Question 1

In transportation model analysis the stepping-stone method is used to

Accepted Answer

A)  obtain an initial optimum solution. 
B)  obtain an initial feasible solution. 
C)  evaluate empty cells for possible degeneracy. 
D)  balance supply and demand. 
E)  evaluate empty cells for potential solution improvements. 
A)  obtain an initial optimum solution. 
B)  obtain an initial feasible solution. 
C)  evaluate empty cells for possible degeneracy. 
D)  balance supply and demand. 
E)  evaluate empty cells for potential solution improvements.

Question 2

For the data below, construct an initial feasible solution using the northwest-corner rule. $\begin{array}{|l|r|r|r|r|r|}
\hline \text { COSTS } & \text { Dest. 1 } & \text { Dest. 2 } & \text { Dest 3 } & \text { Dest. 4 } & \text { Supply } \
\hline \text { Source 1 } & 12 & 18 & 9 & 111 & 105 \
\hline \text { Source 2 } & 19 & 7 & 30 & 15 & 145 \
\hline \text { Source 3 } & 8 & 10 & 14 & 16 & 50 \
\hline \text { Demand } & 80 & 60 & 70 & 90 & 300/300 \
\hline
\end{array}$

Accepted Answer

Step 1: The smaller value at the interse

Question 3

A transportation problem has two origins: A can supply 20 units and B can supply 30 units. This problem has two destinations: C requires 25 units and D requires 35 units. Which of the following is true?

Accepted Answer

A)  The problem will require a dummy demand with a capacity of 10 units. 
B)  The problem is unbalanced and cannot be solved by the transportation method. 
C)  The problem will require a dummy supply with a capacity of 10 units. 
D)  Destinations C and D must each receive 5 units less than they require. 
E)  The problem will require a dummy supply with a capacity of 50 units. 
A)  The problem will require a dummy demand with a capacity of 10 units. 
B)  The problem is unbalanced and cannot be solved by the transportation method. 
C)  The problem will require a dummy supply with a capacity of 10 units. 
D)  Destinations C and D must each receive 5 units less than they require. 
E)  The problem will require a dummy supply with a capacity of 50 units.

Question 4

A transportation problem requires exactly as many origins as destinations.

Accepted Answer

A) True 
 B)False

Question 5

What is transportation modeling?

Accepted Answer

Transportation modeling finds

Question 6

When does degeneracy occur in a transportation model?

Accepted Answer

Degeneracy occurs when the num

Question 7

How might the transportation method be used to help a firm add a facility to an existing distribution network? You may wish to describe a simple example.

Accepted Answer

Assume that the existing network has two

Question 8

Suppose the solution for a transportation model fills 5 cells with quantities to be shipped. Which of the following combinations of sources and destinations would be degenerate?

Accepted Answer

A)  2 sources, 4 destinations 
B)  3 sources, 3 destinations 
C)  4 sources, 2 destinations 
D)  5 sources, 1 destination 
E)  None of the above are degenerate. 
A)  2 sources, 4 destinations 
B)  3 sources, 3 destinations 
C)  4 sources, 2 destinations 
D)  5 sources, 1 destination 
E)  None of the above are degenerate.

Question 9

For the problem below, what is the quantity assigned to the cell Source 3-Destination 1 using the intuitive method for an initial feasible solution? $$\begin{array} { | l | r | r | r | r | } 
\hline \text { COSTS } & \text { Dest. 1 } & \text { Dest. 2 } & \text { Dest. 3 } & \text { Supply } \
\hline \text { Source 1 } & 2 & 1 & 3 & 50 \
\hline \text { Source 2 } & 4 & 7 & 5 & 40 \
\hline \text { Source 3 } & 3 & 12 & 6 & 30 \
\hline \text { Demand } & 50 & 45 & 25 & 120 \backslash 120 \
\hline
\end{array}$$

Accepted Answer

A)  3 
B)  13.333 
C)  30 
D)  45 
E)  50 
A)  3 
B)  13.333 
C)  30 
D)  45 
E)  50

Question 10

Find the minimum cost shipping solution for the transportation problem data set in the table below. Provide a table of shipping quantities and the minimum value for the objective function. $$\begin{array} { | l | r | r | r | } 
\hline \text { COSTS } & \text { Dest. 1 } & \text { Dest. 2 } & \text { Supply } \
\hline \text { Source 1 } & 6 & 10 & 20 \
\hline \text { Source 2 } & 8 & 3 & 30 \
\hline \text { Source 3 } & 4 & 6 & 15 \
\hline \text { Source 4 } & 12 & 11 & 20 \
\hline \text { Source 5 } & 7 & 9 & 25 \
\hline \text { Demand } & 70 & 40 & 110 \backslash 110 \
\hline
\end{array}$$

Accepted Answer

(a) The optimal solu

Question 11

In a minimization problem, a positive improvement index in a cell indicates that

Accepted Answer

A)  the solution is optimal. 
B)  the total cost will increase if units are reallocated to that cell. 
C)  there is degeneracy. 
D)  the total cost will decrease if units are reallocated to that cell. 
E)  the problem has no feasible solution. 
A)  the solution is optimal. 
B)  the total cost will increase if units are reallocated to that cell. 
C)  there is degeneracy. 
D)  the total cost will decrease if units are reallocated to that cell. 
E)  the problem has no feasible solution.

Question 12

Source A has capacity of 40, Source B has capacity of 35, Destination 1 has demand of 20 and Destination 2 has demand of 25. Fill in the following table with the correct initial solution for a Northwest-corner method approach.
 $$\begin{array} { | c | c | c | c | } 
\hline & \text { Destination 1 } & \text { Destination 2 } & \text { Dummy Destination } \
\hline \text { Source A } & 20 & 20 & \
\hline \text { Source B } & & 5 & 10 \
\hline
\end{array}$$

Accepted Answer

Students should realize the ne

Question 13

For the problem data set below, what is the northwest corner allocation to the cell Source 1-Destination 1? $$\begin{array} { | l | r | r | r | r | } 
\hline \text { COSTS } & \text { Dest. 1 } &{ \text { Dest. 2 } } & { \text { Dest. 3 } } & { \text { Supply } } \
\hline \text { Source 1 } & 2 & 1 & 3 & 30 \
\hline \text { Source 2 } & 4 & 2 & 1 & 40 \
\hline \text { Source 3 } & 3 & 8 & 6 & 20 \
\hline \text { Demand } & 15 & 50 & 25 & 90 \backslash 90 \
\hline
\end{array}$$

Accepted Answer

A)  0 
B)  2 
C)  15 
D)  90 
E)  30 
A)  0 
B)  2 
C)  15 
D)  90 
E)  30

Question 14

A transportation problem with 8 sources and 6 destinations will have an optimal solution that uses at most 13 of the 48 possible routes.

Accepted Answer

A) True 
 B)False

Question 15

Consider the transportation problem in the data set and optimal solution below. Verify by hand or by calculator (show your work) the value of the objective function. $\begin{array}{|l|r|r|r|r|r|}
\hline \text { COSTS } & \text { Dest. 1 } & \text { Dest 2 } & \text { Dest. 3 } & \text { Dest. 4 } & \text { Supply } \
\hline \text { Source 1 } & 12 & 18 & 9 & 11 & 105 \
\hline \text { Source 2 } & 19 & 7 & 30 & 15 & 145 \
\hline \text { Source 3 } & 8 & 10 & 14 & 16 & 50 \
\hline \text { Demand } & 80 & 60 & 70 & 90 & 300/300 \
\hline
\end{array}$

$\begin{array}{|lrrrrr|}
\hline \text { Shipments } & \text { Dest. 1 } & \text { Dest. 2 } & \text { Dest. 3 } & \text { Dest. 4 } & \text { Row Total } \
\text { Source 1 } & 30 & 0 & 70 & 5 & 105 \
\text { Source 2 } & 0 & 60 & 0 & 85 & 145 \
\text { Source 3 } & 50 & 0 & 0 & 0 & 50 \
\text { Col. Total } & 80 & 60 & 70 & 90 & 300 \backslash 300 \
\hline
\end{array}$

Accepted Answer

The objective is $12

Question 16

A transportation problem has an optimal solution when

Accepted Answer

A)  all of the improvement indices are greater than or equal to zero. 
B)  all demand and supply constraints are satisfied. 
C)  the number of filled cells is one less than the number of rows plus the number of columns. 
D)  all the squares are used. 
E)  all origin-destination combinations have been made equally low in cost. 
A)  all of the improvement indices are greater than or equal to zero. 
B)  all demand and supply constraints are satisfied. 
C)  the number of filled cells is one less than the number of rows plus the number of columns. 
D)  all the squares are used. 
E)  all origin-destination combinations have been made equally low in cost.

Question 17

A transportation problem has 10 origins and 37 destinations. How many possible routes are there for this problem? How many routes will be used in the optimal solution?

Accepted Answer

The number of possible routes is origins

Question 18

A large transportation problem has 220 origins and 1360 destinations. The optimal solution of this problem will fill no more than about ________ of cells with quantities to be shipped.

Accepted Answer

A)  0.5% 
B)  5% 
C)  10% 
D)  25% 
E)  All cells will be occupied. 
A)  0.5% 
B)  5% 
C)  10% 
D)  25% 
E)  All cells will be occupied.

Question 19

When the number of shipments in a feasible solution is less than the number of rows plus the number of columns minus one

Accepted Answer

A)  the solution is optimal. 
B)  a dummy source must be created. 
C)  a dummy destination must be created. 
D)  there is degeneracy, and an artificial allocation must be created. 
E)  the closed path has a triangular shape. 
A)  the solution is optimal. 
B)  a dummy source must be created. 
C)  a dummy destination must be created. 
D)  there is degeneracy, and an artificial allocation must be created. 
E)  the closed path has a triangular shape.

Question 20

When using the stepping-stone method, the improvement index for an unused cell equals the shipping cost associated with that cell.

Accepted Answer

A) True 
 B)False

Exam 20: Transportation Models

In transportation model analysis the stepping-stone method is used to

For the data below, construct an initial feasible solution using the northwest-corner rule. COSTS Dest. 1 Dest. 2 Dest 3 Dest. 4 Supply Source 1 12 18 9 111 105 Source 2 19 7 30 15 145 Source 3 8 10 14 16 50 Demand 80 60 70 90 300/300

A transportation problem has two origins: A can supply 20 units and B can supply 30 units. This problem has two destinations: C requires 25 units and D requires 35 units. Which of the following is true?

A transportation problem requires exactly as many origins as destinations.

What is transportation modeling?

When does degeneracy occur in a transportation model?

How might the transportation method be used to help a firm add a facility to an existing distribution network? You may wish to describe a simple example.

Suppose the solution for a transportation model fills 5 cells with quantities to be shipped. Which of the following combinations of sources and destinations would be degenerate?

For the problem below, what is the quantity assigned to the cell Source 3-Destination 1 using the intuitive method for an initial feasible solution? COSTS Dest. 1 Dest. 2 Dest. 3 Supply Source 1 2 1 3 50 Source 2 4 7 5 40 Source 3 3 12 6 30 Demand 50 45 25 120\backslash120

In a minimization problem, a positive improvement index in a cell indicates that

For the problem data set below, what is the northwest corner allocation to the cell Source 1-Destination 1? COSTS Dest. 1 Dest. 2 Dest. 3 Supply Source 1 2 1 3 30 Source 2 4 2 1 40 Source 3 3 8 6 20 Demand 15 50 25 90\backslash90

A transportation problem with 8 sources and 6 destinations will have an optimal solution that uses at most 13 of the 48 possible routes.

A transportation problem has an optimal solution when

A transportation problem has 10 origins and 37 destinations. How many possible routes are there for this problem? How many routes will be used in the optimal solution?

A large transportation problem has 220 origins and 1360 destinations. The optimal solution of this problem will fill no more than about ________ of cells with quantities to be shipped.

When the number of shipments in a feasible solution is less than the number of rows plus the number of columns minus one

When using the stepping-stone method, the improvement index for an unused cell equals the shipping cost associated with that cell.

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