponding to each source and demand figures corresponding to each destination:

According to the Northwest Corner method, the initial solution would have a total transportation cost of ________.

Question 24

Given the following transportation tableau where the numbers in each cell represent transportation costs from the specific source to the specific destination with supply figures corresponding to each source and demand figures corresponding to each destination:

According to the Northwest Corner method, the initial solution would give to cell B2 a loading of ________.

Question 25

________ model is a method for determining an initial solution for a transportation problem based on the concept of penalty cost or regret.

Question 26

In a transportation tableau with m rows and n columns, if there are fewer than n+m-1 allocations, the tableau is said to be ________.

Question 27

In using the Vogel's Approximation model, a ________ is the difference between the largest and next largest cell cost in a row.

Question 28

When the number of people and the number of tasks are not equal in an assignment problem then the problem cannot be solved.

Question 29

Vogel's approximation method allocates to the minimum cost cell in the row or column with the ________ penalty cost.

Question 30

When supply exceeds demand, a dummy ________ is added to the solution tableau.

Question 31

In a transportation tableau to rectify a degenerate tableau, an empty cell must artificially be treated as an ________ cell.

Question 32

In the ________ method, the largest possible allocation is made to the cell in the upper-left-hand corner of the tableau, followed by allocations to adjacent feasible cells.

Question 33

A(n) ________ problem is a special form of transportation problem where all supply and demand values equal 1.

Question 34

The three methods for identifying initial feasible solutions to transportation problems are ________, ________, and ________.

Question 35

If the number of unique assignments is less than the number of rows, then a ________ test must be used.

Question 36

When demand exceeds supply, a dummy ________ is added to the solution tableau.

Question 37

A multiple optimal solution occurs when an empty cell has a cost change of ________ and all other empty cells are positive.

Question 38

A(n) ________ table is developed by first subtracting the minimum value in each row from all other row values and then repeating the process for each column.

Question 39

The two solution methods for transportation problems that do not require the use of a computer are ________ and ________.

Question 40

In using the minimum cell cost method, as much as possible is allocated to the cell with the ________ cost.

Question 41

Given the following transportation tableau where the numbers in each cell represent transportation costs from the specific source to the specific destination with supply figures corresponding to each source and demand figures corresponding to each destination:

According to the minimum cell cost method, the initial solution would have a total transportation cost of ________.

Question 42

Canning Transport wants to move goods from three (3) factories to three (3) distribution centers. Information about the move is given below:

Shipping costs are (in $):

According to the Northwest Corner method, the initial solution would give to cell CIII a loading of ________.

Question 43

There are 4 jobs in a 4 person office that must be done as quickly as possible. The supervisor has used the assignment method to assign people to jobs, and has completed the first step. She had to rush off to a meeting and has asked to assign the jobs to the people before she returns. The original matrix which shows the expected completion time for each person for each job, and the one she just completed are both shown below.


Which person should be assigned to which job? How long will the jobs take?

Question 44

Given the following transportation tableau where the numbers in each cell represent transportation costs from the specific source to the specific destination with supply figures corresponding to each source and demand figures corresponding to each destination:

According to the Vogel's Approximation Method, the initial solution would have a total transportation cost of ________.

Question 45

Canning Transport wants to move goods from three (3) factories to three (3) distribution centers. Information about the move is given below:

Shipping costs are (in $):

According to the Vogel's Approximation Method, the initial solution would have a total transportation cost of ________.

Question 46

A large book publisher has five manuscripts that must be edited as soon as possible. Five editors are available for doing the work; however, their working times on the various manuscripts will differ based on their backgrounds and interests. The publisher wants to use an assignment method to determine who does which manuscript. Estimates of editing times (in hours) for each manuscript by each editor are:
How many variables are involved in this assignment method?

Question 47

Given the following transportation tableau where the numbers in each cell represent transportation costs from the specific source to the specific destination with supply figures corresponding to each source and demand figures corresponding to each destination:

According to the Vogel's Approximation Method, the initial solution would give to cell B2 a loading of ________.

Question 48

$$\begin{array} { l l c r } & \text { SS } & 1 & 2 \\\hline 1 & 100 & 5 & 6 \\2 & 200 & 4 & 2 \\3 & 150 & 3 & 6 \\4 & 50 & 9 & 7 \\\hline \text { DD } & & 250 & 250\end{array}$$
What is the objective function?

Question 49

Canning Transport wants to move goods from three (3) factories to three (3) distribution centers. Information about the move is given below:

Shipping costs are (in $):

According to the Vogel's Approximation Method, the initial solution would give to cell CII a loading of ________.

Question 50

$$\begin{array} { l l r r } & \text { SS } & 1 & 2 \\\hline 1 & 100 & 5 & 6 \\2 & 200 & 4 & 2 \\3 & 150 & 3 & 6 \\4 & 50 & 9 & 7 \\\hline \text { DD } & & 250 & 250\end{array}$$
What are the supply-side constraints?

Question 51

Given the following transportation tableau where the numbers in each cell represent transportation costs from the specific source to the specific destination with supply figures corresponding to each source and demand figures corresponding to each destination:

According to the minimum cell cost method, the initial solution would give to cell C1 a loading of ________.

Question 52

$$\begin{array} { l l l l } & \text { SS } & 1 & 2 \\\hline1 & 100 & 5 & 6 \\2 & 200 & 4 & 2 \\3 & 150 & 3 & 6 \\4 & 50 & 9 & 7 \\\hline \text { DD } & & 250 & 250\end{array}$$
What are the demand-side constraints?

Question 53

Canning Transport wants to move goods from three (3) factories to three (3) distribution centers. Information about the move is given below:

Shipping costs are (in $):

According to the minimum cell cost method, the initial solution would give to cell BI a loading of ________.

Question 54

Canning Transport wants to move goods from three (3) factories to three (3) distribution centers. Information about the move is given below:

Shipping costs are (in $):

According to the Northwest Corner method, the initial solution would have a total transportation cost of ________.

Question 55

Canning Transport wants to move goods from three (3) factories to three (3) distribution centers. Information about the move is given below:

Shipping costs are (in $):

According to the minimum cell cost method, the initial solution would have a total transportation cost of ________.

Question 56

Consider the following transportation tableau with the initial solution provided. Use the stepping stone method to identify a better allocation.

Question 57

The student internship director needs as much coverage as possible in the office next week. The more hours that can be put in each day, the better. She has asked the students to provide a list of how many hours they are available each day of the week. Each student can be there on only one day and there must be a student in the office each day of the week. Use the table below and the tables provided to determine the schedule that gives the most coverage. Note that the objective of this problem is to maximize the hours worked, not minimize.

Question 58

In a transportation problem, items are allocated from sources to destinations at a

A) maximum cost.
B) minimum cost.
C) minimum profit.
D) minimum revenue.

Question 59

An independent operator is planning shipments of gasoline from two sources to three destinations. Per ton transportation costs are given in the following table.
There are 1000 tons available at A and 1300 tons available at B. Since the destinations want as much as possible, the owner has decided to ship out all available quantities. Solve using either stepping stone or MODI.

Question 60

A large book publisher has five manuscripts that must be edited as soon as possible. Five editors are available for doing the work; however, their working times on the various manuscripts will differ based on their backgrounds and interests. The publisher wants to use an assignment method to determine who does which manuscript. Estimates of editing times (in hours) for each manuscript by each editor are:
How many constraints are needed?

Question 61

An assignment problem is a special form of transportation problem where all supply and demand values equal:

A) -1 or 1
B) -1
C) 0
D) 1

Question 62

Use the following table and the information to answer the questions below.
In the following transportation matrix, all cells except 2C have been evaluated and show no improvement. Evaluate that cell.

What is the reduced cost if we decide to allocate to cell 2C?

A) -2
B) -1
C) 0
D) +1
E) +2

Question 63

Which of the following are assumptions or requirements of the transportation problem?

A) Minimum quantities must be shipped.
B) Shipping costs per unit do not vary with the quantity shipped.
C) There can only be one source.
D) all of the above

Question 64

The transportation method is a linear programming technique where linearity can be found in which of the following ways?

A) The cost of goods shipped from any source to any destination is a linear function of quantity shipped.
B) The total cost associated with a given plan is a linear function of shipping costs.
C) Cell evaluations assume linear movements through the matrix.
D) The cost of goods shipped from any source to any destination is a linear function of the cost per unit.

Question 65

Use the following table and the information to answer the questions below.
In the following transportation matrix, all cells except 2C have been evaluated and show no improvement. Evaluate that cell.

Make the necessary allocation to cell 2C and determine the total transportation cost.

A) 936
B) 928
C) 908
D) 852
E) 878

Question 66

In the linear programming formulation of a transportation network,

A) there is one variable for each arc.
B) there is one constraint for each node.
C) the sum of variables corresponding to arcs out of an origin node is constrained by the supply at that node.
D) all of the above

Question 67

Consider the following transportation tableau which shows the initial solution. Evaluate the cost of allocating units to cell CR.

A) -12
B) -9
C) -6
D) -2
E) +3

Question 68

The transportation method assumes that

A) the number of rows is equal to the number of columns.
B) there must be at least 2 rows and at least 2 columns.
C) both A and B
D) the product of rows minus 1 and columns minus 1 should not be less than the number of completed cells.

Question 69

Assignments are made to locations with ________ in the opportunity cost table.

A) -1 or 1
B) -1
C) 1
D) 0

Question 70

In a transportation problem, items are allocated from sources to destinations at a ________ cost.

A) maximum
B) minimum
C) high
D) low

Question 71

Use the following table and the information to answer the questions below.
In the following transportation matrix, all cells except 2C have been evaluated and show no improvement. Evaluate that cell.

How many units would be allocated to cell 2C?

A) 10
B) 14
C) 6
D) 0
E) 20

Question 72

The linear programming model for a transportation problem has constraints for

A) supply at each source.
B) supply at each source and demand at each destination.
C) demand at each destination.
D) a feasible solution.

Question 73

The supply and demand values along the outside rim of a tableau are called

A) rim requirements.
B) rim columns.
C) rim rows.
D) all of the above

Question 74

Which of the following assumptions is not an assumption of the transportation model?

A) Shipping costs are constant.
B) There is only one transportation route between source and destination.
C) There is only one transportation mode between source and destination.
D) Actual supply and actual demand must be equal.

Question 75

In a balanced transportation model where supply equals demand, all constraints are

A) inequalities.
B) equalities.
C) A and B
D) none of the above

Question 76

Which of the following assumptions is not an assumption of the transportation model?

A) Shipping costs per unit are constant.
B) There is one transportation route between each source and destination.
C) There is one transportation mode between each source and destination.
D) Actual total supply and actual total demand must be equal.

Question 77

Consider the following transportation tableau which shows the initial solution. Evaluate the cost of allocating units to cell DR.

A) -5
B) -2
C) 0
D) 3
E) 5

Question 78

The problem that deals with the distribution of goods from several sources to several destinations is the

A) network problem.
B) assignment problem.
C) transportation problem.
D) transshipment problem.

Question 79

Which of the following are assumptions or requirements of transportation problems?
I) Goods are the same from each source.
II) There must be a single source.
III) Minimum quantities must be shipped.
IV) Shipping costs per unit do not vary with the quantity shipped.

A) I and III
B) I, II, and IV
C) I and IV
D) II and III

Question 80

The ________ problem deals with the distribution of goods from several sources to several destinations.

A) network
B) assignment
C) transportation
D) transshipment